Yashi_Game.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5eQNHsfxkFx2"
      },
      "source": [
        "# Yashi Game\n",
        "\n",
        "__Federico Chiarello__ - 2058163\n",
        "\n",
        "An instance of the __Yashi game__ is specified by a _n x n_ integer grid for some _n > 2_, on\n",
        "which _p > 2_ nodes are placed.\n",
        "\n",
        "A solution of the game consists in drawing horizontal and vertical segments, satisfying the following conditions:\n",
        "- No two segments cross each other\n",
        "- The segments form a tree (they form a graph without cycles)"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Given an instance G of __Yashi__, develop a\n",
        "SAT based method to answer the following questions:\n",
        "1. Decide if there is a solution for G. If\n",
        "there is, return one solution.\n",
        "2. Decide if there is a solution for G. If there\n",
        "is, return a minimum-length solution.\n"
      ],
      "metadata": {
        "id": "E5VyOAp3EeF2"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "P4SNbKDxkocw"
      },
      "source": [
        "## Setup"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "!pip install python-sat"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tbZTayo0TDR-",
        "outputId": "2a0b2907-3799-4cb8-fd1a-76640e326985"
      },
      "execution_count": 51,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Requirement already satisfied: python-sat in /usr/local/lib/python3.10/dist-packages (0.1.8.dev17)\n",
            "Requirement already satisfied: six in /usr/local/lib/python3.10/dist-packages (from python-sat) (1.16.0)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 52,
      "metadata": {
        "id": "TGAGYD6IV-pO"
      },
      "outputs": [],
      "source": [
        "import pysat\n",
        "import math\n",
        "import random\n",
        "import itertools\n",
        "import matplotlib.pyplot as plt\n",
        "from matplotlib.pyplot import figure\n",
        "\n",
        "from pysat.solvers import Minisat22\n",
        "from pysat.examples.fm import FM\n",
        "from pysat.formula import WCNF"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wwSjFXkUM2Fk"
      },
      "source": [
        "### Generate Points\n",
        "\n",
        "The following function randomly generates an instance of the __Yashi__ game.  \n",
        "It creates a dictionary that contains as keys the points coordinates and as values the points ids."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 53,
      "metadata": {
        "id": "N7ayXv66HoCL"
      },
      "outputs": [],
      "source": [
        "def generate_points(n_points=10, range_points=10):\n",
        "\n",
        "    tuples = []\n",
        "    while len(tuples) < n_points:\n",
        "        new_point = (random.randint(0, range_points), random.randint(0, range_points))\n",
        "        if new_point not in tuples:\n",
        "            tuples.append(new_point)\n",
        "\n",
        "    sorted_tuples = sorted(tuples, key=lambda p: (p[0], p[1]))\n",
        "    points_zip = zip(sorted_tuples, range(len(sorted_tuples)))\n",
        "    points_dict = dict(points_zip)\n",
        "\n",
        "    return points_dict"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 54,
      "metadata": {
        "id": "zYHWiomuