Initial commit

2023-08-21 03:33:46 +02:00
commit 41a0a6e67c
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+# Set Intersection
+
+The use case in this directory computes the intersection of two input
+sets. We provide implementations of five different approaches for 32, 64
+and 128 elements:
+- IO
+- Chain-of-Thought (CoT)
+- Tree of Thought (ToT):
+  - ToT: wider tree, meaning more branches per level
+  - ToT2: tree with more levels, but fewer branches per level
+- Graph of Thoughts (GoT)
+
+## Data
+
+We provide input files with 100 precomputed samples for each set length:
+`set_intersection_<number of elements>.csv`. It is also possible to use
+the data generator `dataset_gen_intersection.py` to generate additional or
+different samples. The parameters can be updated in lines 24 to 28 of
+the main body:
+- set_size = 32 # size of the generated sets
+- int_value_ubound = 64 # (exclusive) upper limit of generated numbers
+- seed = 42 # seed of the random number generator
+- num_sample = 100 # number of samples
+- filename = 'set_intersection_032.csv' # output filename
+
+## Execution
+
+The files to execute the use case are called
+`set_intersection_<number of elements>.py`. In the main body, one can
+select the specific samples to be run (variable sample) and the
+approaches (variable approaches). It is also possible to set a budget in
+dollars (variable budget).
+The input filename for the samples is currently hardcoded to
+`set_intersection_<number of elements>.csv`, but can be updated in the
+function `run`.
+
+The Python scripts will create the directory `result`, if it is not
+already present. In the `result` directory, another directory is created
+for each run: `{name of LLM}_{list of approaches}_{day}_{start time}`.
+Inside each execution specific directory two files (`config.json`,
+`log.log`) and a separate directory for each selected approach are
+created. `config.json` contains the configuration of the run: input data,
+selected approaches, name of the LLM, and the budget. `log.log` contains
+the prompts and responses of the LLM as well as additional debug data.
+The approach directories contain a separate json file for every sample
+and the file contains the Graph Reasoning State (GRS) for that sample.
+
+## Plot Data
+
+Change the results directory in line 170 of `plot.py` and update the
+length parameter in the subsequent line and run `python3 plot.py` to
+plot your data.
@@ -0,0 +1,92 @@
+# Copyright (c) 2023 ETH Zurich.
+#                    All rights reserved.
+#
+# Use of this source code is governed by a BSD-style license that can be
+# found in the LICENSE file.
+#
+# main author: Robert Gerstenberger
+
+import csv
+import numpy as np
+
+
+def scramble(array: np.ndarray, rng: np.random.Generator) -> None:
+    """
+    Helper function to change the order of the elements in an array randomly.
+
+    :param array: Array to be scrambled.
+    :type: numpy.ndarray
+    :param rng: Random number generator.
+    :type rng: numpy.random.Generator
+    """
+
+    size = array.shape[0]
+
+    index_array = rng.integers(0, size, size)
+
+    for i in range(size):
+        temp = array[i]
+        array[i] = array[index_array[i]]
+        array[index_array[i]] = temp
+
+
+if __name__ == "__main__":
+    """
+    Input(u)  : Set size.
+    Input(v)  : Range of the integer numbers in the sets: 0..v (exclusive)
+    Input(w)  : Seed for the random number generator.
+    Input(x)  : Number of samples to be generated.
+    Input(y)  : Filename for the output CSV file.
+    Output(z) : Input sets and intersected set written a file in the CSV format.
+                File contains the sample ID, input set 1, input set 2,
+                intersection set.
+    """
+
+    set_size = 32  # size of the generated sets
+    int_value_ubound = 64  # (exclusive) upper limit of generated numbers
+    seed = 42  # seed of the random number generator
+    num_sample = 100  # number of samples
+    filename = "set_intersection_032.csv"  # output filename
+
+    assert 2 * set_size <= int_value_ubound
+
+    rng = np.random.default_rng(seed)
+
+    intersection_sizes = rng.integers(set_size // 4, 3 * set_size // 4, num_sample)
+
+    np.set_printoptions(
+        linewidth=np.inf
+    )  # no wrapping in the array fields in the output file
+
+    with open(filename, "w") as f:
+        fieldnames = ["ID", "SET1", "SET2", "INTERSECTION"]
+        writer = csv.DictWriter(f, delimiter=",", fieldnames=fieldnames)
+        writer.writeheader()
+
+        for i in range(num_sample):
+            intersection_size = intersection_sizes[i]
+
+            full_set = np.arange(0, int_value_ubound, dtype=np.int16)
+
+            scramble(full_set, rng)
+
+            intersection = full_set[:intersection_size].copy()
+
+            sorted_intersection = np.sort(intersection)
+
+            set1 = full_set[:set_size].copy()
+            set2 = np.concatenate(
+                [intersection, full_set[set_size : 2 * set_size - intersection_size]]
+            )
+
+            scramble(set1, rng)
+            scramble(set2, rng)
+
+            writer.writerow(
+                {
+                    "ID": i,
+                    "SET1": set1.tolist(),
+                    "SET2": set2.tolist(),
+                    "INTERSECTION": sorted_intersection.tolist(),
+                }
+            )
@@ -0,0 +1,184 @@
+# Copyright (c) 2023 ETH Zurich.
+#                    All rights reserved.
+#
+# Use of this source code is governed by a BSD-style license that can be
+# found in the LICENSE file.
+#
+# main author: Nils Blach
+# contributions: Robert Gerstenberger
+
+import json
+import os
+import matplotlib.pyplot as plt
+
+
+def get_complete_results(base_directory):
+    results_complete = {}
+    for folder_name in os.listdir(base_directory):
+        folder_path = os.path.join(base_directory, folder_name)
+        if os.path.isdir(folder_path):
+            results_complete[folder_name] = []
+            for file_name in os.listdir(folder_path):
+                if file_name.endswith(".json"):
+                    file_path = os.path.join(folder_path, file_name)
+                    with open(file_path, "r") as f:
+                        data = json.load(f)
+                        results_complete[folder_name].append(
+                            {"key": int(file_name.split(".")[0]), "data": data}
+                        )
+        for key in results_complete.keys():
+            results_complete[key] = sorted(
+                results_complete[key], key=lambda x: x["key"]
+            )
+    return results_complete
+
+
+def get_final_scores(results_complete):
+    scores = {}
+    for method in results_complete.keys():
+        scores[method] = []
+        for result in results_complete[method]:
+            score = 100
+            solved = False
+            cost = 1
+            prompt_tokens = 0
+            completion_tokens = 0
+            for op in result["data"]:
+                if "operation" in op and op["operation"] == "ground_truth_evaluator":
+                    try:
+                        score = min(op["scores"])
+                        solved = any(op["problem_solved"])
+                    except:
+                        continue
+                if "cost" in op:
+                    cost = op["cost"]
+                    prompt_tokens = op["prompt_tokens"]
+                    completion_tokens = op["completion_tokens"]
+            scores[method].append(
+                [result["key"], score, solved, prompt_tokens, completion_tokens, cost]
+            )
+        scores[method] = sorted(scores[method], key=lambda x: x[0])
+    return scores
+
+
+def get_plotting_data(base_directory):
+    results_complete = get_complete_results(base_directory)
+    scores = get_final_scores(results_complete)
+    results_plotting = {
+        method: {
+            "scores": [x[1] for x in scores[method]],
+            "solved": sum([1 for x in scores[method] if x[2]]),
+            "costs": [x[5] for x in scores[method]],
+        }
+        for method in scores.keys()
+    }
+    return results_plotting
+
+
+def plot_results(
+    results,
+    methods_order=["io", "cot", "tot", "tot2", "got"],
+    model="GPT-3.5",
+    length=32,
+    y_lower=0,
+    cost_upper=0.0,
+    display_solved=True,
+    annotation_offset=0,
+    display_left_ylabel=False,
+    display_right_ylabel=False,
+):
+    methods_order = [method for method in methods_order if method in results]
+    # Extract scores based on the order
+    scores_ordered = [
+        [score for score in results[method]["scores"] if score != 1000]
+        for method in methods_order
+    ]
+    total_costs = [sum(results[method]["costs"]) for method in methods_order]
+
+    # Create figure and axis
+    fig, ax = plt.subplots(dpi=150, figsize=(2.5, 5))
+
+    # Create boxplots
+    positions = range(1, len(methods_order) + 1)
+    ax.boxplot(scores_ordered, positions=positions)
+
+    fig_fontsize = 12
+
+    # Set the ticks and labels
+    methods_labels = ["IO", "CoT", "ToT", "ToT2", "GoT"]
+    plt.yticks(fontsize=fig_fontsize)
+    ax.set_xticks(range(1, len(methods_order) + 1))
+    ax.set_xticks(range(1, len(methods_order) + 1))
+    ax.set_xticklabels(methods_labels, fontsize=fig_fontsize)
+
+    y_upper = length
+
+    range_increase = 1
+    if display_solved:
+        if length < 48:
+            range_increase = 2
+        elif length < 96:
+            range_increase = 4
+        else:
+            range_increase = 8
+
+    ax.set_ylim(y_lower, y_upper + range_increase)
+    ax1_yticks = range(
+        y_lower, y_upper + 1, 2 if length < 48 else (4 if length < 96 else 8)
+    )
+    ax.set_yticks(ax1_yticks)
+    if display_left_ylabel:
+        ax.set_ylabel(
+            f"#incorrect elements; the lower the better", fontsize=fig_fontsize
+        )
+
+    ax.set_title(f"{length} elements")
+
+    ax2 = ax.twinx()
+    ax2.bar(positions, total_costs, alpha=0.5, color="blue", label="Total Cost ($)")
+    ax2.yaxis.set_tick_params(colors="#1919ff", labelsize=fig_fontsize)
+    if cost_upper > 0:
+        ax2.set_ylim(0, cost_upper)
+        number_of_ticks = len(ax.get_yticks())
+        tick_interval = cost_upper / (number_of_ticks)
+        ax2_ticks = [tick_interval * i for i in range(number_of_ticks)]
+
+        # Set custom tick positions for ax2
+        ax2.set_yticks(ax2_ticks)
+
+    if display_right_ylabel:
+        ax2.set_ylabel(
+            "Total Cost ($); the lower the better",
+            color="#1919ff",
+            fontsize=fig_fontsize,
+        )
+
+    if display_solved:
+        annotation_height = y_upper + annotation_offset
+        count = 1
+        for method in methods_order:
+            if method not in results:
+                continue
+            solved = results[method]["solved"]
+            ax.text(
+                count,
+                annotation_height,
+                f"{solved}",
+                ha="center",
+                va="bottom",
+                fontsize=fig_fontsize,
+            )
+            count += 1
+
+    model = model.replace(".", "").replace("-", "").lower()
+    fig.savefig(f"set_intersection_{model}_{length}.pdf", bbox_inches="tight")
+
+
+plot_results(
+    get_plotting_data("results/"),
+    length=32,
+    display_solved=True,
+    model="GPT-3.5",
+    display_left_ylabel=True,
+    display_right_ylabel=True,
+)
@@ -0,0 +1,101 @@
+ID,SET1,SET2,INTERSECTION
+0,"[11, 60, 1, 49, 21, 33, 14, 56, 54, 15, 23, 40, 45, 22, 7, 28, 20, 46, 51, 6, 34, 37, 3, 50, 17, 8, 25, 0, 35, 47, 18, 19]","[31, 11, 4, 63, 38, 58, 59, 24, 61, 14, 32, 39, 27, 46, 48, 19, 52, 57, 50, 56, 3, 2, 53, 29, 5, 37, 62, 41, 36, 12, 49, 16]","[3, 11, 14, 19, 37, 46, 49, 50, 56]"
+1,"[28, 58, 36, 18, 37, 31, 44, 39, 34, 51, 12, 56, 21, 27, 7, 24, 46, 1, 25, 2, 41, 6, 45, 29, 49, 42, 35, 30, 54, 55, 10, 50]","[4, 16, 28, 46, 49, 21, 58, 30, 19, 1, 37, 15, 3, 59, 51, 24, 10, 12, 34, 20, 40, 44, 35, 23, 36, 0, 43, 54, 2, 31, 57, 41]","[1, 2, 10, 12, 21, 24, 28, 30, 31, 34, 35, 36, 37, 41, 44, 46, 49, 51, 54, 58]"
+2,"[32, 24, 17, 27, 51, 19, 50, 59, 8, 18, 41, 36, 43, 39, 49, 4, 5, 31, 30, 60, 48, 61, 10, 16, 47, 58, 9, 54, 40, 37, 1, 11]","[44, 27, 33, 46, 51, 17, 28, 18, 4, 23, 32, 49, 58, 1, 20, 40, 39, 52, 30, 55, 26, 19, 63, 31, 57, 13, 47, 61, 10, 6, 38, 41]","[1, 4, 10, 17, 18, 19, 27, 30, 31, 32, 39, 40, 41, 47, 49, 51, 58, 61]"
+3,"[22, 38, 13, 31, 63, 6, 59, 17, 27, 20, 21, 42, 24, 4, 25, 15, 28, 29, 19, 49, 40, 30, 34, 0, 53, 23, 12, 62, 36, 51, 39, 45]","[21, 29, 30, 28, 31, 55, 2, 22, 19, 4, 46, 32, 37, 43, 23, 15, 58, 56, 11, 50, 48, 54, 41, 45, 51, 7, 42, 38, 18, 9, 6, 1]","[4, 6, 15, 19, 21, 22, 23, 28, 29, 30, 31, 38, 42, 45, 51]"
+4,"[4, 26, 48, 7, 42, 60, 31, 36, 25, 20, 14, 50, 21, 30, 12, 10, 23, 8, 39, 13, 46, 32, 11, 34, 6, 2, 57, 0, 17, 33, 18, 24]","[1, 37, 48, 28, 39, 58, 53, 10, 6, 50, 17, 9, 51, 56, 38, 52, 8, 30, 46, 62, 5, 24, 61, 22, 57, 14, 44, 11, 47, 35, 63, 36]","[6, 8, 10, 11, 14, 17, 24, 30, 36, 39, 46, 48, 50, 57]"
+5,"[48, 50, 19, 59, 57, 63, 49, 61, 14, 11, 29, 39, 4, 17, 21, 12, 3, 35, 23, 2, 58, 60, 38, 43, 28, 47, 5, 44, 15, 55, 8, 26]","[50, 12, 30, 23, 11, 61, 17, 58, 19, 55, 62, 43, 33, 2, 37, 21, 56, 4, 15, 24, 38, 45, 1, 28, 59, 48, 35, 6, 47, 8, 27, 22]","[2, 4, 8, 11, 12, 15, 17, 19, 21, 23, 28, 35, 38, 43, 47, 48, 50, 55, 58, 59, 61]"
+6,"[34, 2, 12, 54, 13, 41, 57, 42, 21, 59, 26, 10, 6, 35, 27, 16, 1, 44, 8, 11, 14, 7, 62, 20, 30, 19, 32, 9, 43, 39, 22, 24]","[18, 41, 49, 56, 1, 3, 45, 36, 17, 34, 50, 46, 29, 30, 61, 32, 14, 52, 24, 51, 5, 25, 31, 55, 37, 0, 23, 40, 28, 20, 22, 63]","[1, 14, 20, 22, 24, 30, 32, 34, 41]"
+7,"[49, 61, 9, 23, 27, 21, 47, 37, 54, 32, 18, 14, 22, 13, 62, 46, 0, 26, 4, 11, 60, 34, 25, 50, 6, 51, 59, 8, 35, 41, 29, 17]","[33, 21, 49, 54, 6, 27, 3, 47, 4, 20, 43, 41, 8, 24, 0, 57, 28, 35, 15, 17, 46, 23, 13, 9, 45, 31, 22, 12, 5, 29, 50, 7]","[0, 4, 6, 8, 9, 13, 17, 21, 22, 23, 27, 29, 35, 41, 46, 47, 49, 50, 54]"
+8,"[55, 59, 60, 13, 41, 15, 38, 52, 35, 5, 9, 61, 57, 34, 47, 22, 21, 1, 27, 11, 36, 2, 6, 58, 62, 51, 23, 50, 8, 39, 28, 54]","[37, 14, 4, 55, 50, 17, 8, 19, 10, 44, 0, 31, 27, 53, 39, 35, 30, 5, 62, 24, 26, 29, 54, 45, 40, 3, 43, 11, 12, 25, 41, 42]","[5, 8, 11, 27, 35, 39, 41, 50, 54, 55, 62]"
+9,"[20, 12, 52, 56, 36, 51, 59, 40, 55, 33, 41, 38, 28, 45, 13, 2, 43, 27, 35, 7, 9, 0, 10, 37, 29, 15, 14, 49, 17, 63, 25, 32]","[11, 13, 19, 6, 21, 54, 36, 14, 58, 26, 2, 39, 53, 22, 50, 51, 24, 16, 5, 17, 1, 60, 57, 23, 35, 33, 42, 18, 61, 29, 47, 8]","[2, 13, 14, 17, 29, 33, 35, 36, 51]"
+10,"[24, 21, 51, 37, 54, 22, 18, 38, 14, 30, 48, 49, 28, 47, 10, 44, 58, 29, 3, 45, 26, 15, 9, 6, 33, 2, 34, 17, 20, 25, 0, 1]","[3, 0, 20, 1, 24, 45, 25, 52, 13, 43, 38, 15, 22, 53, 27, 8, 42, 40, 59, 32, 21, 60, 30, 46, 51, 47, 14, 50, 5, 62, 57, 28]","[0, 1, 3, 14, 15, 20, 21, 22, 24, 25, 28, 30, 38, 45, 47, 51]"
+11,"[58, 52, 51, 15, 42, 26, 19, 30, 28, 6, 40, 11, 25, 53, 18, 47, 21, 12, 41, 45, 43, 7, 35, 48, 27, 3, 32, 2, 4, 62, 17, 29]","[41, 4, 0, 35, 25, 29, 14, 62, 45, 2, 37, 11, 15, 8, 30, 39, 58, 19, 56, 42, 17, 51, 24, 28, 44, 27, 13, 18, 26, 47, 53, 43]","[2, 4, 11, 15, 17, 18, 19, 25, 26, 27, 28, 29, 30, 35, 41, 42, 43, 45, 47, 51, 53, 58, 62]"
+12,"[8, 17, 23, 38, 24, 47, 61, 3, 46, 43, 58, 39, 27, 21, 26, 14, 62, 1, 15, 19, 37, 53, 55, 6, 51, 57, 52, 25, 16, 22, 33, 54]","[2, 18, 15, 17, 23, 45, 14, 36, 53, 7, 27, 32, 31, 21, 8, 38, 16, 61, 6, 58, 3, 39, 49, 19, 22, 42, 0, 12, 30, 60, 26, 46]","[3, 6, 8, 14, 15, 16, 17, 19, 21, 22, 23, 26, 27, 38, 39, 46, 53, 58, 61]"
+13,"[58, 10, 28, 52, 51, 48, 49, 13, 53, 25, 55, 6, 4, 15, 30, 56, 54, 41, 38, 42, 21, 33, 44, 18, 37, 43, 31, 20, 3, 2, 50, 0]","[54, 3, 32, 44, 26, 49, 0, 9, 35, 51, 25, 33, 62, 55, 47, 2, 29, 11, 42, 18, 4, 23, 31, 41, 20, 7, 58, 52, 13, 36, 5, 53]","[0, 2, 3, 4, 13, 18, 20, 25, 31, 33, 41, 42, 44, 49, 51, 52, 53, 54, 55, 58]"
+14,"[12, 18, 22, 38, 6, 23, 54, 37, 40, 44, 19, 46, 35, 47, 7, 10, 16, 24, 4, 42, 31, 30, 0, 63, 25, 57, 39, 51, 3, 60, 49, 28]","[40, 6, 12, 18, 19, 34, 17, 47, 4, 29, 53, 3, 15, 7, 37, 1, 59, 42, 33, 35, 52, 16, 61, 13, 9, 51, 32, 60, 24, 54, 38, 46]","[3, 4, 6, 7, 12, 16, 18, 19, 24, 35, 37, 38, 40, 42, 46, 47, 51, 54, 60]"
+15,"[61, 62, 10, 53, 17, 20, 28, 54, 55, 59, 4, 1, 11, 34, 5, 35, 56, 38, 60, 29, 43, 42, 63, 50, 24, 40, 47, 52, 16, 39, 31, 19]","[60, 24, 50, 45, 23, 18, 20, 31, 29, 35, 43, 44, 59, 41, 51, 46, 16, 63, 38, 3, 42, 25, 4, 17, 5, 9, 61, 7, 27, 54, 19, 39]","[4, 5, 16, 17, 19, 20, 24, 29, 31, 35, 38, 39, 42, 43, 50, 54, 59, 60, 61, 63]"
+16,"[12, 2, 21, 59, 49, 30, 31, 14, 23, 39, 5, 15, 4, 19, 27, 43, 6, 34, 0, 22, 16, 60, 17, 48, 40, 9, 56, 1, 63, 8, 45, 51]","[40, 4, 38, 7, 1, 47, 44, 16, 58, 11, 25, 35, 3, 51, 26, 10, 41, 60, 46, 6, 34, 19, 2, 61, 21, 31, 8, 22, 12, 53, 15, 50]","[1, 2, 4, 6, 8, 12, 15, 16, 19, 21, 22, 31, 34, 40, 51, 60]"
+17,"[26, 8, 53, 37, 45, 60, 32, 44, 19, 39, 36, 16, 25, 9, 6, 50, 38, 47, 30, 63, 42, 52, 57, 10, 7, 27, 14, 1, 41, 58, 59, 62]","[28, 12, 29, 21, 63, 34, 17, 49, 56, 4, 15, 39, 1, 46, 22, 62, 9, 43, 0, 50, 23, 54, 44, 31, 5, 51, 11, 37, 8, 61, 13, 42]","[1, 8, 9, 37, 39, 42, 44, 50, 62, 63]"
+18,"[9, 58, 28, 53, 3, 18, 45, 33, 11, 5, 2, 47, 4, 59, 38, 30, 61, 15, 21, 48, 41, 25, 26, 13, 60, 23, 6, 55, 17, 36, 62, 10]","[43, 15, 16, 10, 33, 5, 13, 62, 41, 53, 0, 32, 54, 23, 26, 19, 25, 9, 37, 49, 38, 21, 28, 27, 40, 45, 4, 61, 29, 3, 55, 18]","[3, 4, 5, 9, 10, 13, 15, 18, 21, 23, 25, 26, 28, 33, 38, 41, 45, 53, 55, 61, 62]"
+19,"[26, 63, 42, 19, 6, 62, 39, 14, 24, 17, 44, 31, 8, 7, 10, 16, 1, 56, 45, 43, 50, 57, 54, 51, 58, 59, 5, 37, 3, 21, 13, 30]","[60, 3, 1, 34, 17, 55, 50, 21, 0, 46, 62, 59, 47, 36, 15, 22, 19, 5, 2, 38, 58, 12, 32, 27, 28, 18, 24, 31, 26, 63, 51, 53]","[1, 3, 5, 17, 19, 21, 24, 26, 31, 50, 51, 58, 59, 62, 63]"
+20,"[30, 31, 28, 56, 54, 29, 61, 18, 1, 46, 34, 5, 15, 63, 26, 45, 4, 47, 40, 21, 3, 9, 2, 27, 7, 6, 24, 19, 42, 11, 35, 41]","[57, 5, 54, 42, 41, 31, 12, 13, 9, 34, 21, 23, 7, 48, 22, 29, 19, 14, 0, 43, 3, 27, 26, 4, 16, 25, 53, 51, 10, 11, 52, 20]","[3, 4, 5, 7, 9, 11, 19, 21, 26, 27, 29, 31, 34, 41, 42, 54]"
+21,"[9, 12, 51, 48, 23, 6, 50, 14, 53, 15, 58, 44, 32, 59, 24, 42, 27, 41, 29, 10, 45, 34, 0, 46, 3, 36, 25, 16, 13, 63, 49, 52]","[16, 15, 51, 37, 20, 27, 47, 36, 45, 59, 0, 41, 40, 2, 28, 31, 17, 1, 21, 22, 5, 58, 18, 57, 34, 39, 54, 9, 53, 33, 60, 19]","[0, 9, 15, 16, 27, 34, 36, 41, 45, 51, 53, 58, 59]"
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+68,"[32, 56, 63, 19, 46, 60, 23, 2, 62, 44, 53, 51, 49, 54, 33, 4, 31, 6, 47, 34, 61, 21, 12, 26, 55, 5, 27, 29, 15, 45, 52, 38]","[49, 8, 24, 36, 0, 3, 33, 51, 16, 11, 43, 40, 2, 29, 41, 38, 7, 39, 17, 55, 18, 62, 25, 20, 48, 14, 10, 13, 30, 22, 19, 50]","[2, 19, 29, 33, 38, 49, 51, 55, 62]"
+69,"[10, 62, 7, 61, 52, 43, 6, 14, 42, 13, 23, 30, 11, 22, 3, 8, 21, 63, 1, 34, 35, 4, 19, 36, 27, 26, 33, 28, 29, 59, 60, 16]","[31, 63, 8, 6, 32, 52, 48, 30, 53, 49, 5, 26, 2, 14, 47, 43, 51, 18, 44, 33, 55, 4, 20, 17, 42, 7, 15, 10, 24, 3, 59, 39]","[3, 4, 6, 7, 8, 10, 14, 26, 30, 33, 42, 43, 52, 59, 63]"
+70,"[9, 22, 57, 5, 0, 10, 56, 20, 8, 23, 4, 3, 58, 50, 38, 18, 1, 14, 17, 40, 21, 11, 48, 36, 27, 31, 2, 30, 34, 37, 49, 7]","[41, 36, 45, 4, 6, 42, 30, 10, 33, 54, 44, 47, 18, 40, 27, 9, 2, 21, 49, 60, 34, 1, 5, 23, 50, 46, 57, 32, 22, 26, 7, 11]","[1, 2, 4, 5, 7, 9, 10, 11, 18, 21, 22, 23, 27, 30, 34, 36, 40, 49, 50, 57]"
+71,"[57, 29, 41, 52, 62, 54, 6, 11, 36, 0, 44, 9, 35, 59, 63, 32, 47, 49, 38, 34, 8, 53, 18, 13, 27, 60, 3, 10, 19, 61, 25, 28]","[10, 62, 39, 11, 16, 28, 14, 37, 23, 8, 17, 25, 58, 45, 7, 56, 36, 61, 48, 12, 13, 4, 33, 55, 27, 42, 20, 46, 32, 31, 43, 21]","[8, 10, 11, 13, 25, 27, 28, 32, 36, 61, 62]"
+72,"[63, 8, 51, 13, 28, 52, 10, 41, 46, 34, 14, 9, 20, 39, 11, 25, 7, 21, 59, 5, 56, 23, 43, 47, 27, 35, 54, 30, 16, 37, 57, 2]","[19, 18, 24, 37, 58, 17, 9, 13, 2, 50, 16, 63, 3, 39, 53, 4, 35, 49, 22, 42, 45, 43, 20, 14, 47, 32, 12, 52, 26, 56, 11, 29]","[2, 9, 11, 13, 14, 16, 20, 35, 37, 39, 43, 47, 52, 56, 63]"
+73,"[56, 35, 29, 20, 24, 27, 31, 12, 2, 4, 33, 11, 60, 16, 7, 8, 58, 63, 46, 49, 36, 52, 53, 41, 30, 32, 51, 47, 62, 21, 15, 0]","[51, 26, 31, 25, 47, 60, 49, 45, 9, 34, 61, 33, 38, 44, 53, 59, 3, 14, 48, 8, 22, 4, 19, 55, 6, 43, 37, 5, 50, 27, 40, 17]","[4, 8, 27, 31, 33, 47, 49, 51, 53, 60]"
+74,"[17, 33, 36, 34, 27, 54, 37, 29, 38, 57, 21, 40, 43, 20, 48, 10, 41, 28, 22, 4, 32, 30, 31, 59, 47, 23, 14, 5, 1, 42, 50, 44]","[13, 23, 10, 14, 51, 12, 21, 40, 32, 3, 29, 56, 33, 50, 37, 22, 63, 47, 24, 38, 35, 43, 5, 26, 16, 27, 31, 1, 49, 46, 8, 52]","[1, 5, 10, 14, 21, 22, 23, 27, 29, 31, 32, 33, 37, 38, 40, 43, 47, 50]"
+75,"[57, 37, 60, 46, 20, 41, 33, 42, 26, 55, 39, 4, 36, 10, 32, 31, 58, 9, 3, 59, 22, 2, 34, 17, 0, 61, 16, 53, 12, 25, 50, 23]","[54, 19, 15, 49, 33, 31, 8, 28, 17, 38, 27, 55, 14, 4, 45, 6, 9, 60, 10, 24, 61, 63, 13, 47, 46, 2, 20, 36, 48, 7, 53, 23]","[2, 4, 9, 10, 17, 20, 23, 31, 33, 36, 46, 53, 55, 60, 61]"
+76,"[20, 56, 53, 3, 34, 4, 2, 6, 27, 15, 63, 23, 55, 39, 14, 36, 42, 25, 35, 38, 43, 1, 37, 51, 16, 29, 31, 47, 26, 28, 10, 45]","[33, 19, 20, 42, 10, 11, 48, 4, 47, 26, 9, 37, 55, 30, 58, 8, 41, 46, 59, 50, 34, 43, 18, 5, 62, 49, 23, 21, 61, 57, 51, 15]","[4, 10, 15, 20, 23, 26, 34, 37, 42, 43, 47, 51, 55]"
+77,"[23, 14, 10, 28, 7, 25, 2, 0, 29, 1, 35, 8, 54, 58, 51, 24, 21, 41, 3, 38, 44, 45, 39, 5, 53, 55, 17, 48, 6, 20, 18, 34]","[2, 53, 46, 41, 62, 43, 12, 63, 10, 32, 22, 59, 51, 13, 25, 23, 14, 36, 16, 11, 58, 57, 9, 61, 42, 47, 37, 50, 33, 3, 6, 15]","[2, 3, 6, 10, 14, 23, 25, 41, 51, 53, 58]"
+78,"[41, 50, 43, 38, 1, 44, 15, 61, 23, 26, 19, 9, 6, 31, 54, 18, 56, 10, 16, 29, 42, 39, 11, 12, 60, 52, 45, 63, 0, 30, 20, 53]","[58, 44, 4, 38, 11, 39, 60, 59, 22, 46, 50, 7, 15, 13, 8, 36, 5, 26, 28, 10, 53, 1, 23, 20, 43, 61, 51, 40, 57, 9, 54, 14]","[1, 9, 10, 11, 15, 20, 23, 26, 38, 39, 43, 44, 50, 53, 54, 60, 61]"
+79,"[33, 36, 54, 26, 59, 28, 0, 10, 1, 63, 45, 11, 53, 56, 6, 4, 27, 40, 39, 61, 55, 18, 3, 48, 9, 22, 2, 34, 15, 16, 60, 42]","[54, 63, 16, 12, 53, 27, 34, 8, 1, 41, 36, 52, 58, 24, 59, 23, 30, 6, 44, 32, 37, 48, 3, 42, 9, 45, 51, 14, 22, 61, 50, 4]","[1, 3, 4, 6, 9, 16, 22, 27, 34, 36, 42, 45, 48, 53, 54, 59, 61, 63]"
+80,"[50, 47, 26, 38, 60, 19, 14, 61, 55, 2, 31, 9, 29, 11, 62, 58, 5, 24, 25, 17, 13, 53, 37, 1, 34, 6, 43, 54, 33, 12, 41, 7]","[16, 62, 31, 60, 50, 29, 10, 20, 39, 2, 42, 14, 22, 1, 13, 59, 0, 26, 11, 34, 19, 6, 7, 54, 8, 38, 33, 61, 17, 25, 58, 47]","[1, 2, 6, 7, 11, 13, 14, 17, 19, 25, 26, 29, 31, 33, 34, 38, 47, 50, 54, 58, 60, 61, 62]"
+81,"[61, 3, 10, 49, 21, 43, 46, 18, 16, 57, 4, 2, 19, 14, 34, 62, 26, 25, 1, 5, 6, 52, 63, 13, 36, 7, 45, 39, 48, 15, 54, 33]","[47, 48, 6, 16, 31, 13, 56, 17, 21, 55, 36, 40, 35, 2, 50, 3, 53, 38, 51, 23, 12, 11, 24, 34, 15, 46, 45, 8, 1, 20, 22, 39]","[1, 2, 3, 6, 13, 15, 16, 21, 34, 36, 39, 45, 46, 48]"
+82,"[30, 47, 32, 19, 28, 45, 23, 13, 37, 0, 40, 16, 14, 26, 5, 43, 12, 41, 3, 6, 53, 51, 63, 24, 7, 61, 20, 22, 39, 11, 33, 34]","[9, 38, 46, 16, 6, 21, 39, 51, 1, 54, 13, 18, 57, 58, 8, 48, 29, 10, 31, 44, 17, 28, 27, 45, 34, 47, 60, 4, 5, 42, 15, 50]","[5, 6, 13, 16, 28, 34, 39, 45, 47, 51]"
+83,"[18, 15, 28, 52, 23, 43, 45, 19, 34, 37, 21, 8, 27, 14, 2, 4, 47, 42, 16, 17, 60, 29, 39, 0, 58, 5, 46, 33, 12, 32, 55, 10]","[51, 27, 18, 40, 45, 32, 60, 0, 53, 4, 23, 28, 10, 15, 29, 17, 24, 2, 5, 34, 21, 22, 52, 11, 12, 50, 44, 9, 3, 42, 39, 48]","[0, 2, 4, 5, 10, 12, 15, 17, 18, 21, 23, 27, 28, 29, 32, 34, 39, 42, 45, 52, 60]"
+84,"[16, 49, 22, 56, 0, 53, 12, 26, 9, 51, 20, 14, 38, 29, 36, 13, 19, 40, 6, 44, 48, 43, 32, 15, 42, 62, 39, 52, 23, 7, 60, 50]","[45, 50, 38, 19, 63, 9, 26, 20, 31, 4, 62, 54, 29, 61, 47, 16, 18, 10, 52, 39, 35, 17, 23, 56, 51, 14, 27, 49, 40, 30, 58, 15]","[9, 14, 15, 16, 19, 20, 23, 26, 29, 38, 39, 40, 49, 50, 51, 52, 56, 62]"
+85,"[41, 56, 11, 28, 36, 57, 6, 23, 49, 29, 20, 5, 63, 39, 58, 51, 42, 37, 18, 0, 19, 31, 47, 10, 32, 48, 38, 7, 13, 44, 45, 8]","[29, 5, 60, 63, 11, 12, 43, 20, 42, 30, 21, 3, 6, 49, 58, 17, 36, 15, 1, 44, 24, 41, 59, 51, 53, 32, 38, 56, 37, 57, 23, 33]","[5, 6, 11, 20, 23, 29, 32, 36, 37, 38, 41, 42, 44, 49, 51, 56, 57, 58, 63]"
+86,"[19, 38, 45, 33, 6, 24, 36, 10, 29, 30, 21, 9, 59, 25, 32, 11, 4, 2, 5, 57, 20, 40, 35, 55, 15, 1, 34, 44, 3, 8, 23, 18]","[37, 42, 17, 16, 6, 55, 43, 0, 56, 53, 31, 14, 21, 44, 26, 61, 49, 25, 12, 27, 28, 18, 32, 51, 13, 50, 52, 19, 54, 58, 30, 48]","[6, 18, 19, 21, 25, 30, 32, 44, 55]"
+87,"[28, 38, 31, 55, 61, 37, 62, 60, 25, 6, 41, 15, 9, 4, 18, 7, 12, 49, 24, 0, 23, 46, 44, 3, 30, 59, 5, 8, 2, 34, 13, 11]","[22, 34, 53, 40, 60, 36, 27, 43, 1, 10, 17, 15, 25, 51, 48, 57, 13, 33, 54, 7, 30, 16, 38, 29, 26, 0, 44, 14, 12, 19, 42, 31]","[0, 7, 12, 13, 15, 25, 30, 31, 34, 38, 44, 60]"
+88,"[60, 43, 34, 28, 48, 25, 29, 15, 16, 46, 26, 54, 4, 38, 11, 61, 39, 20, 17, 50, 27, 2, 49, 14, 36, 24, 5, 53, 41, 55, 10, 3]","[56, 48, 63, 6, 54, 38, 21, 42, 39, 47, 20, 11, 49, 14, 28, 46, 53, 61, 23, 9, 24, 34, 10, 43, 0, 52, 5, 29, 44, 59, 27, 16]","[5, 10, 11, 14, 16, 20, 24, 27, 28, 29, 34, 38, 39, 43, 46, 48, 49, 53, 54, 61]"
+89,"[24, 23, 8, 45, 17, 37, 35, 10, 58, 57, 3, 61, 18, 29, 15, 4, 13, 43, 5, 19, 26, 49, 0, 1, 27, 39, 6, 20, 16, 50, 14, 34]","[38, 63, 5, 49, 47, 18, 39, 60, 29, 26, 44, 3, 0, 10, 52, 61, 14, 4, 15, 35, 59, 8, 57, 50, 54, 20, 28, 24, 16, 1, 55, 25]","[0, 1, 3, 4, 5, 8, 10, 14, 15, 16, 18, 20, 24, 26, 29, 35, 39, 49, 50, 57, 61]"
+90,"[21, 35, 6, 49, 16, 39, 20, 27, 28, 57, 13, 29, 32, 61, 33, 46, 60, 38, 54, 45, 19, 59, 43, 36, 51, 31, 24, 4, 52, 50, 9, 63]","[13, 2, 42, 49, 59, 5, 27, 53, 33, 44, 16, 25, 15, 48, 52, 11, 47, 32, 7, 56, 17, 10, 14, 43, 24, 31, 0, 37, 51, 4, 30, 19]","[4, 13, 16, 19, 24, 27, 31, 32, 33, 43, 49, 51, 52, 59]"
+91,"[38, 36, 34, 17, 18, 46, 20, 3, 15, 57, 23, 42, 4, 25, 2, 7, 55, 24, 19, 51, 52, 31, 21, 28, 16, 62, 9, 12, 27, 13, 48, 1]","[52, 28, 54, 22, 51, 18, 19, 8, 26, 43, 55, 4, 21, 35, 1, 37, 46, 9, 44, 39, 0, 23, 15, 42, 57, 25, 27, 49, 34, 17, 13, 11]","[1, 4, 9, 13, 15, 17, 18, 19, 21, 23, 25, 27, 28, 34, 42, 46, 51, 52, 55, 57]"
+92,"[59, 17, 41, 57, 60, 46, 5, 52, 20, 38, 28, 45, 50, 58, 22, 54, 36, 56, 47, 32, 27, 3, 1, 10, 53, 24, 31, 23, 49, 6, 35, 0]","[59, 41, 20, 24, 53, 19, 46, 5, 35, 31, 38, 37, 36, 0, 52, 16, 2, 45, 17, 33, 21, 57, 50, 61, 56, 11, 8, 29, 18, 54, 10, 47]","[0, 5, 10, 17, 20, 24, 31, 35, 36, 38, 41, 45, 46, 47, 50, 52, 53, 54, 56, 57, 59]"
+93,"[11, 52, 33, 43, 9, 23, 21, 61, 10, 49, 20, 15, 58, 63, 62, 16, 45, 2, 37, 28, 35, 34, 31, 24, 3, 44, 29, 30, 19, 8, 32, 38]","[49, 29, 32, 0, 20, 53, 39, 26, 44, 23, 6, 35, 10, 15, 57, 7, 61, 56, 60, 17, 4, 42, 18, 55, 46, 28, 21, 41, 24, 33, 13, 47]","[10, 15, 20, 21, 23, 24, 28, 29, 32, 33, 35, 44, 49, 61]"
+94,"[8, 3, 10, 61, 33, 57, 38, 37, 20, 0, 35, 40, 58, 19, 25, 4, 24, 22, 13, 56, 45, 16, 27, 51, 46, 29, 59, 34, 15, 31, 44, 39]","[58, 55, 44, 60, 31, 8, 40, 18, 13, 26, 7, 61, 38, 19, 37, 51, 57, 53, 29, 4, 50, 46, 35, 33, 39, 5, 45, 24, 36, 34, 3, 63]","[3, 4, 8, 13, 19, 24, 29, 31, 33, 34, 35, 37, 38, 39, 40, 44, 45, 46, 51, 57, 58, 61]"
+95,"[12, 23, 31, 47, 17, 22, 27, 29, 16, 37, 0, 7, 4, 50, 39, 45, 46, 19, 20, 3, 30, 41, 62, 60, 8, 18, 35, 56, 11, 32, 14, 24]","[16, 13, 5, 49, 42, 12, 40, 34, 23, 48, 36, 51, 18, 7, 62, 31, 19, 61, 25, 58, 53, 54, 60, 17, 46, 59, 41, 52, 10, 33, 63, 26]","[7, 12, 16, 17, 18, 19, 23, 31, 41, 46, 60, 62]"
+96,"[22, 41, 48, 14, 11, 34, 2, 16, 3, 6, 21, 56, 61, 29, 19, 52, 18, 38, 49, 15, 12, 43, 62, 50, 63, 46, 55, 28, 0, 30, 51, 27]","[5, 2, 11, 26, 30, 40, 49, 47, 62, 54, 4, 17, 60, 44, 61, 28, 18, 35, 39, 24, 37, 57, 8, 7, 20, 45, 10, 12, 25, 3, 38, 36]","[2, 3, 11, 12, 18, 28, 30, 38, 49, 61, 62]"
+97,"[2, 62, 8, 22, 15, 60, 59, 14, 0, 10, 33, 34, 50, 4, 19, 31, 58, 1, 16, 53, 17, 24, 27, 18, 32, 11, 51, 43, 54, 42, 28, 39]","[57, 54, 13, 47, 2, 15, 7, 58, 43, 16, 22, 0, 36, 35, 23, 38, 21, 55, 33, 19, 46, 8, 29, 42, 60, 27, 32, 53, 49, 31, 9, 28]","[0, 2, 8, 15, 16, 19, 22, 27, 28, 31, 32, 33, 42, 43, 53, 54, 58, 60]"
+98,"[62, 54, 43, 14, 61, 0, 42, 40, 15, 12, 50, 30, 29, 47, 37, 27, 20, 33, 7, 38, 2, 5, 53, 60, 11, 16, 35, 25, 6, 21, 55, 17]","[38, 7, 54, 31, 47, 28, 34, 8, 12, 20, 3, 63, 0, 52, 36, 55, 60, 25, 17, 15, 13, 46, 33, 56, 26, 11, 14, 16, 40, 4, 37, 45]","[0, 7, 11, 12, 14, 15, 16, 17, 20, 25, 33, 37, 38, 40, 47, 54, 55, 60]"
+99,"[2, 41, 3, 17, 26, 4, 9, 58, 7, 42, 49, 21, 55, 40, 53, 8, 50, 18, 29, 0, 13, 44, 63, 5, 39, 48, 24, 36, 47, 54, 19, 38]","[10, 45, 1, 18, 8, 0, 16, 15, 55, 39, 25, 6, 61, 14, 3, 34, 49, 51, 43, 46, 36, 33, 28, 57, 52, 12, 9, 35, 23, 42, 11, 31]","[0, 3, 8, 9, 18, 36, 39, 42, 49, 55]"
@@ -0,0 +1,730 @@
+# Copyright (c) 2023 ETH Zurich.
+#                    All rights reserved.
+#
+# Use of this source code is governed by a BSD-style license that can be
+# found in the LICENSE file.
+#
+# The source code is adapted from the sorting source code written by
+# Nils Blach.
+#
+# main author: Robert Gerstenberger
+
+import os
+import logging
+import datetime
+import json
+import csv
+from typing import Dict, List, Callable, Union
+from graph_of_thoughts import controller, operations, prompter, parser
+
+from . import utils
+
+
+class SetIntersectionPrompter(prompter.Prompter):
+    """
+    SetIntersectionPrompter provides the generation of prompts specific to the
+    set intersection example for the language models.
+
+    Inherits from the Prompter class and implements its abstract methods.
+    """
+
+    intersection_prompt = """<Instruction> Find the intersection of two sets of numbers. Output only the set of numbers that are present in both sets, no additional text. </Instruction>
+
+<Examples>
+Input Set 1: [13, 16, 30, 6, 21, 7, 31, 15, 11, 1, 24, 10, 9, 3, 20, 8]
+Input Set 2: [25, 24, 10, 4, 27, 0, 14, 12, 8, 2, 29, 20, 17, 19, 26, 23]
+Output: [24, 10, 20, 8]
+
+Input Set 1: [26, 40, 42, 57, 15, 31, 5, 32, 11, 4, 24, 28, 51, 54, 12, 22, 33, 35, 7, 13, 2, 59, 8, 23, 43, 16, 29, 55, 25, 63, 21, 18]
+Input Set 2: [16, 60, 36, 48, 0, 15, 5, 19, 46, 24, 1, 6, 61, 10, 38, 53, 58, 9, 44, 14, 35, 63, 52, 20, 27, 17, 39, 47, 34, 56, 40, 59]
+Output: [40, 15, 5, 24, 35, 59, 16, 63]
+
+Input Set 1: [115, 61, 35, 103, 90, 117, 86, 44, 63, 45, 40, 30, 74, 33, 31, 1, 118, 48, 38, 0, 119, 51, 64, 78, 15, 121, 89, 101, 79, 69, 120, 29, 58, 50, 116, 11, 60, 12, 39, 95, 23, 2, 109, 84, 7, 43, 99, 98, 52, 70, 75, 102, 57, 19, 94, 36, 114, 88, 71, 56, 83, 6, 96, 107]
+Input Set 2: [13, 35, 20, 96, 34, 18, 47, 127, 126, 9, 21, 16, 77, 22, 111, 122, 85, 73, 42, 105, 123, 15, 33, 59, 67, 57, 104, 8, 30, 89, 76, 12, 65, 84, 32, 40, 7, 100, 108, 50, 14, 28, 24, 53, 90, 17, 91, 81, 124, 63, 5, 46, 125, 93, 49, 66, 117, 37, 115, 113, 2, 106, 41, 72]
+Output: [115, 35, 90, 117, 63, 40, 30, 33, 15, 89, 50, 12, 2, 84, 7, 57, 96]
+</Examples>
+
+Input Set 1: {set1}
+Input Set 2: {set2}"""
+
+    intersection_prompt_cot = """<Instruction> Find the intersection of two sets of numbers. You can generate any intermediate solutions, but the final output should be the set of numbers that are present in both sets, prefixed with "Output: ". </Instruction>
+
+<Approach>
+To find the intersection of the two sets follow these steps:
+1. Split the second input set of numbers into two to four subsets, each containing an equal number of elements from the original set (make sure they don't overlap).
+2. For each subset find the set of numbers that are present in the subset and the first input set.
+3. Merge the resulting sets into a single output set.
+</Approach>
+
+<Examples>
+Input Set 1: [13, 16, 30, 6, 21, 7, 31, 15, 11, 1, 24, 10, 9, 3, 20, 8]
+Input Set 2: [25, 24, 10, 4, 27, 0, 14, 12, 8, 2, 29, 20, 17, 19, 26, 23]
+Subsets of Input Set 2:
+[25, 24, 10, 4, 27, 0, 14, 12]
+[8, 2, 29, 20, 17, 19, 26, 23]
+Intersected Subsets with Input Set 1:
+[24, 10]
+[8, 20]
+Output: [24, 10, 8, 20]
+
+Input Set 1: [26, 40, 42, 57, 15, 31, 5, 32, 11, 4, 24, 28, 51, 54, 12, 22, 33, 35, 7, 13, 2, 59, 8, 23, 43, 16, 29, 55, 25, 63, 21, 18]
+Input Set 2: [16, 60, 36, 48, 0, 15, 5, 19, 46, 24, 1, 6, 61, 10, 38, 53, 58, 9, 44, 14, 35, 63, 52, 20, 27, 17, 39, 47, 34, 56, 40, 59]
+Subsets of Input Set 2:
+[16, 60, 36, 48, 0, 15, 5, 19, 46, 24, 1, 6, 61, 10, 38, 53]
+[58, 9, 44, 14, 35, 63, 52, 20, 27, 17, 39, 47, 34, 56, 40, 59]
+Intersected Subsets with Input Set 1:
+[16, 15, 5, 24]
+[35, 63, 40, 59]
+Output: [16, 15, 5, 24, 35, 63, 40, 59]
+
+Input Set 1: [115, 61, 35, 103, 90, 117, 86, 44, 63, 45, 40, 30, 74, 33, 31, 1, 118, 48, 38, 0, 119, 51, 64, 78, 15, 121, 89, 101, 79, 69, 120, 29, 58, 50, 116, 11, 60, 12, 39, 95, 23, 2, 109, 84, 7, 43, 99, 98, 52, 70, 75, 102, 57, 19, 94, 36, 114, 88, 71, 56, 83, 6, 96, 107]
+Input Set 2: [13, 35, 20, 96, 34, 18, 47, 127, 126, 9, 21, 16, 77, 22, 111, 122, 85, 73, 42, 105, 123, 15, 33, 59, 67, 57, 104, 8, 30, 89, 76, 12, 65, 84, 32, 40, 7, 100, 108, 50, 14, 28, 24, 53, 90, 17, 91, 81, 124, 63, 5, 46, 125, 93, 49, 66, 117, 37, 115, 113, 2, 106, 41, 72]
+Subsets of Input Set 2:
+[13, 35, 20, 96, 34, 18, 47, 127, 126, 9, 21, 16, 77, 22, 111, 122]
+[85, 73, 42, 105, 123, 15, 33, 59, 67, 57, 104, 8, 30, 89, 76, 12]
+[65, 84, 32, 40, 7, 100, 108, 50, 14, 28, 24, 53, 90, 17, 91, 81]
+[124, 63, 5, 46, 125, 93, 49, 66, 117, 37, 115, 113, 2, 106, 41, 72]
+Intersected Subsets with Input Set 1:
+[35, 96]
+[15, 33, 57, 30, 89, 12]
+[84, 40, 7, 50, 90]
+[63, 117, 115, 2]
+Output: [35, 96, 15, 33, 57, 30, 89, 12, 84, 40, 7, 50, 90, 63, 117, 115, 2]
+</Examples>
+
+Input Set 1: {set1}
+Input Set 2: {set2}"""
+
+    tot_improve_prompt = """<Instruction> The following three sets represent two sets and an intersection set of those two sets. The intersection set is not correct. Fix the intersection set so that it is correct.
+Make sure that the numbers in the intersection set can be found in both input sets. </Instruction>
+
+<Approach>
+To fix the incorrectly intersection set follow these steps:
+1. Check for each number in the incorrect intersection set, whether it can be found in both input sets. If not, remove that number from the intersection set.
+2. Iterate through the second input set and check whether each number is already in the incorrect intersection set and if not, check whether that number can also be found in the first input set. If so, add that number to the intersection set.
+</Approach>
+
+<Examples>
+Input Set 1: [13, 16, 30, 6, 21, 7, 31, 15, 11, 1, 24, 10, 9, 3, 20, 8]
+Input Set 2: [25, 24, 10, 4, 27, 0, 14, 12, 8, 2, 29, 20, 17, 19, 26, 23]
+Incorrect Intersection Set: [24, 20, 25]
+Reason: The incorrect intersection set contains the number 25, which is not present in the first input set and is missing the numbers 10 and 8.
+Output: [24, 10, 20, 8]
+
+Input Set 1: [26, 40, 42, 57, 15, 31, 5, 32, 11, 4, 24, 28, 51, 54, 12, 22, 33, 35, 7, 13, 2, 59, 8, 23, 43, 16, 29, 55, 25, 63, 21, 18]
+Input Set 2: [16, 60, 36, 48, 0, 15, 5, 19, 46, 24, 1, 6, 61, 10, 38, 53, 58, 9, 44, 14, 35, 63, 52, 20, 27, 17, 39, 47, 34, 56, 40, 59]
+Incorrect Intersection Set: [57, 16, 15, 24, 35, 10, 40]
+Reason: The incorrect intersection set contains the numbers 57, which is not present in the second input set, and 10, which is not present in the first input set, and is missing the numbers 5, 63 and 59.
+Output: [16, 15, 5, 24, 35, 63, 40, 59]
+
+Input Set 1: [115, 61, 35, 103, 90, 117, 86, 44, 63, 45, 40, 30, 74, 33, 31, 1, 118, 48, 38, 0, 119, 51, 64, 78, 15, 121, 89, 101, 79, 69, 120, 29, 58, 50, 116, 11, 60, 12, 39, 95, 23, 2, 109, 84, 7, 43, 99, 98, 52, 70, 75, 102, 57, 19, 94, 36, 114, 88, 71, 56, 83, 6, 96, 107]
+Input Set 2: [13, 35, 20, 96, 34, 18, 47, 127, 126, 9, 21, 16, 77, 22, 111, 122, 85, 73, 42, 105, 123, 15, 33, 59, 67, 57, 104, 8, 30, 89, 76, 12, 65, 84, 32, 40, 7, 100, 108, 50, 14, 28, 24, 53, 90, 17, 91, 81, 124, 63, 5, 46, 125, 93, 49, 66, 117, 37, 115, 113, 2, 106, 41, 72]
+Incorrect Intersection Set: [35, 96, 44, 15, 33, 57, 30, 50, 90, 119, 123, 63, 117, 115, 2]
+Reason: The incorrect intersection set contains the numbers 44 and 119, which are not present in the second input set, and 123, which is not present in the first input set, and is missing the numbers 89, 12, 84, 40 and 7.
+Output: [35, 96, 15, 33, 57, 30, 89, 12, 84, 40, 7, 50, 90, 63, 117, 115, 2]
+</Examples>
+
+Input Set 1: {set1}
+Input Set 2: {set2}
+Incorrect Intersection Set: {incorrect_intersection}
+"""
+
+    got_split_prompt = """<Instruction> Split the following list of 32 numbers into 2 lists of 16 numbers each, the first list should contain the first 16 numbers and the second list the second 16 numbers.
+Only output the 2 lists in the following format without any additional text or thoughts!:
+{{
+    "List 1": [13, 16, 30, 6, 21, 7, 31, ...],
+    "List 2": [25, 24, 10, 4, 27, 0, 14, ...]
+}} </Instruction>
+
+<Example>
+Input: [26, 40, 42, 57, 15, 31, 5, 32, 11, 4, 24, 28, 51, 54, 12, 22, 33, 35, 7, 13, 2, 59, 8, 23, 43, 16, 29, 55, 25, 63, 21, 18]
+Output:
+{{
+    "List 1": [26, 40, 42, 57, 15, 31, 5, 32, 11, 4, 24, 28, 51, 54, 12, 22],
+    "List 2": [33, 35, 7, 13, 2, 59, 8, 23, 43, 16, 29, 55, 25, 63, 21, 18]
+}}
+</Example>
+
+Input: {input}"""
+
+    got_merge_prompt = """<Instruction> Merge the following 2 lists of length {length1} each, into one list of length {length2} by appending the second list to the first list.
+Only output the final list without any additional text or thoughts! </Instruction>
+
+List 1: {input1}
+List 2: {input2}
+"""
+
+    def aggregation_prompt(self, state_dicts: List[Dict], **kwargs) -> str:
+        """
+        Generate an aggregation prompt for the language model.
+
+        :param state_dicts: The thought states that should be aggregated.
+        :type state_dicts: List[Dict]
+        :param kwargs: Additional keyword arguments.
+        :return: The aggregation prompt.
+        :rtype: str
+        :raise AssertionError: If not exactly two thought states are provided.
+        """
+        assert len(state_dicts) == 2, "Expected two states for aggregation prompt."
+        len_input1 = len(utils.string_to_list(state_dicts[0]["current"]))
+        len_input2 = len(utils.string_to_list(state_dicts[1]["current"]))
+        if len_input1 == len_input2:
+            length = len_input1
+        elif len_input1 + len_input2 - 32 <= 16:
+            length = 16
+        else:
+            length = 32
+
+        return self.got_merge_prompt.format(
+            input1=state_dicts[0]["current"],
+            input2=state_dicts[1]["current"],
+            length1=length,
+            length2=length * 2,
+        )
+
+    def generate_prompt(
+        self,
+        num_branches: int,
+        set1: str,
+        set2: str,
+        current: str,
+        method: str,
+        **kwargs,
+    ) -> str:
+        """
+        Generate a generate prompt for the language model.
+
+        :param num_branches: The number of responses the prompt should ask the LM to generate.
+        :type num_branches: int
+        :param set1: First input set.
+        :type set1: str
+        :param set2: Second input set.
+        :type set2: str
+        :param current: Intermediate solution.
+        :type current: str
+        :param method: Method for which the generate prompt is generated.
+        :type method: str
+        :param kwargs: Additional keyword arguments.
+        :return: The generate prompt.
+        :rtype: str
+        :raise AssertionError: If the requested number of branches is not one.
+        """
+
+        assert num_branches == 1, "Branching should be done via multiple requests."
+        if method.startswith("io"):
+            return self.intersection_prompt.format(set1=set1, set2=set2)
+        elif method.startswith("cot"):
+            return self.intersection_prompt_cot.format(set1=set1, set2=set2)
+        elif method.startswith("tot"):
+            if current is None or current == "":
+                return self.intersection_prompt.format(set1=set1, set2=set2)
+            return self.tot_improve_prompt.format(
+                set1=set1, set2=set2, incorrect_intersection=current
+            )
+        elif method.startswith("got"):
+            if kwargs["phase"] == 0:
+                return self.got_split_prompt.format(input=set2)
+
+            input_set = set2
+            if "subset" in kwargs and kwargs["subset"] != "":
+                input_set = kwargs["subset"]
+
+            return self.intersection_prompt.format(set1=set1, set2=input_set)
+
+    def improve_prompt(self, **kwargs) -> str:
+        """
+        Generate an improve prompt for the language model.
+
+        :param kwargs: Additional keyword arguments.
+        :return: The improve prompt.
+        :rtype: str
+        """
+        pass
+
+    def validation_prompt(self, **kwargs) -> str:
+        """
+        Generate a validation prompt for the language model.
+
+        :param kwargs: Additional keyword arguments.
+        :return: The validation prompt.
+        :rtype: str
+        """
+        pass
+
+    def score_prompt(self, state_dicts: List[Dict], **kwargs) -> str:
+        """
+        Generate a score prompt for the language model.
+
+        :param state_dicts: The thought states that should be scored,
+                            if more than one, they should be scored together.
+        :type state_dicts: List[Dict]
+        :param kwargs: Additional keyword arguments.
+        :return: The score prompt.
+        :rtype: str
+        """
+        pass
+
+
+class SetIntersectionParser(parser.Parser):
+    """
+    SetIntersectionParser provides the parsing of language model reponses
+    specific to the set intersection example.
+
+    Inherits from the Parser class and implements its abstract methods.
+    """
+
+    def __init__(self) -> None:
+        """
+        Inits the response cache.
+        """
+        self.cache = {}
+
+    def parse_aggregation_answer(
+        self, states: List[Dict], texts: List[str]
+    ) -> Union[Dict, List[Dict]]:
+        """
+        Parse the response from the language model for an aggregation prompt.
+
+        :param states: The thought states used to generate the prompt.
+        :type states: List[Dict]
+        :param texts: The responses to the prompt from the language model.
+        :type texts: List[str]
+        :return: The new thought states after parsing the respones from the language model.
+        :rtype: Union[Dict, List[Dict]]
+        :raise AssertionError: If not exactly two thought states are provided.
+        """
+
+        assert len(states) == 2, "Expected two states for aggregation answer."
+        new_states = []
+        for text in texts:
+            answers = text.strip().split("\n")
+            if any(["Output" in answer for answer in answers]):
+                # cut elements until last output is found
+                for answer in reversed(answers):
+                    if "Output" in answer:
+                        answers = answers[answers.index(answer) :]
+                        break
+
+            answers_stripped = [
+                answer for answer in answers if "[" in answer and "]" in answer
+            ]
+            if len(answers_stripped) == 0:
+                for answer in answers:
+                    answer = "[" + answer + "]"
+                    try:
+                        answer_converted = utils.string_to_list(answer)
+                        if len(answer_converted) > 0:
+                            answers_stripped.append(answer)
+                    except:
+                        pass
+            if len(answers_stripped) == 0:
+                logging.warning(
+                    f"Could not parse aggregation answer: {text}. Returning empty list."
+                )
+                answer = "[]"
+            else:
+                answer = [
+                    answer[answer.index("[") : answer.index("]") + 1]
+                    for answer in answers_stripped
+                ][0]
+            states = sorted(states, key=lambda x: x["part"])
+            merged_subsets = states[0]["subset"][:-1] + ", " + states[1]["subset"][1:]
+            new_state = states[0].copy()
+            new_state["current"] = answer
+            new_state["subset"] = merged_subsets
+            new_states.append(new_state)
+        return new_states
+
+    def parse_improve_answer(self, state: Dict, texts: List[str]) -> Dict:
+        """
+        Parse the response from the language model for an improve prompt.
+
+        :param state: The thought state used to generate the prompt.
+        :type state: Dict
+        :param texts: The responses to the prompt from the language model.
+        :type texts: List[str]
+        :return: The new thought state after parsing the responses from the language model.
+        :rtype: Dict
+        """
+        pass
+
+    def parse_generate_answer(self, state: Dict, texts: List[str]) -> List[Dict]:
+        """
+        Parse the response from the language model for a generate prompt.
+
+        :param state: The thought state used to generate the prompt.
+        :type state: Dict
+        :param texts: The responses to the prompt from the language model.
+        :type texts: List[str]
+        :return: The new thought states after parsing the respones from the language model.
+        :rtype: List[Dict]
+        """
+
+        new_states = []
+        for text in texts:
+            if state["method"].startswith("got") and state["phase"] == 0:
+                # We expect a json which contains the two lists named "List 1" and "List 2"
+                # cut everything until the opening bracket and everything after the closing bracket
+
+                try:
+                    text = text[text.index("{") : text.index("}") + 1]
+                    json_dict = json.loads(text)
+                    if len(json_dict.keys()) != 2:
+                        logging.warning(
+                            f"Expected 2 lists in json, but found {len(json_dict.keys())}."
+                        )
+                    for key, value in json_dict.items():
+                        if "List" not in key:
+                            logging.warning(
+                                f"Expected key to contain 'List', but found {key}."
+                            )
+                            continue
+                        if not isinstance(value, list):
+                            value = utils.string_to_list(value)
+                        new_state = state.copy()
+                        new_state["current"] = ""
+                        new_state["subset"] = str(value)
+                        new_state["phase"] = 1
+                        new_state["part"] = key
+                        new_states.append(new_state)
+                except Exception as e:
+                    logging.error(
+                        f"Could not parse step answer: {text}. Encountered exception: {e}"
+                    )
+            else:
+                answers = text.strip().split("\n")
+                answers = [
+                    answer for answer in answers if "[" in answer and "]" in answer
+                ]
+                if any(["Output" in answer for answer in answers]):
+                    # cut elements until last output is found
+                    for answer in reversed(answers):
+                        if "Output" in answer:
+                            answers = answers[answers.index(answer) :]
+                            break
+
+                answers = [
+                    answer[answer.index("[") : answer.index("]") + 1]
+                    for answer in answers
+                ]
+                if len(answers) == 0:
+                    logging.warning(
+                        f"Could not parse step answer: {text}. Returning empty list."
+                    )
+                    answer = "[]"
+                else:
+                    if len(answers) > 1:
+                        logging.warning(
+                            f"Multiple answers found for step answer: {text}. Using the first one."
+                        )
+                    answer = answers[0]
+
+                new_state = state.copy()
+                new_state["current"] = answer
+                new_state["phase"] = 2
+                new_states.append(new_state)
+        return new_states
+
+    def parse_validation_answer(self, state: Dict, texts: List[str]) -> bool:
+        """
+        Parse the response from the language model for a validation prompt.
+
+        :param state: The thought state used to generate the prompt.
+        :type state: Dict
+        :param texts: The responses to the prompt from the language model.
+        :type texts: List[str]
+        :return: Whether the thought state is valid or not.
+        :rtype: bool
+        """
+        pass
+
+    def parse_score_answer(self, states: List[Dict], texts: List[str]) -> List[float]:
+        """
+        Parse the response from the language model for a score prompt.
+
+        :param states: The thought states used to generate the prompt.
+        :type states: List[Dict]
+        :param texts: The responses to the prompt from the language model.
+        :type texts: List[str]
+        :return: The scores for the thought states.
+        :rtype: List[float]
+        """
+        pass
+
+
+def io() -> operations.GraphOfOperations:
+    """
+    Generates the Graph of Operations for the IO method.
+
+    :return: Graph of Operations
+    :rtype: GraphOfOperations
+    """
+    operations_graph = operations.GraphOfOperations()
+
+    operations_graph.append_operation(operations.Generate(1, 1))
+    operations_graph.append_operation(operations.Score(1, False, utils.num_errors))
+    operations_graph.append_operation(
+        operations.GroundTruth(utils.test_set_intersection)
+    )
+
+    return operations_graph
+
+
+def cot() -> operations.GraphOfOperations:
+    """
+    Generates the Graph of Operations for the CoT method.
+
+    :return: Graph of Operations
+    :rtype: GraphOfOperations
+    """
+    operations_graph = operations.GraphOfOperations()
+
+    operations_graph.append_operation(operations.Generate(1, 1))
+    operations_graph.append_operation(operations.Score(1, False, utils.num_errors))
+    operations_graph.append_operation(
+        operations.GroundTruth(utils.test_set_intersection)
+    )
+
+    return operations_graph
+
+
+def tot() -> operations.GraphOfOperations:
+    """
+    Generates the Graph of Operations for the ToT method.
+    ToT uses a wider tree, where on each level there are more branches.
+
+    :return: Graph of Operations
+    :rtype: GraphOfOperations
+    """
+    operations_graph = operations.GraphOfOperations()
+
+    operations_graph.append_operation(operations.Generate(1, 20))
+    operations_graph.append_operation(operations.Score(1, False, utils.num_errors))
+    op_1 = operations.KeepBestN(1, False)
+    operations_graph.append_operation(op_1)
+
+    for _ in range(1):
+        operations_graph.append_operation(operations.Generate(1, 20))
+        operations_graph.append_operation(operations.Score(1, False, utils.num_errors))
+        op_2 = operations.KeepBestN(1, False)
+        op_2.add_predecessor(op_1)
+        operations_graph.append_operation(op_2)
+        op_1 = op_2
+
+    operations_graph.append_operation(
+        operations.GroundTruth(utils.test_set_intersection)
+    )
+
+    return operations_graph
+
+
+def tot2() -> operations.GraphOfOperations:
+    """
+    Generates the Graph of Operations for the ToT2 method.
+    ToT2 uses a tree with more levels, but with fewer branches per level.
+
+    :return: Graph of Operations
+    :rtype: GraphOfOperations
+    """
+    operations_graph = operations.GraphOfOperations()
+
+    operations_graph.append_operation(operations.Generate(1, 10))
+    operations_graph.append_operation(operations.Score(1, False, utils.num_errors))
+    op_1 = operations.KeepBestN(1, False)
+    operations_graph.append_operation(op_1)
+
+    for _ in range(2):
+        operations_graph.append_operation(operations.Generate(1, 10))
+        operations_graph.append_operation(operations.Score(1, False, utils.num_errors))
+        op_2 = operations.KeepBestN(1, False)
+        op_2.add_predecessor(op_1)
+        operations_graph.append_operation(op_2)
+        op_1 = op_2
+
+    operations_graph.append_operation(
+        operations.GroundTruth(utils.test_set_intersection)
+    )
+
+    return operations_graph
+
+
+def got() -> operations.GraphOfOperations:
+    """
+    Generates the Graph of Operations for the GoT method.
+
+    :return: Graph of Operations
+    :rtype: GraphOfOperations
+    """
+    operations_graph = operations.GraphOfOperations()
+
+    plans = operations.Generate(1, 1)
+    operations_graph.append_operation(plans)  # generate the sublists
+    for i in range(1, 3):
+        list_id = f"List {i}"
+        sub_list = operations.Selector(
+            lambda thoughts, list_id=list_id: [
+                thought for thought in thoughts if thought.state["part"] == list_id
+            ]
+        )
+        sub_list.add_predecessor(plans)
+        operations_graph.add_operation(sub_list)
+        intersected_subset = operations.Generate(1, 5)
+        intersected_subset.add_predecessor(sub_list)
+        operations_graph.add_operation(intersected_subset)
+        score_sub_list = operations.Score(1, False, utils.num_errors)
+        score_sub_list.add_predecessor(intersected_subset)
+        operations_graph.add_operation(score_sub_list)
+        keep_best_sub_list = operations.KeepBestN(1, False)
+        keep_best_sub_list.add_predecessor(score_sub_list)
+        operations_graph.add_operation(keep_best_sub_list)
+
+    final_aggregate = operations.Aggregate(10)
+    operations_graph.append_operation(final_aggregate)
+    operations_graph.append_operation(operations.Score(1, False, utils.num_errors))
+    keep_best_aggregate_final = operations.KeepBestN(1, False)
+    operations_graph.append_operation(keep_best_aggregate_final)
+
+    operations_graph.append_operation(
+        operations.GroundTruth(utils.test_set_intersection)
+    )
+
+    return operations_graph
+
+
+def run(
+    data_ids: List[int],
+    methods: List[Callable[[], operations.GraphOfOperations]],
+    budget: float,
+    lm_name: str,
+) -> float:
+    """
+    Controller function that executes each specified method for each specified
+    sample while the budget is not exhausted.
+
+    :param data_ids: Indices of the sample to be run.
+    :type data_ids: List[int]
+    :param methods: List of functions to generate Graphs of Operations.
+    :type methods: Each function generates a Graph of Operation.
+    :param budget: Language model budget for the execution in dollars.
+    :type budget: float
+    :param lm_name: Name of the language model to be used.
+    :type lm_name: str
+    :return: Spent budget in dollars.
+    :rtype: float
+    """
+
+    orig_budget = budget
+    path = os.path.join(os.path.dirname(__file__), "set_intersection_032.csv")
+    data = []
+    with open(path, "r") as f:
+        reader = csv.reader(f)
+        next(reader)
+        for row in reader:
+            data.append([int(row[0]), row[1], row[2], row[3]])
+
+    if data_ids is None or len(data_ids) == 0:
+        data_ids = list(range(len(data)))
+    selected_data = [data[i] for i in data_ids]
+
+    if not os.path.exists(os.path.join(os.path.dirname(__file__), "results")):
+        os.makedirs(os.path.join(os.path.dirname(__file__), "results"))
+    timestamp = datetime.datetime.now().strftime("%Y-%m-%d_%H-%M-%S")
+    extra_info = f"{lm_name}_{'-'.join([method.__name__ for method in methods])}"
+    folder_name = f"results/{extra_info}_{timestamp}"
+    os.makedirs(os.path.join(os.path.dirname(__file__), folder_name))
+
+    config = {
+        "data": selected_data,
+        "methods": [method.__name__ for method in methods],
+        "lm": lm_name,
+        "budget": budget,
+    }
+    with open(
+        os.path.join(os.path.dirname(__file__), folder_name, "config.json"), "w"
+    ) as f:
+        json.dump(config, f)
+
+    logging.basicConfig(
+        filename=f"{folder_name}/log.log",
+        filemode="w",
+        format="%(name)s - %(levelname)s - %(message)s",
+        level=logging.DEBUG,
+    )
+
+    for method in methods:
+        # create a results directory for the method
+        os.makedirs(
+            os.path.join(os.path.dirname(__file__), folder_name, method.__name__)
+        )
+
+    for data in selected_data:
+        logging.info(f"Running data {data[0]}: {data[1]} {data[2]}")
+        if budget <= 0.0:
+            logging.error(
+                f"Budget has been depleted, stopping. Data {data[0]} has not been run."
+            )
+            break
+        for method in methods:
+            logging.info(f"Running method {method.__name__}")
+            logging.info(f"Budget left: {budget}")
+            if budget <= 0.0:
+                logging.error(
+                    f"Budget has been depleted, stopping. Method {method.__name__} has not been run."
+                )
+                break
+            lm = controller.ChatGPT(
+                "../../graph_of_thoughts/controller/config.json",
+                model_name=lm_name,
+                cache=True,
+            )
+            operations_graph = method()
+            executor = controller.Controller(
+                lm,
+                operations_graph,
+                SetIntersectionPrompter(),
+                SetIntersectionParser(),
+                {
+                    "set1": data[1],
+                    "set2": data[2],
+                    "result": data[3],
+                    "current": "",
+                    "phase": 0,
+                    "method": method.__name__,
+                },
+            )
+            try:
+                executor.run()
+            except Exception as e:
+                logging.error(f"Exception: {e}")
+            path = os.path.join(
+                os.path.dirname(__file__),
+                folder_name,
+                method.__name__,
+                f"{data[0]}.json",
+            )
+            executor.output_graph(path)
+            budget -= lm.cost
+
+    return orig_budget - budget
+
+
+if __name__ == "__main__":
+    """
+    Input(x)  : a list of 32 numbers between 0 and 63 (inclusive)
+    Input(y)  : a list of 32 numbers between 0 and 63 (inclusive)
+    Output(z) : a list of the intersection between x and y
+    Correct   : z = intersection(x, y)
+    Input Example:
+        [13, 16, 30, 6, 21, 7, 31, 15, 11, 1, 24, 10, 9, 3, 20, 8]
+        [25, 24, 10, 4, 27, 0, 14, 12, 8, 2, 29, 20, 17, 19, 26, 23]
+    Output Example:
+        [24, 10, 20, 8]
+    """
+
+    budget = 15
+    samples = [item for item in range(0, 100)]
+    approaches = [io, cot, tot, tot2, got]
+
+    spent = run(samples, approaches, budget, "chatgpt")
+
+    logging.info(f"Spent {spent} out of {budget} budget.")
@@ -0,0 +1,101 @@
+ID,SET1,SET2,INTERSECTION
+0,"[42, 73, 86, 39, 85, 77, 69, 59, 43, 127, 121, 88, 109, 53, 70, 66, 25, 51, 34, 78, 45, 11, 40, 99, 68, 47, 49, 41, 101, 31, 24, 84, 36, 29, 118, 75, 3, 27, 30, 80, 125, 8, 37, 46, 90, 21, 60, 83, 19, 6, 95, 117, 87, 18, 100, 13, 22, 10, 110, 102, 35, 81, 17, 63]","[34, 49, 116, 106, 112, 23, 5, 80, 18, 62, 90, 54, 32, 103, 37, 43, 9, 25, 92, 16, 111, 79, 64, 91, 107, 58, 72, 94, 7, 60, 33, 14, 19, 104, 28, 74, 96, 76, 38, 52, 114, 50, 17, 0, 3, 100, 69, 98, 2, 1, 99, 12, 95, 97, 123, 4, 126, 124, 82, 27, 67, 57, 115, 46]","[3, 17, 18, 19, 25, 27, 34, 37, 43, 46, 49, 60, 69, 80, 90, 95, 99, 100]"
+1,"[50, 23, 70, 14, 54, 85, 106, 108, 6, 113, 79, 48, 99, 112, 28, 69, 0, 19, 64, 37, 90, 4, 15, 30, 94, 109, 96, 87, 71, 43, 21, 117, 8, 63, 35, 66, 83, 40, 119, 26, 46, 5, 53, 62, 12, 126, 116, 100, 111, 29, 97, 27, 25, 36, 82, 42, 127, 11, 56, 121, 59, 52, 124, 2]","[112, 74, 109, 56, 57, 5, 43, 126, 61, 95, 60, 79, 21, 20, 100, 85, 66, 84, 19, 37, 67, 15, 75, 30, 106, 70, 11, 121, 55, 28, 34, 76, 62, 6, 53, 97, 69, 80, 114, 39, 82, 27, 26, 14, 23, 77, 65, 40, 108, 2, 50, 118, 59, 41, 54, 45, 0, 42, 110, 94, 92, 38, 91, 4]","[0, 2, 4, 5, 6, 11, 14, 15, 19, 21, 23, 26, 27, 28, 30, 37, 40, 42, 43, 50, 53, 54, 56, 59, 62, 66, 69, 70, 79, 82, 85, 94, 97, 100, 106, 108, 109, 112, 121, 126]"
+2,"[91, 23, 41, 37, 31, 22, 50, 35, 111, 115, 77, 55, 2, 97, 68, 85, 122, 62, 110, 87, 27, 113, 96, 81, 117, 18, 83, 71, 34, 64, 32, 92, 116, 3, 1, 10, 106, 42, 30, 86, 121, 52, 108, 84, 102, 8, 100, 125, 16, 39, 58, 29, 24, 38, 15, 17, 6, 40, 9, 94, 51, 61, 54, 65]","[41, 50, 8, 115, 51, 91, 29, 104, 6, 85, 21, 5, 42, 58, 36, 93, 89, 113, 1, 46, 119, 90, 55, 123, 98, 84, 34, 71, 117, 94, 53, 65, 26, 86, 28, 44, 33, 37, 95, 22, 87, 63, 100, 17, 81, 68, 72, 39, 127, 2, 74, 30, 76, 111, 66, 106, 107, 4, 73, 121, 0, 67, 9, 10]","[1, 2, 6, 8, 9, 10, 17, 22, 29, 30, 34, 37, 39, 41, 42, 50, 51, 55, 58, 65, 68, 71, 81, 84, 85, 86, 87, 91, 94, 100, 106, 111, 113, 115, 117, 121]"
+3,"[12, 43, 39, 18, 95, 36, 51, 26, 30, 100, 85, 29, 75, 32, 79, 57, 101, 34, 108, 10, 23, 106, 16, 9, 7, 72, 82, 68, 105, 0, 37, 65, 64, 67, 62, 25, 13, 66, 77, 33, 121, 15, 122, 17, 3, 8, 45, 1, 70, 119, 76, 69, 92, 5, 2, 28, 110, 20, 102, 6, 93, 44, 98, 103]","[83, 118, 32, 94, 115, 39, 91, 74, 34, 70, 79, 76, 61, 126, 106, 31, 25, 11, 123, 5, 40, 58, 78, 24, 101, 82, 4, 109, 71, 86, 17, 29, 37, 92, 73, 66, 50, 111, 95, 30, 124, 116, 62, 0, 84, 108, 63, 104, 107, 38, 27, 18, 33, 9, 49, 64, 26, 13, 42, 35, 20, 43, 77, 127]","[0, 5, 9, 13, 17, 18, 20, 25, 26, 29, 30, 32, 33, 34, 37, 39, 43, 62, 64, 66, 70, 76, 77, 79, 82, 92, 95, 101, 106, 108]"
+4,"[20, 116, 36, 54, 27, 67, 105, 51, 43, 57, 55, 44, 113, 38, 114, 64, 63, 37, 92, 76, 90, 35, 42, 117, 69, 2, 14, 81, 6, 78, 68, 11, 30, 52, 58, 98, 104, 21, 4, 85, 13, 47, 87, 62, 48, 109, 101, 0, 34, 53, 56, 59, 19, 88, 112, 28, 71, 18, 80, 50, 121, 75, 111, 49]","[5, 34, 55, 53, 113, 60, 22, 98, 16, 92, 126, 27, 70, 30, 61, 37, 64, 9, 36, 123, 79, 101, 15, 90, 62, 52, 72, 3, 29, 4, 110, 102, 17, 125, 26, 99, 86, 1, 20, 112, 24, 28, 31, 47, 85, 11, 42, 78, 25, 91, 7, 104, 12, 74, 71, 89, 48, 95, 43, 100, 103, 97, 107, 2]","[2, 4, 11, 20, 27, 28, 30, 34, 36, 37, 42, 43, 47, 48, 52, 53, 55, 62, 64, 71, 78, 85, 90, 92, 98, 101, 104, 112, 113]"
+5,"[123, 114, 111, 64, 115, 14, 75, 67, 4, 125, 61, 11, 38, 104, 105, 7, 45, 113, 93, 41, 86, 77, 44, 0, 89, 112, 90, 52, 57, 74, 26, 29, 69, 108, 32, 121, 107, 102, 19, 42, 60, 51, 116, 39, 24, 37, 118, 68, 92, 87, 95, 79, 106, 13, 40, 53, 81, 85, 99, 36, 23, 97, 48, 47]","[61, 53, 116, 0, 75, 43, 89, 38, 101, 60, 51, 83, 29, 112, 36, 81, 55, 34, 94, 125, 68, 64, 84, 26, 40, 107, 82, 16, 24, 42, 108, 19, 111, 54, 6, 41, 120, 79, 9, 48, 44, 4, 106, 93, 30, 13, 39, 20, 124, 66, 33, 52, 57, 11, 105, 114, 72, 123, 67, 102, 71, 113, 3, 69]","[0, 4, 11, 13, 19, 24, 26, 29, 36, 38, 39, 40, 41, 42, 44, 48, 51, 52, 53, 57, 60, 61, 64, 67, 68, 69, 75, 79, 81, 89, 93, 102, 105, 106, 107, 108, 111, 112, 113, 114, 116, 123, 125]"
+6,"[118, 20, 53, 85, 46, 51, 22, 52, 98, 28, 49, 64, 35, 124, 69, 58, 125, 34, 104, 106, 2, 74, 67, 111, 96, 0, 3, 33, 8, 91, 23, 43, 92, 72, 76, 26, 50, 6, 18, 68, 56, 101, 97, 37, 47, 24, 7, 57, 54, 75, 73, 1, 61, 12, 114, 87, 19, 48, 40, 62, 10, 36, 16, 123]","[94, 59, 117, 86, 6, 22, 110, 82, 34, 13, 89, 19, 122, 30, 7, 27, 44, 85, 112, 42, 17, 24, 31, 56, 43, 39, 115, 23, 15, 46, 83, 57, 127, 116, 47, 63, 102, 78, 121, 21, 103, 113, 88, 38, 16, 76, 100, 84, 9, 14, 49, 8, 60, 109, 41, 79, 99, 37, 105, 55, 108, 107, 77, 4]","[6, 7, 8, 16, 19, 22, 23, 24, 34, 37, 43, 46, 47, 49, 56, 57, 76, 85]"
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+9,"[122, 95, 15, 106, 92, 43, 38, 117, 75, 64, 16, 96, 71, 105, 1, 49, 57, 80, 101, 116, 77, 63, 39, 21, 66, 35, 120, 100, 85, 26, 99, 2, 46, 19, 74, 3, 113, 37, 108, 65, 32, 67, 11, 47, 27, 81, 73, 17, 22, 4, 121, 60, 40, 9, 87, 50, 119, 104, 28, 79, 124, 78, 94, 34]","[100, 37, 17, 8, 7, 75, 51, 107, 10, 93, 94, 124, 38, 6, 109, 24, 26, 47, 59, 86, 123, 0, 5, 54, 70, 18, 27, 19, 4, 56, 101, 68, 48, 61, 41, 112, 117, 125, 77, 69, 13, 102, 35, 97, 111, 110, 89, 72, 115, 83, 52, 76, 2, 44, 120, 42, 30, 53, 36, 88, 31, 55, 64, 103]","[2, 4, 17, 19, 26, 27, 35, 37, 38, 47, 64, 75, 77, 94, 100, 101, 117, 120, 124]"
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+11,"[51, 76, 124, 93, 123, 53, 67, 4, 125, 103, 46, 64, 83, 72, 104, 106, 55, 7, 44, 114, 23, 58, 37, 31, 19, 63, 101, 42, 60, 92, 57, 2, 81, 21, 115, 32, 12, 66, 1, 112, 38, 5, 50, 35, 59, 34, 47, 78, 79, 127, 13, 9, 61, 96, 97, 8, 126, 86, 118, 6, 56, 48, 0, 121]","[108, 101, 72, 34, 124, 123, 0, 82, 121, 126, 70, 116, 104, 77, 61, 118, 112, 96, 95, 45, 71, 39, 115, 51, 48, 79, 66, 78, 58, 37, 44, 5, 42, 53, 57, 32, 56, 6, 16, 103, 80, 92, 35, 50, 127, 12, 69, 1, 102, 47, 97, 4, 109, 55, 86, 67, 9, 33, 100, 10, 38, 23, 19, 63]","[0, 1, 4, 5, 6, 9, 12, 19, 23, 32, 34, 35, 37, 38, 42, 44, 47, 48, 50, 51, 53, 55, 56, 57, 58, 61, 63, 66, 67, 72, 78, 79, 86, 92, 96, 97, 101, 103, 104, 112, 115, 118, 121, 123, 124, 126, 127]"
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+15,"[70, 41, 44, 50, 67, 77, 7, 81, 38, 125, 32, 115, 109, 61, 60, 56, 13, 85, 27, 4, 21, 19, 114, 68, 105, 14, 107, 31, 126, 0, 84, 54, 34, 108, 106, 98, 127, 92, 121, 95, 57, 3, 99, 48, 79, 110, 104, 45, 30, 73, 87, 111, 49, 93, 33, 103, 15, 42, 78, 94, 47, 58, 40, 80]","[90, 30, 17, 119, 56, 80, 16, 105, 34, 97, 48, 58, 19, 93, 84, 1, 98, 23, 110, 117, 118, 75, 126, 35, 25, 123, 114, 121, 33, 86, 67, 54, 49, 91, 41, 78, 15, 77, 14, 7, 61, 113, 79, 102, 109, 47, 92, 101, 31, 0, 72, 32, 52, 103, 68, 42, 100, 122, 13, 95, 3, 81, 18, 38]","[0, 3, 7, 13, 14, 15, 19, 30, 31, 32, 33, 34, 38, 41, 42, 47, 48, 49, 54, 56, 58, 61, 67, 68, 77, 78, 79, 80, 81, 84, 92, 93, 95, 98, 103, 105, 109, 110, 114, 121, 126]"
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+89,"[101, 65, 94, 68, 0, 96, 37, 81, 79, 107, 60, 109, 3, 11, 78, 36, 38, 52, 14, 41, 71, 23, 64, 93, 45, 21, 48, 54, 120, 6, 83, 43, 34, 121, 56, 63, 51, 61, 2, 115, 104, 40, 95, 17, 44, 55, 114, 4, 80, 39, 12, 99, 16, 8, 35, 32, 86, 91, 72, 5, 18, 15, 97, 59]","[83, 13, 45, 6, 66, 108, 5, 124, 99, 35, 119, 10, 43, 107, 94, 82, 15, 86, 65, 81, 95, 16, 101, 80, 4, 97, 56, 72, 39, 0, 77, 102, 69, 37, 122, 91, 114, 74, 41, 89, 11, 113, 64, 32, 21, 61, 53, 90, 63, 24, 48, 71, 60, 93, 120, 59, 20, 54, 23, 123, 7, 76, 36, 46]","[0, 4, 5, 6, 11, 15, 16, 21, 23, 32, 35, 36, 37, 39, 41, 43, 45, 48, 54, 56, 59, 60, 61, 63, 64, 65, 71, 72, 80, 81, 83, 86, 91, 93, 94, 95, 97, 99, 101, 107, 114, 120]"
+90,"[25, 2, 118, 120, 0, 53, 21, 7, 55, 117, 37, 97, 72, 94, 122, 88, 29, 13, 24, 91, 19, 115, 27, 34, 4, 75, 112, 65, 116, 119, 31, 80, 42, 82, 79, 78, 111, 33, 93, 85, 41, 48, 49, 123, 95, 64, 108, 92, 32, 106, 12, 105, 38, 46, 124, 103, 77, 26, 30, 125, 8, 23, 16, 74]","[13, 28, 15, 70, 55, 76, 87, 24, 22, 119, 123, 20, 122, 92, 31, 35, 126, 98, 30, 14, 29, 68, 88, 115, 42, 41, 1, 57, 83, 8, 97, 54, 85, 21, 81, 113, 19, 109, 63, 37, 40, 51, 27, 104, 34, 3, 32, 79, 121, 18, 58, 59, 25, 0, 103, 16, 11, 6, 67, 84, 45, 73, 106, 5]","[0, 8, 13, 16, 19, 21, 24, 25, 27, 29, 30, 31, 32, 34, 37, 41, 42, 55, 79, 85, 88, 92, 97, 103, 106, 115, 119, 122, 123]"
+91,"[15, 24, 121, 26, 100, 32, 107, 19, 48, 2, 49, 4, 0, 104, 94, 101, 5, 82, 86, 14, 90, 40, 22, 55, 20, 71, 97, 125, 98, 16, 119, 85, 6, 41, 117, 61, 63, 58, 37, 73, 12, 120, 17, 50, 127, 38, 66, 45, 109, 80, 115, 84, 88, 29, 54, 76, 99, 89, 11, 79, 59, 75, 23, 42]","[59, 34, 95, 14, 104, 20, 121, 127, 36, 19, 50, 76, 49, 63, 65, 97, 116, 66, 94, 17, 93, 84, 120, 55, 3, 16, 100, 107, 82, 69, 33, 83, 109, 7, 105, 12, 41, 64, 71, 67, 37, 23, 91, 10, 26, 38, 62, 115, 24, 72, 112, 98, 40, 117, 35, 99, 22, 45, 101, 48, 15, 47, 8, 1]","[12, 14, 15, 16, 17, 19, 20, 22, 23, 24, 26, 37, 38, 40, 41, 45, 48, 49, 50, 55, 59, 63, 66, 71, 76, 82, 84, 94, 97, 98, 99, 100, 101, 104, 107, 109, 115, 117, 120, 121, 127]"
+92,"[8, 52, 23, 16, 2, 66, 123, 94, 4, 31, 24, 44, 28, 75, 113, 82, 17, 53, 98, 124, 117, 45, 99, 87, 6, 57, 102, 15, 108, 37, 0, 114, 120, 9, 126, 46, 71, 116, 25, 49, 65, 110, 12, 92, 50, 21, 88, 18, 26, 90, 11, 68, 77, 14, 51, 33, 104, 72, 109, 69, 40, 81, 61, 34]","[100, 1, 76, 125, 54, 82, 67, 45, 2, 127, 116, 123, 6, 52, 0, 41, 124, 27, 77, 58, 57, 72, 25, 104, 8, 75, 5, 34, 30, 9, 91, 51, 95, 15, 113, 71, 35, 79, 87, 73, 24, 83, 126, 110, 66, 90, 49, 117, 16, 81, 31, 50, 23, 37, 120, 43, 68, 106, 40, 46, 55, 26, 85, 109]","[0, 2, 6, 8, 9, 15, 16, 23, 24, 25, 26, 31, 34, 37, 40, 45, 46, 49, 50, 51, 52, 57, 66, 68, 71, 72, 75, 77, 81, 82, 87, 90, 104, 109, 110, 113, 116, 117, 120, 123, 124, 126]"
+93,"[18, 26, 30, 96, 37, 115, 48, 29, 31, 42, 24, 64, 47, 81, 8, 41, 59, 14, 25, 105, 110, 52, 70, 17, 10, 127, 54, 76, 124, 88, 82, 63, 67, 9, 100, 90, 92, 84, 0, 66, 51, 79, 68, 20, 97, 72, 62, 28, 60, 7, 33, 65, 95, 35, 5, 23, 119, 2, 106, 108, 102, 22, 123, 12]","[67, 110, 62, 63, 65, 7, 2, 119, 120, 98, 125, 86, 123, 93, 5, 91, 77, 37, 89, 108, 39, 69, 117, 3, 54, 97, 112, 101, 68, 25, 48, 87, 53, 116, 94, 51, 72, 103, 84, 109, 22, 99, 49, 27, 26, 4, 104, 118, 80, 96, 111, 126, 0, 81, 33, 113, 71, 31, 47, 32, 73, 107, 50, 15]","[0, 2, 5, 7, 22, 25, 26, 31, 33, 37, 47, 48, 51, 54, 62, 63, 65, 67, 68, 72, 81, 84, 96, 97, 108, 110, 119, 123]"
+94,"[17, 84, 49, 51, 65, 67, 123, 90, 20, 35, 44, 11, 79, 94, 62, 110, 25, 3, 80, 113, 5, 64, 7, 32, 16, 59, 19, 100, 4, 78, 0, 29, 2, 86, 24, 27, 102, 58, 47, 82, 45, 68, 42, 37, 112, 55, 34, 14, 96, 85, 39, 116, 66, 77, 56, 125, 74, 88, 63, 48, 87, 26, 106, 69]","[85, 25, 15, 44, 68, 0, 17, 3, 49, 96, 9, 113, 55, 67, 121, 110, 107, 91, 59, 5, 7, 57, 102, 92, 119, 48, 109, 56, 62, 123, 101, 53, 90, 118, 87, 122, 19, 14, 74, 72, 76, 26, 112, 43, 79, 60, 42, 29, 77, 51, 47, 31, 106, 86, 18, 39, 20, 64, 32, 78, 1, 84, 16, 65]","[0, 3, 5, 7, 14, 16, 17, 19, 20, 25, 26, 29, 32, 39, 42, 44, 47, 48, 49, 51, 55, 56, 59, 62, 64, 65, 67, 68, 74, 77, 78, 79, 84, 85, 86, 87, 90, 96, 102, 106, 110, 112, 113, 123]"
+95,"[123, 63, 33, 14, 0, 47, 6, 29, 70, 1, 85, 26, 19, 23, 112, 10, 51, 17, 104, 36, 82, 55, 27, 60, 81, 125, 64, 94, 5, 2, 22, 101, 15, 28, 41, 119, 62, 77, 67, 42, 120, 116, 127, 24, 48, 11, 97, 69, 39, 37, 89, 110, 103, 115, 3, 43, 49, 58, 32, 106, 122, 95, 53, 46]","[2, 80, 104, 109, 21, 7, 91, 123, 37, 78, 41, 35, 22, 33, 38, 4, 47, 34, 114, 108, 56, 81, 8, 39, 43, 124, 51, 0, 71, 113, 83, 3, 74, 87, 26, 59, 73, 10, 95, 52, 20, 17, 119, 99, 53, 58, 121, 107, 65, 111, 93, 69, 96, 49, 127, 29, 25, 18, 105, 50, 13, 100, 30, 40]","[0, 2, 3, 10, 17, 22, 26, 29, 33, 37, 39, 41, 43, 47, 49, 51, 53, 58, 69, 81, 95, 104, 119, 123, 127]"
+96,"[19, 119, 55, 69, 33, 44, 6, 88, 20, 62, 8, 41, 3, 71, 101, 26, 65, 22, 53, 77, 84, 100, 57, 106, 5, 47, 80, 16, 114, 116, 112, 32, 12, 79, 60, 102, 35, 70, 87, 117, 11, 83, 66, 10, 113, 120, 61, 0, 118, 90, 108, 98, 68, 39, 36, 54, 111, 31, 7, 28, 86, 92, 126, 23]","[50, 84, 88, 29, 43, 107, 40, 68, 72, 123, 4, 93, 57, 85, 30, 124, 78, 18, 69, 81, 13, 115, 103, 109, 38, 110, 19, 79, 113, 5, 3, 89, 2, 53, 24, 102, 25, 125, 15, 116, 86, 1, 64, 112, 94, 61, 96, 49, 91, 67, 32, 73, 90, 59, 83, 63, 34, 7, 121, 28, 42, 122, 71, 16]","[3, 5, 7, 16, 19, 28, 32, 53, 57, 61, 68, 69, 71, 79, 83, 84, 86, 88, 90, 102, 112, 113, 116]"
+97,"[32, 52, 10, 96, 43, 70, 103, 100, 55, 119, 28, 98, 41, 67, 54, 71, 66, 3, 15, 81, 9, 104, 97, 108, 22, 34, 42, 106, 1, 86, 61, 78, 21, 76, 4, 127, 40, 107, 5, 7, 112, 75, 74, 8, 57, 14, 6, 17, 90, 117, 44, 27, 20, 115, 83, 85, 63, 16, 51, 69, 60, 38, 53, 13]","[81, 79, 75, 58, 97, 77, 83, 90, 7, 54, 29, 37, 6, 118, 43, 107, 22, 96, 88, 15, 127, 3, 51, 10, 69, 80, 71, 17, 27, 101, 111, 95, 31, 0, 94, 1, 100, 82, 116, 52, 72, 41, 59, 113, 16, 34, 28, 18, 67, 122, 114, 86, 33, 9, 103, 73, 64, 119, 13, 87, 14, 76, 12, 106]","[1, 3, 6, 7, 9, 10, 13, 14, 15, 16, 17, 22, 27, 28, 34, 41, 43, 51, 52, 54, 67, 69, 71, 75, 76, 81, 83, 86, 90, 96, 97, 100, 103, 106, 107, 119, 127]"
+98,"[108, 111, 30, 21, 113, 120, 70, 0, 72, 78, 41, 82, 54, 6, 89, 20, 22, 96, 115, 87, 61, 52, 116, 64, 66, 34, 65, 74, 118, 7, 50, 60, 59, 24, 126, 5, 16, 18, 51, 71, 104, 124, 28, 69, 1, 33, 79, 48, 95, 42, 122, 25, 81, 105, 43, 67, 77, 100, 36, 31, 107, 56, 2, 37]","[34, 12, 76, 98, 82, 96, 102, 70, 75, 113, 116, 125, 106, 63, 122, 3, 10, 57, 49, 84, 6, 72, 11, 83, 118, 37, 52, 31, 20, 4, 123, 46, 62, 108, 38, 69, 54, 25, 95, 119, 126, 100, 45, 124, 103, 71, 51, 41, 115, 67, 50, 86, 53, 78, 88, 42, 21, 2, 87, 13, 28, 39, 1, 81]","[1, 2, 6, 20, 21, 25, 28, 31, 34, 37, 41, 42, 50, 51, 52, 54, 67, 69, 70, 71, 72, 78, 81, 82, 87, 95, 96, 100, 108, 113, 115, 116, 118, 122, 124, 126]"
+99,"[58, 108, 54, 110, 77, 65, 56, 98, 83, 99, 61, 12, 15, 116, 14, 67, 103, 63, 17, 39, 104, 51, 52, 5, 100, 49, 76, 48, 41, 25, 35, 111, 43, 81, 23, 47, 62, 127, 1, 88, 26, 69, 75, 85, 7, 24, 18, 112, 66, 71, 42, 73, 40, 107, 64, 87, 11, 9, 109, 45, 0, 31, 28, 29]","[46, 63, 9, 89, 111, 26, 101, 98, 84, 122, 53, 83, 42, 37, 4, 5, 79, 24, 92, 113, 57, 117, 126, 16, 121, 82, 114, 103, 70, 34, 115, 48, 6, 93, 15, 87, 107, 124, 66, 68, 97, 74, 60, 0, 32, 102, 10, 95, 105, 21, 120, 88, 2, 52, 33, 47, 86, 123, 55, 119, 96, 50, 14, 59]","[0, 5, 9, 14, 15, 24, 26, 42, 47, 48, 52, 63, 66, 83, 87, 88, 98, 103, 107, 111]"
@@ -0,0 +1,760 @@
+# Copyright (c) 2023 ETH Zurich.
+#                    All rights reserved.
+#
+# Use of this source code is governed by a BSD-style license that can be
+# found in the LICENSE file.
+#
+# The source code is adapted from the sorting source code written by
+# Nils Blach.
+#
+# main author: Robert Gerstenberger
+
+import os
+import logging
+import datetime
+import json
+import csv
+from typing import Dict, List, Callable, Union
+from graph_of_thoughts import controller, operations, prompter, parser
+
+from . import utils
+
+
+class SetIntersectionPrompter(prompter.Prompter):
+    """
+    SetIntersectionPrompter provides the generation of prompts specific to the
+    set intersection example for the language models.
+
+    Inherits from the Prompter class and implements its abstract methods.
+    """
+
+    intersection_prompt = """<Instruction> Find the intersection of two sets of numbers. Output only the set of numbers that are present in both sets, no additional text. </Instruction>
+
+<Examples>
+Input Set 1: [13, 16, 30, 6, 21, 7, 31, 15, 11, 1, 24, 10, 9, 3, 20, 8]
+Input Set 2: [25, 24, 10, 4, 27, 0, 14, 12, 8, 2, 29, 20, 17, 19, 26, 23]
+Output: [24, 10, 20, 8]
+
+Input Set 1: [26, 40, 42, 57, 15, 31, 5, 32, 11, 4, 24, 28, 51, 54, 12, 22, 33, 35, 7, 13, 2, 59, 8, 23, 43, 16, 29, 55, 25, 63, 21, 18]
+Input Set 2: [16, 60, 36, 48, 0, 15, 5, 19, 46, 24, 1, 6, 61, 10, 38, 53, 58, 9, 44, 14, 35, 63, 52, 20, 27, 17, 39, 47, 34, 56, 40, 59]
+Output: [40, 15, 5, 24, 35, 59, 16, 63]
+
+Input Set 1: [115, 61, 35, 103, 90, 117, 86, 44, 63, 45, 40, 30, 74, 33, 31, 1, 118, 48, 38, 0, 119, 51, 64, 78, 15, 121, 89, 101, 79, 69, 120, 29, 58, 50, 116, 11, 60, 12, 39, 95, 23, 2, 109, 84, 7, 43, 99, 98, 52, 70, 75, 102, 57, 19, 94, 36, 114, 88, 71, 56, 83, 6, 96, 107]
+Input Set 2: [13, 35, 20, 96, 34, 18, 47, 127, 126, 9, 21, 16, 77, 22, 111, 122, 85, 73, 42, 105, 123, 15, 33, 59, 67, 57, 104, 8, 30, 89, 76, 12, 65, 84, 32, 40, 7, 100, 108, 50, 14, 28, 24, 53, 90, 17, 91, 81, 124, 63, 5, 46, 125, 93, 49, 66, 117, 37, 115, 113, 2, 106, 41, 72]
+Output: [115, 35, 90, 117, 63, 40, 30, 33, 15, 89, 50, 12, 2, 84, 7, 57, 96]
+</Examples>
+
+Input Set 1: {set1}
+Input Set 2: {set2}"""
+
+    intersection_prompt_cot = """<Instruction> Find the intersection of two sets of numbers. You can generate any intermediate solutions, but the final output should be the set of numbers that are present in both sets, prefixed with "Output: ". </Instruction>
+
+<Approach>
+To find the intersection of the two sets follow these steps:
+1. Split the second input set of numbers into two to four subsets, each containing an equal number of elements from the original set (make sure they don't overlap).
+2. For each subset find the set of numbers that are present in the subset and the first input set.
+3. Merge the resulting sets into a single output set.
+</Approach>
+
+<Examples>
+Input Set 1: [13, 16, 30, 6, 21, 7, 31, 15, 11, 1, 24, 10, 9, 3, 20, 8]
+Input Set 2: [25, 24, 10, 4, 27, 0, 14, 12, 8, 2, 29, 20, 17, 19, 26, 23]
+Subsets of Input Set 2:
+[25, 24, 10, 4, 27, 0, 14, 12]
+[8, 2, 29, 20, 17, 19, 26, 23]
+Intersected Subsets with Input Set 1:
+[24, 10]
+[8, 20]
+Output: [24, 10, 8, 20]
+
+Input Set 1: [26, 40, 42, 57, 15, 31, 5, 32, 11, 4, 24, 28, 51, 54, 12, 22, 33, 35, 7, 13, 2, 59, 8, 23, 43, 16, 29, 55, 25, 63, 21, 18]
+Input Set 2: [16, 60, 36, 48, 0, 15, 5, 19, 46, 24, 1, 6, 61, 10, 38, 53, 58, 9, 44, 14, 35, 63, 52, 20, 27, 17, 39, 47, 34, 56, 40, 59]
+Subsets of Input Set 2:
+[16, 60, 36, 48, 0, 15, 5, 19, 46, 24, 1, 6, 61, 10, 38, 53]
+[58, 9, 44, 14, 35, 63, 52, 20, 27, 17, 39, 47, 34, 56, 40, 59]
+Intersected Subsets with Input Set 1:
+[16, 15, 5, 24]
+[35, 63, 40, 59]
+Output: [16, 15, 5, 24, 35, 63, 40, 59]
+
+Input Set 1: [115, 61, 35, 103, 90, 117, 86, 44, 63, 45, 40, 30, 74, 33, 31, 1, 118, 48, 38, 0, 119, 51, 64, 78, 15, 121, 89, 101, 79, 69, 120, 29, 58, 50, 116, 11, 60, 12, 39, 95, 23, 2, 109, 84, 7, 43, 99, 98, 52, 70, 75, 102, 57, 19, 94, 36, 114, 88, 71, 56, 83, 6, 96, 107]
+Input Set 2: [13, 35, 20, 96, 34, 18, 47, 127, 126, 9, 21, 16, 77, 22, 111, 122, 85, 73, 42, 105, 123, 15, 33, 59, 67, 57, 104, 8, 30, 89, 76, 12, 65, 84, 32, 40, 7, 100, 108, 50, 14, 28, 24, 53, 90, 17, 91, 81, 124, 63, 5, 46, 125, 93, 49, 66, 117, 37, 115, 113, 2, 106, 41, 72]
+Subsets of Input Set 2:
+[13, 35, 20, 96, 34, 18, 47, 127, 126, 9, 21, 16, 77, 22, 111, 122]
+[85, 73, 42, 105, 123, 15, 33, 59, 67, 57, 104, 8, 30, 89, 76, 12]
+[65, 84, 32, 40, 7, 100, 108, 50, 14, 28, 24, 53, 90, 17, 91, 81]
+[124, 63, 5, 46, 125, 93, 49, 66, 117, 37, 115, 113, 2, 106, 41, 72]
+Intersected Subsets with Input Set 1:
+[35, 96]
+[15, 33, 57, 30, 89, 12]
+[84, 40, 7, 50, 90]
+[63, 117, 115, 2]
+Output: [35, 96, 15, 33, 57, 30, 89, 12, 84, 40, 7, 50, 90, 63, 117, 115, 2]
+</Examples>
+
+Input Set 1: {set1}
+Input Set 2: {set2}"""
+
+    tot_improve_prompt = """<Instruction> The following three sets represent two sets and an intersection set of those two sets. The intersection set is not correct. Fix the intersection set so that it is correct.
+Make sure that the numbers in the intersection set can be found in both input sets. </Instruction>
+
+<Approach>
+To fix the incorrectly intersection set follow these steps:
+1. Check for each number in the incorrect intersection set, whether it can be found in both input sets. If not, remove that number from the intersection set.
+2. Iterate through the second input set and check whether each number is already in the incorrect intersection set and if not, check whether that number can also be found in the first input set. If so, add that number to the intersection set.
+</Approach>
+
+<Examples>
+Input Set 1: [13, 16, 30, 6, 21, 7, 31, 15, 11, 1, 24, 10, 9, 3, 20, 8]
+Input Set 2: [25, 24, 10, 4, 27, 0, 14, 12, 8, 2, 29, 20, 17, 19, 26, 23]
+Incorrect Intersection Set: [24, 20, 25]
+Reason: The incorrect intersection set contains the number 25, which is not present in the first input set and is missing the numbers 10 and 8.
+Output: [24, 10, 20, 8]
+
+Input Set 1: [26, 40, 42, 57, 15, 31, 5, 32, 11, 4, 24, 28, 51, 54, 12, 22, 33, 35, 7, 13, 2, 59, 8, 23, 43, 16, 29, 55, 25, 63, 21, 18]
+Input Set 2: [16, 60, 36, 48, 0, 15, 5, 19, 46, 24, 1, 6, 61, 10, 38, 53, 58, 9, 44, 14, 35, 63, 52, 20, 27, 17, 39, 47, 34, 56, 40, 59]
+Incorrect Intersection Set: [57, 16, 15, 24, 35, 10, 40]
+Reason: The incorrect intersection set contains the numbers 57, which is not present in the second input set, and 10, which is not present in the first input set, and is missing the numbers 5, 63 and 59.
+Output: [16, 15, 5, 24, 35, 63, 40, 59]
+
+Input Set 1: [115, 61, 35, 103, 90, 117, 86, 44, 63, 45, 40, 30, 74, 33, 31, 1, 118, 48, 38, 0, 119, 51, 64, 78, 15, 121, 89, 101, 79, 69, 120, 29, 58, 50, 116, 11, 60, 12, 39, 95, 23, 2, 109, 84, 7, 43, 99, 98, 52, 70, 75, 102, 57, 19, 94, 36, 114, 88, 71, 56, 83, 6, 96, 107]
+Input Set 2: [13, 35, 20, 96, 34, 18, 47, 127, 126, 9, 21, 16, 77, 22, 111, 122, 85, 73, 42, 105, 123, 15, 33, 59, 67, 57, 104, 8, 30, 89, 76, 12, 65, 84, 32, 40, 7, 100, 108, 50, 14, 28, 24, 53, 90, 17, 91, 81, 124, 63, 5, 46, 125, 93, 49, 66, 117, 37, 115, 113, 2, 106, 41, 72]
+Incorrect Intersection Set: [35, 96, 44, 15, 33, 57, 30, 50, 90, 119, 123, 63, 117, 115, 2]
+Reason: The incorrect intersection set contains the numbers 44 and 119, which are not present in the second input set, and 123, which is not present in the first input set, and is missing the numbers 89, 12, 84, 40 and 7.
+Output: [35, 96, 15, 33, 57, 30, 89, 12, 84, 40, 7, 50, 90, 63, 117, 115, 2]
+</Examples>
+
+Input Set 1: {set1}
+Input Set 2: {set2}
+Incorrect Intersection Set: {incorrect_intersection}
+"""
+
+    got_split_prompt = """<Instruction> Split the following list of 64 numbers into 4 lists of 16 numbers each, the first list should contain the first 16 numbers, the second list the second 16 numbers, the third list the third 16 numbers and the fourth list the fourth 16 numbers.
+Only output the 4 lists in the following format without any additional text or thoughts!:
+{{
+    "List 1": [13, 35, 20, 96, 34, 18, 47, ...],
+    "List 2": [127, 126, 9, 21, 16, 77, 22, ...],
+    "List 3": [111, 122, 85, 73, 42, 105, 123, ...],
+    "List 4": [15, 33, 59, 67, 57, 104, 8, ...]
+}} </Instruction>
+
+<Example>
+Input: [115, 61, 35, 103, 90, 117, 86, 44, 63, 45, 40, 30, 74, 33, 31, 1, 118, 48, 38, 0, 119, 51, 64, 78, 15, 121, 89, 101, 79, 69, 120, 29, 58, 50, 116, 11, 60, 12, 39, 95, 23, 2, 109, 84, 7, 43, 99, 98, 52, 70, 75, 102, 57, 19, 94, 36, 114, 88, 71, 56, 83, 6, 96, 107]
+Output:
+{{
+    "List 1": [115, 61, 35, 103, 90, 117, 86, 44, 63, 45, 40, 30, 74, 33, 31, 1],
+    "List 2": [118, 48, 38, 0, 119, 51, 64, 78, 15, 121, 89, 101, 79, 69, 120, 29],
+    "List 3": [58, 50, 116, 11, 60, 12, 39, 95, 23, 2, 109, 84, 7, 43, 99, 98],
+    "List 4": [52, 70, 75, 102, 57, 19, 94, 36, 114, 88, 71, 56, 83, 6, 96, 107]
+}}
+</Example>
+
+Input: {input}"""
+
+    got_merge_prompt = """<Instruction> Merge the following 2 lists of length {length1} each, into one list of length {length2} by appending the second list to the first list.
+Only output the final list without any additional text or thoughts! </Instruction>
+
+List 1: {input1}
+List 2: {input2}
+"""
+
+    def aggregation_prompt(self, state_dicts: List[Dict], **kwargs) -> str:
+        """
+        Generate an aggregation prompt for the language model.
+
+        :param state_dicts: The thought states that should be aggregated.
+        :type state_dicts: List[Dict]
+        :param kwargs: Additional keyword arguments.
+        :return: The aggregation prompt.
+        :rtype: str
+        :raise AssertionError: If not exactly two thought states are provided.
+        """
+
+        assert len(state_dicts) == 2, "Expected two states for aggregation prompt."
+        len_input1 = len(utils.string_to_list(state_dicts[0]["current"]))
+        len_input2 = len(utils.string_to_list(state_dicts[1]["current"]))
+        if len_input1 == len_input2:
+            length = len_input1
+        elif len_input1 + len_input2 - 32 <= 16:
+            length = 16
+        else:
+            length = 32
+
+        return self.got_merge_prompt.format(
+            input1=state_dicts[0]["current"],
+            input2=state_dicts[1]["current"],
+            length1=length,
+            length2=length * 2,
+        )
+
+    def generate_prompt(
+        self,
+        num_branches: int,
+        set1: str,
+        set2: str,
+        current: str,
+        method: str,
+        **kwargs,
+    ) -> str:
+        """
+        Generate a generate prompt for the language model.
+
+        :param num_branches: The number of responses the prompt should ask the LM to generate.
+        :type num_branches: int
+        :param set1: First input set.
+        :type set1: str
+        :param set2: Second input set.
+        :type set2: str
+        :param current: Intermediate solution.
+        :type current: str
+        :param method: Method for which the generate prompt is generated.
+        :type method: str
+        :param kwargs: Additional keyword arguments.
+        :return: The generate prompt.
+        :rtype: str
+        :raise AssertionError: If the requested number of branches is not one.
+        """
+
+        assert num_branches == 1, "Branching should be done via multiple requests."
+        if method.startswith("io"):
+            return self.intersection_prompt.format(set1=set1, set2=set2)
+        elif method.startswith("cot"):
+            return self.intersection_prompt_cot.format(set1=set1, set2=set2)
+        elif method.startswith("tot"):
+            if current is None or current == "":
+                return self.intersection_prompt.format(set1=set1, set2=set2)
+            return self.tot_improve_prompt.format(
+                set1=set1, set2=set2, incorrect_intersection=current
+            )
+        elif method.startswith("got"):
+            if kwargs["phase"] == 0:
+                return self.got_split_prompt.format(input=set2)
+
+            input_set = set2
+            if "subset" in kwargs and kwargs["subset"] != "":
+                input_set = kwargs["subset"]
+
+            return self.intersection_prompt.format(set1=set1, set2=input_set)
+
+    def improve_prompt(self, **kwargs) -> str:
+        """
+        Generate an improve prompt for the language model.
+
+        :param kwargs: Additional keyword arguments.
+        :return: The improve prompt.
+        :rtype: str
+        """
+        pass
+
+    def validation_prompt(self, **kwargs) -> str:
+        """
+        Generate a validation prompt for the language model.
+
+        :param kwargs: Additional keyword arguments.
+        :return: The validation prompt.
+        :rtype: str
+        """
+        pass
+
+    def score_prompt(self, state_dicts: List[Dict], **kwargs) -> str:
+        """
+        Generate a score prompt for the language model.
+
+        :param state_dicts: The thought states that should be scored,
+                            if more than one, they should be scored together.
+        :type state_dicts: List[Dict]
+        :param kwargs: Additional keyword arguments.
+        :return: The score prompt.
+        :rtype: str
+        """
+        pass
+
+
+class SetIntersectionParser(parser.Parser):
+    """
+    SetIntersectionParser provides the parsing of language model reponses
+    specific to the set intersection example.
+
+    Inherits from the Parser class and implements its abstract methods.
+    """
+
+    def __init__(self) -> None:
+        """
+        Inits the response cache.
+        """
+        self.cache = {}
+
+    def parse_aggregation_answer(
+        self, states: List[Dict], texts: List[str]
+    ) -> Union[Dict, List[Dict]]:
+        """
+        Parse the response from the language model for an aggregation prompt.
+
+        :param states: The thought states used to generate the prompt.
+        :type states: List[Dict]
+        :param texts: The responses to the prompt from the language model.
+        :type texts: List[str]
+        :return: The new thought states after parsing the respones from the language model.
+        :rtype: Union[Dict, List[Dict]]
+        :raise AssertionError: If not exactly two thought states are provided.
+        """
+
+        assert len(states) == 2, "Expected two states for aggregation answer."
+        new_states = []
+        for text in texts:
+            answers = text.strip().split("\n")
+            if any(["Output" in answer for answer in answers]):
+                # cut elements until last output is found
+                for answer in reversed(answers):
+                    if "Output" in answer:
+                        answers = answers[answers.index(answer) :]
+                        break
+
+            answers_stripped = [
+                answer for answer in answers if "[" in answer and "]" in answer
+            ]
+            if len(answers_stripped) == 0:
+                for answer in answers:
+                    answer = "[" + answer + "]"
+                    try:
+                        answer_converted = utils.string_to_list(answer)
+                        if len(answer_converted) > 0:
+                            answers_stripped.append(answer)
+                    except:
+                        pass
+            if len(answers_stripped) == 0:
+                logging.warning(
+                    f"Could not parse aggregation answer: {text}. Returning empty list."
+                )
+                answer = "[]"
+            else:
+                answer = [
+                    answer[answer.index("[") : answer.index("]") + 1]
+                    for answer in answers_stripped
+                ][0]
+            states = sorted(states, key=lambda x: x["part"])
+            merged_subsets = states[0]["subset"][:-1] + ", " + states[1]["subset"][1:]
+            new_state = states[0].copy()
+            new_state["current"] = answer
+            new_state["subset"] = merged_subsets
+            new_states.append(new_state)
+        return new_states
+
+    def parse_improve_answer(self, state: Dict, texts: List[str]) -> Dict:
+        """
+        Parse the response from the language model for an improve prompt.
+
+        :param state: The thought state used to generate the prompt.
+        :type state: Dict
+        :param texts: The responses to the prompt from the language model.
+        :type texts: List[str]
+        :return: The new thought state after parsing the responses from the language model.
+        :rtype: Dict
+        """
+        pass
+
+    def parse_generate_answer(self, state: Dict, texts: List[str]) -> List[Dict]:
+        """
+        Parse the response from the language model for a generate prompt.
+
+        :param state: The thought state used to generate the prompt.
+        :type state: Dict
+        :param texts: The responses to the prompt from the language model.
+        :type texts: List[str]
+        :return: The new thought states after parsing the respones from the language model.
+        :rtype: List[Dict]
+        """
+
+        new_states = []
+        for text in texts:
+            if state["method"].startswith("got") and state["phase"] == 0:
+                # We expect a json which contains the two lists named "List 1" and "List 2"
+                # cut everything until the opening bracket and everything after the closing bracket
+
+                try:
+                    text = text[text.index("{") : text.index("}") + 1]
+                    json_dict = json.loads(text)
+                    if len(json_dict.keys()) != 4:
+                        logging.warning(
+                            f"Expected 4 lists in json, but found {len(json_dict.keys())}."
+                        )
+                    for key, value in json_dict.items():
+                        if "List" not in key:
+                            logging.warning(
+                                f"Expected key to contain 'List', but found {key}."
+                            )
+                            continue
+                        if not isinstance(value, list):
+                            value = utils.string_to_list(value)
+                        new_state = state.copy()
+                        new_state["current"] = ""
+                        new_state["subset"] = str(value)
+                        new_state["phase"] = 1
+                        new_state["part"] = key
+                        new_states.append(new_state)
+                except Exception as e:
+                    logging.error(
+                        f"Could not parse step answer: {text}. Encountered exception: {e}"
+                    )
+            else:
+                answers = text.strip().split("\n")
+                answers = [
+                    answer for answer in answers if "[" in answer and "]" in answer
+                ]
+                if any(["Output" in answer for answer in answers]):
+                    # cut elements until last output is found
+                    for answer in reversed(answers):
+                        if "Output" in answer:
+                            answers = answers[answers.index(answer) :]
+                            break
+
+                answers = [
+                    answer[answer.index("[") : answer.index("]") + 1]
+                    for answer in answers
+                ]
+                if len(answers) == 0:
+                    logging.warning(
+                        f"Could not parse step answer: {text}. Returning empty list."
+                    )
+                    answer = "[]"
+                else:
+                    if len(answers) > 1:
+                        logging.warning(
+                            f"Multiple answers found for step answer: {text}. Using the first one."
+                        )
+                    answer = answers[0]
+
+                new_state = state.copy()
+                new_state["current"] = answer
+                new_state["phase"] = 2
+                new_states.append(new_state)
+        return new_states
+
+    def parse_validation_answer(self, state: Dict, texts: List[str]) -> bool:
+        """
+        Parse the response from the language model for a validation prompt.
+
+        :param state: The thought state used to generate the prompt.
+        :type state: Dict
+        :param texts: The responses to the prompt from the language model.
+        :type texts: List[str]
+        :return: Whether the thought state is valid or not.
+        :rtype: bool
+        """
+        pass
+
+    def parse_score_answer(self, states: List[Dict], texts: List[str]) -> List[float]:
+        """
+        Parse the response from the language model for a score prompt.
+
+        :param states: The thought states used to generate the prompt.
+        :type states: List[Dict]
+        :param texts: The responses to the prompt from the language model.
+        :type texts: List[str]
+        :return: The scores for the thought states.
+        :rtype: List[float]
+        """
+        pass
+
+
+def io() -> operations.GraphOfOperations:
+    """
+    Generates the Graph of Operations for the IO method.
+
+    :return: Graph of Operations
+    :rtype: GraphOfOperations
+    """
+    operations_graph = operations.GraphOfOperations()
+
+    operations_graph.append_operation(operations.Generate(1, 1))
+    operations_graph.append_operation(operations.Score(1, False, utils.num_errors))
+    operations_graph.append_operation(
+        operations.GroundTruth(utils.test_set_intersection)
+    )
+
+    return operations_graph
+
+
+def cot() -> operations.GraphOfOperations:
+    """
+    Generates the Graph of Operations for the CoT method.
+
+    :return: Graph of Operations
+    :rtype: GraphOfOperations
+    """
+    operations_graph = operations.GraphOfOperations()
+
+    operations_graph.append_operation(operations.Generate(1, 1))
+    operations_graph.append_operation(operations.Score(1, False, utils.num_errors))
+    operations_graph.append_operation(
+        operations.GroundTruth(utils.test_set_intersection)
+    )
+
+    return operations_graph
+
+
+def tot() -> operations.GraphOfOperations:
+    """
+    Generates the Graph of Operations for the ToT method.
+    ToT uses a wider tree, where on each level there are more branches.
+
+    :return: Graph of Operations
+    :rtype: GraphOfOperations
+    """
+    operations_graph = operations.GraphOfOperations()
+
+    operations_graph.append_operation(operations.Generate(1, 20))
+    operations_graph.append_operation(operations.Score(1, False, utils.num_errors))
+    op_1 = operations.KeepBestN(1, False)
+    operations_graph.append_operation(op_1)
+
+    for _ in range(3):
+        operations_graph.append_operation(operations.Generate(1, 20))
+        operations_graph.append_operation(operations.Score(1, False, utils.num_errors))
+        op_2 = operations.KeepBestN(1, False)
+        op_2.add_predecessor(op_1)
+        operations_graph.append_operation(op_2)
+        op_1 = op_2
+
+    operations_graph.append_operation(
+        operations.GroundTruth(utils.test_set_intersection)
+    )
+
+    return operations_graph
+
+
+def tot2() -> operations.GraphOfOperations:
+    """
+    Generates the Graph of Operations for the ToT2 method.
+    ToT2 uses a tree with more levels, but with fewer branches per level.
+
+    :return: Graph of Operations
+    :rtype: GraphOfOperations
+    """
+    operations_graph = operations.GraphOfOperations()
+
+    operations_graph.append_operation(operations.Generate(1, 10))
+    operations_graph.append_operation(operations.Score(1, False, utils.num_errors))
+    op_1 = operations.KeepBestN(1, False)
+    operations_graph.append_operation(op_1)
+
+    for _ in range(6):
+        operations_graph.append_operation(operations.Generate(1, 10))
+        operations_graph.append_operation(operations.Score(1, False, utils.num_errors))
+        op_2 = operations.KeepBestN(1, False)
+        op_2.add_predecessor(op_1)
+        operations_graph.append_operation(op_2)
+        op_1 = op_2
+
+    operations_graph.append_operation(
+        operations.GroundTruth(utils.test_set_intersection)
+    )
+
+    return operations_graph
+
+
+def got() -> operations.GraphOfOperations:
+    """
+    Generates the Graph of Operations for the GoT method.
+
+    :return: Graph of Operations
+    :rtype: GraphOfOperations
+    """
+    operations_graph = operations.GraphOfOperations()
+
+    plans = operations.Generate(1, 1)
+    operations_graph.append_operation(plans)  # generate the sublists
+    solved_subsets = []
+    for i in range(1, 5):
+        list_id = f"List {i}"
+        sub_list = operations.Selector(
+            lambda thoughts, list_id=list_id: [
+                thought for thought in thoughts if thought.state["part"] == list_id
+            ]
+        )
+        sub_list.add_predecessor(plans)
+        operations_graph.add_operation(sub_list)
+        intersected_subset = operations.Generate(1, 5)
+        intersected_subset.add_predecessor(sub_list)
+        operations_graph.add_operation(intersected_subset)
+        score_sub_list = operations.Score(1, False, utils.num_errors)
+        score_sub_list.add_predecessor(intersected_subset)
+        operations_graph.add_operation(score_sub_list)
+        keep_best_sub_list = operations.KeepBestN(1, False)
+        keep_best_sub_list.add_predecessor(score_sub_list)
+        operations_graph.add_operation(keep_best_sub_list)
+
+        solved_subsets.append(keep_best_sub_list)
+
+    aggregate_1 = operations.Aggregate(10)
+    aggregate_1.add_predecessor(solved_subsets[0])
+    aggregate_1.add_predecessor(solved_subsets[1])
+    operations_graph.add_operation(aggregate_1)
+    score_aggregate_1 = operations.Score(1, False, utils.num_errors)
+    score_aggregate_1.add_predecessor(aggregate_1)
+    operations_graph.add_operation(score_aggregate_1)
+    keep_best_aggregate_1 = operations.KeepBestN(1, False)
+    keep_best_aggregate_1.add_predecessor(score_aggregate_1)
+    operations_graph.add_operation(keep_best_aggregate_1)
+
+    aggregate_2 = operations.Aggregate(10)
+    aggregate_2.add_predecessor(solved_subsets[2])
+    aggregate_2.add_predecessor(solved_subsets[3])
+    operations_graph.add_operation(aggregate_2)
+    score_aggregate_2 = operations.Score(1, False, utils.num_errors)
+    score_aggregate_2.add_predecessor(aggregate_2)
+    operations_graph.add_operation(score_aggregate_2)
+    keep_best_aggregate_2 = operations.KeepBestN(1, False)
+    keep_best_aggregate_2.add_predecessor(score_aggregate_2)
+    operations_graph.add_operation(keep_best_aggregate_2)
+
+    final_aggregate = operations.Aggregate(10)
+    operations_graph.append_operation(final_aggregate)
+    operations_graph.append_operation(operations.Score(1, False, utils.num_errors))
+    keep_best_aggregate_final = operations.KeepBestN(1, False)
+    operations_graph.append_operation(keep_best_aggregate_final)
+
+    operations_graph.append_operation(
+        operations.GroundTruth(utils.test_set_intersection)
+    )
+
+    return operations_graph
+
+
+def run(
+    data_ids: List[int],
+    methods: List[Callable[[], operations.GraphOfOperations]],
+    budget: float,
+    lm_name: str,
+) -> float:
+    """
+    Controller function that executes each specified method for each specified
+    sample while the budget is not exhausted.
+
+    :param data_ids: Indices of the sample to be run.
+    :type data_ids: List[int]
+    :param methods: List of functions to generate Graphs of Operations.
+    :type methods: Each function generates a Graph of Operation.
+    :param budget: Language model budget for the execution in dollars.
+    :type budget: float
+    :param lm_name: Name of the language model to be used.
+    :type lm_name: str
+    :return: Spent budget in dollars.
+    :rtype: float
+    """
+
+    orig_budget = budget
+    path = os.path.join(os.path.dirname(__file__), "set_intersection_064.csv")
+    data = []
+    with open(path, "r") as f:
+        reader = csv.reader(f)
+        next(reader)
+        for row in reader:
+            data.append([int(row[0]), row[1], row[2], row[3]])
+
+    if data_ids is None or len(data_ids) == 0:
+        data_ids = list(range(len(data)))
+    selected_data = [data[i] for i in data_ids]
+
+    if not os.path.exists(os.path.join(os.path.dirname(__file__), "results")):
+        os.makedirs(os.path.join(os.path.dirname(__file__), "results"))
+    timestamp = datetime.datetime.now().strftime("%Y-%m-%d_%H-%M-%S")
+    extra_info = f"{lm_name}_{'-'.join([method.__name__ for method in methods])}"
+    folder_name = f"results/{extra_info}_{timestamp}"
+    os.makedirs(os.path.join(os.path.dirname(__file__), folder_name))
+
+    config = {
+        "data": selected_data,
+        "methods": [method.__name__ for method in methods],
+        "lm": lm_name,
+        "budget": budget,
+    }
+    with open(
+        os.path.join(os.path.dirname(__file__), folder_name, "config.json"), "w"
+    ) as f:
+        json.dump(config, f)
+
+    logging.basicConfig(
+        filename=f"{folder_name}/log.log",
+        filemode="w",
+        format="%(name)s - %(levelname)s - %(message)s",
+        level=logging.DEBUG,
+    )
+
+    for method in methods:
+        # create a results directory for the method
+        os.makedirs(
+            os.path.join(os.path.dirname(__file__), folder_name, method.__name__)
+        )
+
+    for data in selected_data:
+        logging.info(f"Running data {data[0]}: {data[1]} {data[2]}")
+        if budget <= 0.0:
+            logging.error(
+                f"Budget has been depleted, stopping. Data {data[0]} has not been run."
+            )
+            break
+        for method in methods:
+            logging.info(f"Running method {method.__name__}")
+            logging.info(f"Budget left: {budget}")
+            if budget <= 0.0:
+                logging.error(
+                    f"Budget has been depleted, stopping. Method {method.__name__} has not been run."
+                )
+                break
+            lm = controller.ChatGPT(
+                "../../graph_of_thoughts/controller/config.json",
+                model_name=lm_name,
+                cache=True,
+            )
+            operations_graph = method()
+            executor = controller.Controller(
+                lm,
+                operations_graph,
+                SetIntersectionPrompter(),
+                SetIntersectionParser(),
+                {
+                    "set1": data[1],
+                    "set2": data[2],
+                    "result": data[3],
+                    "current": "",
+                    "phase": 0,
+                    "method": method.__name__,
+                },
+            )
+            try:
+                executor.run()
+            except Exception as e:
+                logging.error(f"Exception: {e}")
+            path = os.path.join(
+                os.path.dirname(__file__),
+                folder_name,
+                method.__name__,
+                f"{data[0]}.json",
+            )
+            executor.output_graph(path)
+            budget -= lm.cost
+
+    return orig_budget - budget
+
+
+if __name__ == "__main__":
+    """
+    Input(x)  : a list of 64 numbers between 0 and 127 (inclusive)
+    Input(y)  : a list of 64 numbers between 0 and 127 (inclusive)
+    Output(z) : a list of the intersection between x and y
+    Correct   : z = intersection(x, y)
+    Input Example:
+        [26, 40, 42, 57, 15, 31, 5, 32, 11, 4, 24, 28, 51, 54, 12, 22, 33, 35, 7, 13, 2, 59, 8, 23, 43, 16, 29, 55, 25, 63, 21, 18]
+        [16, 60, 36, 48, 0, 15, 5, 19, 46, 24, 1, 6, 61, 10, 38, 53, 58, 9, 44, 14, 35, 63, 52, 20, 27, 17, 39, 47, 34, 56, 40, 59]
+    Output Example:
+        [40, 15, 5, 24, 35, 59, 16, 63]
+    """
+
+    budget = 15
+    samples = [item for item in range(0, 100)]
+    approaches = [io, cot, tot, tot2, got]
+
+    spent = run(samples, approaches, budget, "chatgpt")
+
+    logging.info(f"Spent {spent} out of {budget} budget.")
@@ -0,0 +1,101 @@
+ID,SET1,SET2,INTERSECTION
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@@ -0,0 +1,812 @@
+# Copyright (c) 2023 ETH Zurich.
+#                    All rights reserved.
+#
+# Use of this source code is governed by a BSD-style license that can be
+# found in the LICENSE file.
+#
+# The source code is adapted from the sorting source code written by
+# Nils Blach.
+#
+# main author: Robert Gerstenberger
+
+import os
+import logging
+import datetime
+import json
+import csv
+from typing import Dict, List, Callable, Union
+from graph_of_thoughts import controller, operations, prompter, parser
+
+from . import utils
+
+
+class SetIntersectionPrompter(prompter.Prompter):
+    """
+    SetIntersectionPrompter provides the generation of prompts specific to the
+    set intersection example for the language models.
+
+    Inherits from the Prompter class and implements its abstract methods.
+    """
+
+    intersection_prompt = """<Instruction> Find the intersection of two sets of numbers. Output only the set of numbers that are present in both sets, no additional text. </Instruction>
+
+<Examples>
+Input Set 1: [13, 16, 30, 6, 21, 7, 31, 15, 11, 1, 24, 10, 9, 3, 20, 8]
+Input Set 2: [25, 24, 10, 4, 27, 0, 14, 12, 8, 2, 29, 20, 17, 19, 26, 23]
+Output: [24, 10, 20, 8]
+
+Input Set 1: [26, 40, 42, 57, 15, 31, 5, 32, 11, 4, 24, 28, 51, 54, 12, 22, 33, 35, 7, 13, 2, 59, 8, 23, 43, 16, 29, 55, 25, 63, 21, 18]
+Input Set 2: [16, 60, 36, 48, 0, 15, 5, 19, 46, 24, 1, 6, 61, 10, 38, 53, 58, 9, 44, 14, 35, 63, 52, 20, 27, 17, 39, 47, 34, 56, 40, 59]
+Output: [40, 15, 5, 24, 35, 59, 16, 63]
+
+Input Set 1: [115, 61, 35, 103, 90, 117, 86, 44, 63, 45, 40, 30, 74, 33, 31, 1, 118, 48, 38, 0, 119, 51, 64, 78, 15, 121, 89, 101, 79, 69, 120, 29, 58, 50, 116, 11, 60, 12, 39, 95, 23, 2, 109, 84, 7, 43, 99, 98, 52, 70, 75, 102, 57, 19, 94, 36, 114, 88, 71, 56, 83, 6, 96, 107]
+Input Set 2: [13, 35, 20, 96, 34, 18, 47, 127, 126, 9, 21, 16, 77, 22, 111, 122, 85, 73, 42, 105, 123, 15, 33, 59, 67, 57, 104, 8, 30, 89, 76, 12, 65, 84, 32, 40, 7, 100, 108, 50, 14, 28, 24, 53, 90, 17, 91, 81, 124, 63, 5, 46, 125, 93, 49, 66, 117, 37, 115, 113, 2, 106, 41, 72]
+Output: [115, 35, 90, 117, 63, 40, 30, 33, 15, 89, 50, 12, 2, 84, 7, 57, 96]
+</Examples>
+
+Input Set 1: {set1}
+Input Set 2: {set2}"""
+
+    intersection_prompt_cot = """<Instruction> Find the intersection of two sets of numbers. You can generate any intermediate solutions, but the final output should be the set of numbers that are present in both sets, prefixed with "Output: ". </Instruction>
+
+<Approach>
+To find the intersection of the two sets follow these steps:
+1. Split the second input set of numbers into two to four subsets, each containing an equal number of elements from the original set (make sure they don't overlap).
+2. For each subset find the set of numbers that are present in the subset and the first input set.
+3. Merge the resulting sets into a single output set.
+</Approach>
+
+<Examples>
+Input Set 1: [13, 16, 30, 6, 21, 7, 31, 15, 11, 1, 24, 10, 9, 3, 20, 8]
+Input Set 2: [25, 24, 10, 4, 27, 0, 14, 12, 8, 2, 29, 20, 17, 19, 26, 23]
+Subsets of Input Set 2:
+[25, 24, 10, 4, 27, 0, 14, 12]
+[8, 2, 29, 20, 17, 19, 26, 23]
+Intersected Subsets with Input Set 1:
+[24, 10]
+[8, 20]
+Output: [24, 10, 8, 20]
+
+Input Set 1: [26, 40, 42, 57, 15, 31, 5, 32, 11, 4, 24, 28, 51, 54, 12, 22, 33, 35, 7, 13, 2, 59, 8, 23, 43, 16, 29, 55, 25, 63, 21, 18]
+Input Set 2: [16, 60, 36, 48, 0, 15, 5, 19, 46, 24, 1, 6, 61, 10, 38, 53, 58, 9, 44, 14, 35, 63, 52, 20, 27, 17, 39, 47, 34, 56, 40, 59]
+Subsets of Input Set 2:
+[16, 60, 36, 48, 0, 15, 5, 19, 46, 24, 1, 6, 61, 10, 38, 53]
+[58, 9, 44, 14, 35, 63, 52, 20, 27, 17, 39, 47, 34, 56, 40, 59]
+Intersected Subsets with Input Set 1:
+[16, 15, 5, 24]
+[35, 63, 40, 59]
+Output: [16, 15, 5, 24, 35, 63, 40, 59]
+
+Input Set 1: [115, 61, 35, 103, 90, 117, 86, 44, 63, 45, 40, 30, 74, 33, 31, 1, 118, 48, 38, 0, 119, 51, 64, 78, 15, 121, 89, 101, 79, 69, 120, 29, 58, 50, 116, 11, 60, 12, 39, 95, 23, 2, 109, 84, 7, 43, 99, 98, 52, 70, 75, 102, 57, 19, 94, 36, 114, 88, 71, 56, 83, 6, 96, 107]
+Input Set 2: [13, 35, 20, 96, 34, 18, 47, 127, 126, 9, 21, 16, 77, 22, 111, 122, 85, 73, 42, 105, 123, 15, 33, 59, 67, 57, 104, 8, 30, 89, 76, 12, 65, 84, 32, 40, 7, 100, 108, 50, 14, 28, 24, 53, 90, 17, 91, 81, 124, 63, 5, 46, 125, 93, 49, 66, 117, 37, 115, 113, 2, 106, 41, 72]
+Subsets of Input Set 2:
+[13, 35, 20, 96, 34, 18, 47, 127, 126, 9, 21, 16, 77, 22, 111, 122]
+[85, 73, 42, 105, 123, 15, 33, 59, 67, 57, 104, 8, 30, 89, 76, 12]
+[65, 84, 32, 40, 7, 100, 108, 50, 14, 28, 24, 53, 90, 17, 91, 81]
+[124, 63, 5, 46, 125, 93, 49, 66, 117, 37, 115, 113, 2, 106, 41, 72]
+Intersected Subsets with Input Set 1:
+[35, 96]
+[15, 33, 57, 30, 89, 12]
+[84, 40, 7, 50, 90]
+[63, 117, 115, 2]
+Output: [35, 96, 15, 33, 57, 30, 89, 12, 84, 40, 7, 50, 90, 63, 117, 115, 2]
+</Examples>
+
+Input Set 1: {set1}
+Input Set 2: {set2}"""
+
+    tot_improve_prompt = """<Instruction> The following three sets represent two sets and an intersection set of those two sets. The intersection set is not correct. Fix the intersection set so that it is correct.
+Make sure that the numbers in the intersection set can be found in both input sets. </Instruction>
+
+<Approach>
+To fix the incorrectly intersection set follow these steps:
+1. Check for each number in the incorrect intersection set, whether it can be found in both input sets. If not, remove that number from the intersection set.
+2. Iterate through the second input set and check whether each number is already in the incorrect intersection set and if not, check whether that number can also be found in the first input set. If so, add that number to the intersection set.
+</Approach>
+
+<Examples>
+Input Set 1: [13, 16, 30, 6, 21, 7, 31, 15, 11, 1, 24, 10, 9, 3, 20, 8]
+Input Set 2: [25, 24, 10, 4, 27, 0, 14, 12, 8, 2, 29, 20, 17, 19, 26, 23]
+Incorrect Intersection Set: [24, 20, 25]
+Reason: The incorrect intersection set contains the number 25, which is not present in the first input set and is missing the numbers 10 and 8.
+Output: [24, 10, 20, 8]
+
+Input Set 1: [26, 40, 42, 57, 15, 31, 5, 32, 11, 4, 24, 28, 51, 54, 12, 22, 33, 35, 7, 13, 2, 59, 8, 23, 43, 16, 29, 55, 25, 63, 21, 18]
+Input Set 2: [16, 60, 36, 48, 0, 15, 5, 19, 46, 24, 1, 6, 61, 10, 38, 53, 58, 9, 44, 14, 35, 63, 52, 20, 27, 17, 39, 47, 34, 56, 40, 59]
+Incorrect Intersection Set: [57, 16, 15, 24, 35, 10, 40]
+Reason: The incorrect intersection set contains the numbers 57, which is not present in the second input set, and 10, which is not present in the first input set, and is missing the numbers 5, 63 and 59.
+Output: [16, 15, 5, 24, 35, 63, 40, 59]
+
+Input Set 1: [115, 61, 35, 103, 90, 117, 86, 44, 63, 45, 40, 30, 74, 33, 31, 1, 118, 48, 38, 0, 119, 51, 64, 78, 15, 121, 89, 101, 79, 69, 120, 29, 58, 50, 116, 11, 60, 12, 39, 95, 23, 2, 109, 84, 7, 43, 99, 98, 52, 70, 75, 102, 57, 19, 94, 36, 114, 88, 71, 56, 83, 6, 96, 107]
+Input Set 2: [13, 35, 20, 96, 34, 18, 47, 127, 126, 9, 21, 16, 77, 22, 111, 122, 85, 73, 42, 105, 123, 15, 33, 59, 67, 57, 104, 8, 30, 89, 76, 12, 65, 84, 32, 40, 7, 100, 108, 50, 14, 28, 24, 53, 90, 17, 91, 81, 124, 63, 5, 46, 125, 93, 49, 66, 117, 37, 115, 113, 2, 106, 41, 72]
+Incorrect Intersection Set: [35, 96, 44, 15, 33, 57, 30, 50, 90, 119, 123, 63, 117, 115, 2]
+Reason: The incorrect intersection set contains the numbers 44 and 119, which are not present in the second input set, and 123, which is not present in the first input set, and is missing the numbers 89, 12, 84, 40 and 7.
+Output: [35, 96, 15, 33, 57, 30, 89, 12, 84, 40, 7, 50, 90, 63, 117, 115, 2]
+</Examples>
+
+Input Set 1: {set1}
+Input Set 2: {set2}
+Incorrect Intersection Set: {incorrect_intersection}
+"""
+
+    got_split_prompt = """<Instruction> Split the following list of 128 numbers into 8 lists of 16 numbers each, the first list should contain the first 16 numbers, the second list the second 16 numbers, the third list the third 16 numbers and the fourth list the fourth 16 numbers, the fifth list the fifth 16 numbers and so on.
+Only output the 8 lists in the following format without any additional text or thoughts!:
+{{
+    "List 1": [13, 35, 20, 96, 34, 18, 47, ...],
+    "List 2": [127, 126, 9, 21, 16, 77, 22, ...],
+    "List 3": [111, 122, 85, 73, 42, 105, 123, ...],
+    "List 4": [15, 33, 59, 67, 57, 104, 8, ...],
+    "List 5": [30, 89, 76, 12, 65, 84, 32, ...],
+    "List 6": [40, 7, 100, 108, 50, 14, 28, ...],
+    "List 7": [24, 53, 90, 17, 91, 81, 124, ...],
+    "List 8": [63, 5, 46, 125, 93, 49, 66, ...]
+}} </Instruction>
+
+<Example>
+Input: [124, 100, 176, 65, 28, 214, 201, 67, 127, 40, 193, 26, 212, 196, 12, 205, 39, 162, 190, 152, 186, 182, 125, 229, 114, 70, 189, 242, 155, 32, 47, 113, 99, 177, 57, 103, 156, 107, 226, 188, 31, 25, 49, 171, 17, 64, 254, 217, 35, 22, 248, 88, 251, 219, 84, 82, 167, 14, 116, 92, 105, 148, 119, 58, 13, 160, 81, 120, 74, 94, 173, 38, 101, 104, 91, 135, 208, 118, 136, 87, 75, 41, 197, 76, 249, 240, 86, 246, 231, 44, 29, 141, 241, 227, 239, 142, 222, 115, 129, 255, 216, 153, 0, 110, 36, 130, 6, 102, 209, 37, 143, 30, 51, 146, 71, 27, 181, 183, 2, 122, 77, 184, 56, 225, 108, 83, 106, 15]
+Output:
+{{
+    "List 1": [124, 100, 176, 65, 28, 214, 201, 67, 127, 40, 193, 26, 212, 196, 12, 205],
+    "List 2": [39, 162, 190, 152, 186, 182, 125, 229, 114, 70, 189, 242, 155, 32, 47, 113],
+    "List 3": [99, 177, 57, 103, 156, 107, 226, 188, 31, 25, 49, 171, 17, 64, 254, 217],
+    "List 4": [35, 22, 248, 88, 251, 219, 84, 82, 167, 14, 116, 92, 105, 148, 119, 58],
+    "List 5": [13, 160, 81, 120, 74, 94, 173, 38, 101, 104, 91, 135, 208, 118, 136, 87],
+    "List 6": [75, 41, 197, 76, 249, 240, 86, 246, 231, 44, 29, 141, 241, 227, 239, 142],
+    "List 7": [222, 115, 129, 255, 216, 153, 0, 110, 36, 130, 6, 102, 209, 37, 143, 30],
+    "List 8": [51, 146, 71, 27, 181, 183, 2, 122, 77, 184, 56, 225, 108, 83, 106, 15]
+}}
+</Example>
+
+Input: {input}"""
+
+    got_merge_prompt = """<Instruction> Merge the following 2 lists of length {length1} each, into one list of length {length2} by appending the second list to the first list.
+Only output the final list without any additional text or thoughts! </Instruction>
+
+List 1: {input1}
+List 2: {input2}
+"""
+
+    def aggregation_prompt(self, state_dicts: List[Dict], **kwargs) -> str:
+        """
+        Generate an aggregation prompt for the language model.
+
+        :param state_dicts: The thought states that should be aggregated.
+        :type state_dicts: List[Dict]
+        :param kwargs: Additional keyword arguments.
+        :return: The aggregation prompt.
+        :rtype: str
+        :raise AssertionError: If not exactly two thought states are provided.
+        """
+        assert len(state_dicts) == 2, "Expected two states for aggregation prompt."
+        len_input1 = len(utils.string_to_list(state_dicts[0]["current"]))
+        len_input2 = len(utils.string_to_list(state_dicts[1]["current"]))
+        if len_input1 == len_input2:
+            length = len_input1
+        elif len_input1 + len_input2 - 32 <= 16:
+            length = 16
+        elif len_input1 + len_input2 - 64 <= 32:
+            length = 32
+        else:
+            length = 64
+
+        return self.got_merge_prompt.format(
+            input1=state_dicts[0]["current"],
+            input2=state_dicts[1]["current"],
+            length1=length,
+            length2=length * 2,
+        )
+
+    def generate_prompt(
+        self,
+        num_branches: int,
+        set1: str,
+        set2: str,
+        current: str,
+        method: str,
+        **kwargs,
+    ) -> str:
+        """
+        Generate a generate prompt for the language model.
+
+        :param num_branches: The number of responses the prompt should ask the LM to generate.
+        :type num_branches: int
+        :param set1: First input set.
+        :type set1: str
+        :param set2: Second input set.
+        :type set2: str
+        :param current: Intermediate solution.
+        :type current: str
+        :param method: Method for which the generate prompt is generated.
+        :type method: str
+        :param kwargs: Additional keyword arguments.
+        :return: The generate prompt.
+        :rtype: str
+        :raise AssertionError: If the requested number of branches is not one.
+        """
+
+        assert num_branches == 1, "Branching should be done via multiple requests."
+        if method.startswith("io"):
+            return self.intersection_prompt.format(set1=set1, set2=set2)
+        elif method.startswith("cot"):
+            return self.intersection_prompt_cot.format(set1=set1, set2=set2)
+        elif method.startswith("tot"):
+            if current is None or current == "":
+                return self.intersection_prompt.format(set1=set1, set2=set2)
+            return self.tot_improve_prompt.format(
+                set1=set1, set2=set2, incorrect_intersection=current
+            )
+        elif method.startswith("got"):
+            if kwargs["phase"] == 0:
+                return self.got_split_prompt.format(input=set2)
+
+            input_set = set2
+            if "subset" in kwargs and kwargs["subset"] != "":
+                input_set = kwargs["subset"]
+
+            return self.intersection_prompt.format(set1=set1, set2=input_set)
+
+    def improve_prompt(self, **kwargs) -> str:
+        """
+        Generate an improve prompt for the language model.
+
+        :param kwargs: Additional keyword arguments.
+        :return: The improve prompt.
+        :rtype: str
+        """
+        pass
+
+    def validation_prompt(self, **kwargs) -> str:
+        """
+        Generate a validation prompt for the language model.
+
+        :param kwargs: Additional keyword arguments.
+        :return: The validation prompt.
+        :rtype: str
+        """
+        pass
+
+    def score_prompt(self, state_dicts: List[Dict], **kwargs) -> str:
+        """
+        Generate a score prompt for the language model.
+
+        :param state_dicts: The thought states that should be scored,
+                            if more than one, they should be scored together.
+        :type state_dicts: List[Dict]
+        :param kwargs: Additional keyword arguments.
+        :return: The score prompt.
+        :rtype: str
+        """
+        pass
+
+
+class SetIntersectionParser(parser.Parser):
+    """
+    SetIntersectionParser provides the parsing of language model reponses
+    specific to the set intersection example.
+
+    Inherits from the Parser class and implements its abstract methods.
+    """
+
+    def __init__(self) -> None:
+        """
+        Inits the response cache.
+        """
+        self.cache = {}
+
+    def parse_aggregation_answer(
+        self, states: List[Dict], texts: List[str]
+    ) -> Union[Dict, List[Dict]]:
+        """
+        Parse the response from the language model for an aggregation prompt.
+
+        :param states: The thought states used to generate the prompt.
+        :type states: List[Dict]
+        :param texts: The responses to the prompt from the language model.
+        :type texts: List[str]
+        :return: The new thought states after parsing the respones from the language model.
+        :rtype: Union[Dict, List[Dict]]
+        :raise AssertionError: If not exactly two thought states are provided.
+        """
+
+        assert len(states) == 2, "Expected two states for aggregation answer."
+        new_states = []
+        for text in texts:
+            answers = text.strip().split("\n")
+            if any(["Output" in answer for answer in answers]):
+                # cut elements until last output is found
+                for answer in reversed(answers):
+                    if "Output" in answer:
+                        answers = answers[answers.index(answer) :]
+                        break
+
+            answers_stripped = [
+                answer for answer in answers if "[" in answer and "]" in answer
+            ]
+            if len(answers_stripped) == 0:
+                for answer in answers:
+                    answer = "[" + answer + "]"
+                    try:
+                        answer_converted = utils.string_to_list(answer)
+                        if len(answer_converted) > 0:
+                            answers_stripped.append(answer)
+                    except:
+                        pass
+            if len(answers_stripped) == 0:
+                logging.warning(
+                    f"Could not parse aggregation answer: {text}. Returning empty list."
+                )
+                answer = "[]"
+            else:
+                answer = [
+                    answer[answer.index("[") : answer.index("]") + 1]
+                    for answer in answers_stripped
+                ][0]
+            states = sorted(states, key=lambda x: x["part"])
+            merged_subsets = states[0]["subset"][:-1] + ", " + states[1]["subset"][1:]
+            new_state = states[0].copy()
+            new_state["current"] = answer
+            new_state["subset"] = merged_subsets
+            new_states.append(new_state)
+        return new_states
+
+    def parse_improve_answer(self, state: Dict, texts: List[str]) -> Dict:
+        """
+        Parse the response from the language model for an improve prompt.
+
+        :param state: The thought state used to generate the prompt.
+        :type state: Dict
+        :param texts: The responses to the prompt from the language model.
+        :type texts: List[str]
+        :return: The new thought state after parsing the responses from the language model.
+        :rtype: Dict
+        """
+        pass
+
+    def parse_generate_answer(self, state: Dict, texts: List[str]) -> List[Dict]:
+        """
+        Parse the response from the language model for a generate prompt.
+
+        :param state: The thought state used to generate the prompt.
+        :type state: Dict
+        :param texts: The responses to the prompt from the language model.
+        :type texts: List[str]
+        :return: The new thought states after parsing the respones from the language model.
+        :rtype: List[Dict]
+        """
+        new_states = []
+        for text in texts:
+            if state["method"].startswith("got") and state["phase"] == 0:
+                # We expect a json which contains the two lists named "List 1" and "List 2"
+                # cut everything until the opening bracket and everything after the closing bracket
+
+                try:
+                    text = text[text.index("{") : text.index("}") + 1]
+                    json_dict = json.loads(text)
+                    if len(json_dict.keys()) != 8:
+                        logging.warning(
+                            f"Expected 8 lists in json, but found {len(json_dict.keys())}."
+                        )
+                    for key, value in json_dict.items():
+                        if "List" not in key:
+                            logging.warning(
+                                f"Expected key to contain 'List', but found {key}."
+                            )
+                            continue
+                        if not isinstance(value, list):
+                            value = utils.string_to_list(value)
+                        new_state = state.copy()
+                        new_state["current"] = ""
+                        new_state["subset"] = str(value)
+                        new_state["phase"] = 1
+                        new_state["part"] = key
+                        new_states.append(new_state)
+                except Exception as e:
+                    logging.error(
+                        f"Could not parse step answer: {text}. Encountered exception: {e}"
+                    )
+            else:
+                answers = text.strip().split("\n")
+                answers = [
+                    answer for answer in answers if "[" in answer and "]" in answer
+                ]
+                if any(["Output" in answer for answer in answers]):
+                    # cut elements until last output is found
+                    for answer in reversed(answers):
+                        if "Output" in answer:
+                            answers = answers[answers.index(answer) :]
+                            break
+
+                answers = [
+                    answer[answer.index("[") : answer.index("]") + 1]
+                    for answer in answers
+                ]
+                if len(answers) == 0:
+                    logging.warning(
+                        f"Could not parse step answer: {text}. Returning empty list."
+                    )
+                    answer = "[]"
+                else:
+                    if len(answers) > 1:
+                        logging.warning(
+                            f"Multiple answers found for step answer: {text}. Using the first one."
+                        )
+                    answer = answers[0]
+
+                new_state = state.copy()
+                new_state["current"] = answer
+                new_state["phase"] = 2
+                new_states.append(new_state)
+        return new_states
+
+    def parse_validation_answer(self, state: Dict, texts: List[str]) -> bool:
+        """
+        Parse the response from the language model for a validation prompt.
+
+        :param state: The thought state used to generate the prompt.
+        :type state: Dict
+        :param texts: The responses to the prompt from the language model.
+        :type texts: List[str]
+        :return: Whether the thought state is valid or not.
+        :rtype: bool
+        """
+        pass
+
+    def parse_score_answer(self, states: List[Dict], texts: List[str]) -> List[float]:
+        """
+        Parse the response from the language model for a score prompt.
+
+        :param states: The thought states used to generate the prompt.
+        :type states: List[Dict]
+        :param texts: The responses to the prompt from the language model.
+        :type texts: List[str]
+        :return: The scores for the thought states.
+        :rtype: List[float]
+        """
+        pass
+
+
+def io() -> operations.GraphOfOperations:
+    """
+    Generates the Graph of Operations for the IO method.
+
+    :return: Graph of Operations
+    :rtype: GraphOfOperations
+    """
+    operations_graph = operations.GraphOfOperations()
+
+    operations_graph.append_operation(operations.Generate(1, 1))
+    operations_graph.append_operation(operations.Score(1, False, utils.num_errors))
+    operations_graph.append_operation(
+        operations.GroundTruth(utils.test_set_intersection)
+    )
+
+    return operations_graph
+
+
+def cot() -> operations.GraphOfOperations:
+    """
+    Generates the Graph of Operations for the CoT method.
+
+    :return: Graph of Operations
+    :rtype: GraphOfOperations
+    """
+    operations_graph = operations.GraphOfOperations()
+
+    operations_graph.append_operation(operations.Generate(1, 1))
+    operations_graph.append_operation(operations.Score(1, False, utils.num_errors))
+    operations_graph.append_operation(
+        operations.GroundTruth(utils.test_set_intersection)
+    )
+
+    return operations_graph
+
+
+def tot() -> operations.GraphOfOperations:
+    """
+    Generates the Graph of Operations for the ToT method.
+    ToT uses a wider tree, where on each level there are more branches.
+
+    :return: Graph of Operations
+    :rtype: GraphOfOperations
+    """
+    operations_graph = operations.GraphOfOperations()
+
+    operations_graph.append_operation(operations.Generate(1, 25))
+    operations_graph.append_operation(operations.Score(1, False, utils.num_errors))
+    op_1 = operations.KeepBestN(1, False)
+    operations_graph.append_operation(op_1)
+
+    for _ in range(3):
+        operations_graph.append_operation(operations.Generate(1, 25))
+        operations_graph.append_operation(operations.Score(1, False, utils.num_errors))
+        op_2 = operations.KeepBestN(1, False)
+        op_2.add_predecessor(op_1)
+        operations_graph.append_operation(op_2)
+        op_1 = op_2
+
+    operations_graph.append_operation(
+        operations.GroundTruth(utils.test_set_intersection)
+    )
+
+    return operations_graph
+
+
+def tot2() -> operations.GraphOfOperations:
+    """
+    Generates the Graph of Operations for the ToT2 method.
+    ToT2 uses a tree with more levels, but with fewer branches per level.
+
+    :return: Graph of Operations
+    :rtype: GraphOfOperations
+    """
+    operations_graph = operations.GraphOfOperations()
+
+    operations_graph.append_operation(operations.Generate(1, 10))
+    operations_graph.append_operation(operations.Score(1, False, utils.num_errors))
+    op_1 = operations.KeepBestN(1, False)
+    operations_graph.append_operation(op_1)
+
+    for _ in range(8):
+        operations_graph.append_operation(operations.Generate(1, 10))
+        operations_graph.append_operation(operations.Score(1, False, utils.num_errors))
+        op_2 = operations.KeepBestN(1, False)
+        op_2.add_predecessor(op_1)
+        operations_graph.append_operation(op_2)
+        op_1 = op_2
+
+    operations_graph.append_operation(
+        operations.GroundTruth(utils.test_set_intersection)
+    )
+
+    return operations_graph
+
+
+def got() -> operations.GraphOfOperations:
+    """
+    Generates the Graph of Operations for the GoT method.
+
+    :return: Graph of Operations
+    :rtype: GraphOfOperations
+    """
+    operations_graph = operations.GraphOfOperations()
+
+    plans = operations.Generate(1, 1)
+    operations_graph.append_operation(plans)  # generate the sublists
+    solved_subsets = []
+    for i in range(1, 9):
+        list_id = f"List {i}"
+        sub_list = operations.Selector(
+            lambda thoughts, list_id=list_id: [
+                thought for thought in thoughts if thought.state["part"] == list_id
+            ]
+        )
+        sub_list.add_predecessor(plans)
+        operations_graph.add_operation(sub_list)
+        intersected_subset = operations.Generate(1, 5)
+        intersected_subset.add_predecessor(sub_list)
+        operations_graph.add_operation(intersected_subset)
+        score_sub_list = operations.Score(1, False, utils.num_errors)
+        score_sub_list.add_predecessor(intersected_subset)
+        operations_graph.add_operation(score_sub_list)
+        keep_best_sub_list = operations.KeepBestN(1, False)
+        keep_best_sub_list.add_predecessor(score_sub_list)
+        operations_graph.add_operation(keep_best_sub_list)
+
+        solved_subsets.append(keep_best_sub_list)
+
+    aggregate_1 = operations.Aggregate(5)
+    aggregate_1.add_predecessor(solved_subsets[0])
+    aggregate_1.add_predecessor(solved_subsets[1])
+    operations_graph.add_operation(aggregate_1)
+    score_aggregate_1 = operations.Score(1, False, utils.num_errors)
+    score_aggregate_1.add_predecessor(aggregate_1)
+    operations_graph.add_operation(score_aggregate_1)
+    keep_best_aggregate_1 = operations.KeepBestN(1, False)
+    keep_best_aggregate_1.add_predecessor(score_aggregate_1)
+    operations_graph.add_operation(keep_best_aggregate_1)
+
+    aggregate_2 = operations.Aggregate(5)
+    aggregate_2.add_predecessor(solved_subsets[2])
+    aggregate_2.add_predecessor(solved_subsets[3])
+    operations_graph.add_operation(aggregate_2)
+    score_aggregate_2 = operations.Score(1, False, utils.num_errors)
+    score_aggregate_2.add_predecessor(aggregate_2)
+    operations_graph.add_operation(score_aggregate_2)
+    keep_best_aggregate_2 = operations.KeepBestN(1, False)
+    keep_best_aggregate_2.add_predecessor(score_aggregate_2)
+    operations_graph.add_operation(keep_best_aggregate_2)
+
+    aggregate_3 = operations.Aggregate(5)
+    aggregate_3.add_predecessor(solved_subsets[4])
+    aggregate_3.add_predecessor(solved_subsets[5])
+    operations_graph.add_operation(aggregate_3)
+    score_aggregate_3 = operations.Score(1, False, utils.num_errors)
+    score_aggregate_3.add_predecessor(aggregate_3)
+    operations_graph.add_operation(score_aggregate_3)
+    keep_best_aggregate_3 = operations.KeepBestN(1, False)
+    keep_best_aggregate_3.add_predecessor(score_aggregate_3)
+    operations_graph.add_operation(keep_best_aggregate_3)
+
+    aggregate_4 = operations.Aggregate(5)
+    aggregate_4.add_predecessor(solved_subsets[6])
+    aggregate_4.add_predecessor(solved_subsets[7])
+    operations_graph.add_operation(aggregate_4)
+    score_aggregate_4 = operations.Score(1, False, utils.num_errors)
+    score_aggregate_4.add_predecessor(aggregate_4)
+    operations_graph.add_operation(score_aggregate_4)
+    keep_best_aggregate_4 = operations.KeepBestN(1, False)
+    keep_best_aggregate_4.add_predecessor(score_aggregate_4)
+    operations_graph.add_operation(keep_best_aggregate_4)
+
+    aggregate_1_2 = operations.Aggregate(5)
+    aggregate_1_2.add_predecessor(keep_best_aggregate_1)
+    aggregate_1_2.add_predecessor(keep_best_aggregate_2)
+    operations_graph.add_operation(aggregate_1_2)
+    score_aggregate_1_2 = operations.Score(1, False, utils.num_errors)
+    score_aggregate_1_2.add_predecessor(aggregate_1_2)
+    operations_graph.add_operation(score_aggregate_1_2)
+    keep_best_aggregate_1_2 = operations.KeepBestN(1, False)
+    keep_best_aggregate_1_2.add_predecessor(score_aggregate_1_2)
+    operations_graph.add_operation(keep_best_aggregate_1_2)
+
+    aggregate_3_4 = operations.Aggregate(5)
+    aggregate_3_4.add_predecessor(keep_best_aggregate_3)
+    aggregate_3_4.add_predecessor(keep_best_aggregate_4)
+    operations_graph.add_operation(aggregate_3_4)
+    score_aggregate_3_4 = operations.Score(1, False, utils.num_errors)
+    score_aggregate_3_4.add_predecessor(aggregate_3_4)
+    operations_graph.add_operation(score_aggregate_3_4)
+    keep_best_aggregate_3_4 = operations.KeepBestN(1, False)
+    keep_best_aggregate_3_4.add_predecessor(score_aggregate_3_4)
+    operations_graph.add_operation(keep_best_aggregate_3_4)
+
+    final_aggregate = operations.Aggregate(5)
+    operations_graph.append_operation(final_aggregate)
+    operations_graph.append_operation(operations.Score(1, False, utils.num_errors))
+    keep_best_aggregate_final = operations.KeepBestN(1, False)
+    operations_graph.append_operation(keep_best_aggregate_final)
+
+    operations_graph.append_operation(
+        operations.GroundTruth(utils.test_set_intersection)
+    )
+
+    return operations_graph
+
+
+def run(
+    data_ids: List[int],
+    methods: List[Callable[[], operations.GraphOfOperations]],
+    budget: float,
+    lm_name: str,
+) -> float:
+    """
+    Controller function that executes each specified method for each specified
+    sample while the budget is not exhausted.
+
+    :param data_ids: Indices of the sample to be run.
+    :type data_ids: List[int]
+    :param methods: List of functions to generate Graphs of Operations.
+    :type methods: Each function generates a Graph of Operation.
+    :param budget: Language model budget for the execution in dollars.
+    :type budget: float
+    :param lm_name: Name of the language model to be used.
+    :type lm_name: str
+    :return: Spent budget in dollars.
+    :rtype: float
+    """
+
+    orig_budget = budget
+    path = os.path.join(os.path.dirname(__file__), "set_intersection_128.csv")
+    data = []
+    with open(path, "r") as f:
+        reader = csv.reader(f)
+        next(reader)
+        for row in reader:
+            data.append([int(row[0]), row[1], row[2], row[3]])
+
+    if data_ids is None or len(data_ids) == 0:
+        data_ids = list(range(len(data)))
+    selected_data = [data[i] for i in data_ids]
+
+    if not os.path.exists(os.path.join(os.path.dirname(__file__), "results")):
+        os.makedirs(os.path.join(os.path.dirname(__file__), "results"))
+    timestamp = datetime.datetime.now().strftime("%Y-%m-%d_%H-%M-%S")
+    extra_info = f"{lm_name}_{'-'.join([method.__name__ for method in methods])}"
+    folder_name = f"results/{extra_info}_{timestamp}"
+    os.makedirs(os.path.join(os.path.dirname(__file__), folder_name))
+
+    config = {
+        "data": selected_data,
+        "methods": [method.__name__ for method in methods],
+        "lm": lm_name,
+        "budget": budget,
+    }
+    with open(
+        os.path.join(os.path.dirname(__file__), folder_name, "config.json"), "w"
+    ) as f:
+        json.dump(config, f)
+
+    logging.basicConfig(
+        filename=f"{folder_name}/log.log",
+        filemode="w",
+        format="%(name)s - %(levelname)s - %(message)s",
+        level=logging.DEBUG,
+    )
+
+    for method in methods:
+        # create a results directory for the method
+        os.makedirs(
+            os.path.join(os.path.dirname(__file__), folder_name, method.__name__)
+        )
+
+    for data in selected_data:
+        logging.info(f"Running data {data[0]}: {data[1]} {data[2]}")
+        if budget <= 0.0:
+            logging.error(
+                f"Budget has been depleted, stopping. Data {data[0]} has not been run."
+            )
+            break
+        for method in methods:
+            logging.info(f"Running method {method.__name__}")
+            logging.info(f"Budget left: {budget}")
+            if budget <= 0.0:
+                logging.error(
+                    f"Budget has been depleted, stopping. Method {method.__name__} has not been run."
+                )
+                break
+            lm = controller.ChatGPT(
+                "../../graph_of_thoughts/controller/config.json",
+                model_name=lm_name,
+                cache=True,
+            )
+            operations_graph = method()
+            executor = controller.Controller(
+                lm,
+                operations_graph,
+                SetIntersectionPrompter(),
+                SetIntersectionParser(),
+                {
+                    "set1": data[1],
+                    "set2": data[2],
+                    "result": data[3],
+                    "current": "",
+                    "phase": 0,
+                    "method": method.__name__,
+                },
+            )
+            try:
+                executor.run()
+            except Exception as e:
+                logging.error(f"Exception: {e}")
+            path = os.path.join(
+                os.path.dirname(__file__),
+                folder_name,
+                method.__name__,
+                f"{data[0]}.json",
+            )
+            executor.output_graph(path)
+            budget -= lm.cost
+
+    return orig_budget - budget
+
+
+if __name__ == "__main__":
+    """
+    Input(x)  : a list of 128 numbers between 0 and 255 (inclusive)
+    Input(y)  : a list of 128 numbers between 0 and 255 (inclusive)
+    Output(z) : a list of the intersection between x and y
+    Correct   : z = intersection(x, y)
+    Input Example:
+       [115, 61, 35, 103, 90, 117, 86, 44, 63, 45, 40, 30, 74, 33, 31, 1, 118, 48, 38, 0, 119, 51, 64, 78, 15, 121, 89, 101, 79, 69, 120, 29, 58, 50, 116, 11, 60, 12, 39, 95, 23, 2, 109, 84, 7, 43, 99, 98, 52, 70, 75, 102, 57, 19, 94, 36, 114, 88, 71, 56, 83, 6, 96, 107]
+       [13, 35, 20, 96, 34, 18, 47, 127, 126, 9, 21, 16, 77, 22, 111, 122, 85, 73, 42, 105, 123, 15, 33, 59, 67, 57, 104, 8, 30, 89, 76, 12, 65, 84, 32, 40, 7, 100, 108, 50, 14, 28, 24, 53, 90, 17, 91, 81, 124, 63, 5, 46, 125, 93, 49, 66, 117, 37, 115, 113, 2, 106, 41, 72]
+    Output Example:
+        [115, 35, 90, 117, 63, 40, 30, 33, 15, 89, 50, 12, 2, 84, 7, 57, 96]
+    """
+
+    budget = 25
+    samples = [item for item in range(0, 100)]
+    approaches = [io, cot, tot, tot2, got]
+
+    spent = run(samples, approaches, budget, "chatgpt")
+
+    logging.info(f"Spent {spent} out of {budget} budget.")
@@ -0,0 +1,99 @@
+# Copyright (c) 2023 ETH Zurich.
+#                    All rights reserved.
+#
+# Use of this source code is governed by a BSD-style license that can be
+# found in the LICENSE file.
+#
+# The source code is adapted from the sorting source code written by
+# Nils Blach.
+#
+# main author: Robert Gerstenberger
+
+from typing import Dict, List, Set
+
+
+def string_to_list(string: str) -> List[int]:
+    """
+    Helper function to convert a list encoded inside a string into a Python
+    list object of integer elements.
+
+    :param string: Input string containing a list.
+    :type string: str
+    :return: List of integer elements.
+    :rtype: List[int]
+    :raise AssertionError: If input string does not contain a list.
+    """
+
+    assert string[0] == "[" and string[-1] == "]", "String is not a list."
+    return [int(num) for num in string[1:-1].split(",")]
+
+
+def string_to_set(string: str) -> Set[int]:
+    """
+    Helper function to convert a list encoded inside a string into a Python
+    set object of integer elements.
+
+    :param string: Input string containing a list.
+    :type string: str
+    :return: Set of integer elements.
+    :rtype: Set[int]
+    :raise AssertionError: If input string does not contain a list.
+    """
+
+    assert string[0] == "[" and string[-1] == "]", "String is not a list."
+    return {int(num) for num in string[1:-1].split(",")}
+
+
+def test_set_intersection(state: Dict) -> bool:
+    """
+    Function to test whether the final solution matches ground truth.
+
+    :param state: Thought state that represents the final solution.
+    :type state: Dict
+    :return: Returns whether the solution matches the ground truth.
+    :rtype: bool
+    """
+
+    # convert string to list
+    try:
+        correct_list = string_to_list(state["result"])
+        sorted_list = sorted(string_to_list(state["current"]))
+        return sorted_list == correct_list
+    except:
+        return False
+
+
+def num_errors(state: Dict) -> float:
+    """
+    Function to locally count the number of errors that serves as a score.
+
+    :param state: Thought state to be scored.
+    :type state: Dict
+    :return: Number of errors.
+    :rtype: float
+    """
+
+    try:
+        set1 = string_to_set(state["set1"])
+        set2 = string_to_set(state["set2"])
+        if "subset" in state and state["subset"] != "" and state["subset"] is not None:
+            set2 = string_to_set(state["subset"])
+        common = sorted(list(set1 & set2))
+        llm_solution = sorted(string_to_list(state["current"]))
+        num_errors = 0
+        common_idx = 0
+        llm_idx = 0
+        while common_idx < len(common) and llm_idx < len(llm_solution):
+            if common[common_idx] == llm_solution[llm_idx]:
+                common_idx += 1
+                llm_idx += 1
+            elif common[common_idx] < llm_solution[llm_idx]:
+                common_idx += 1
+                num_errors += 1
+            elif common[common_idx] > llm_solution[llm_idx]:
+                llm_idx += 1
+                num_errors += 1
+        num_errors += len(common) - common_idx + len(llm_solution) - llm_idx
+        return num_errors
+    except:
+        return 1000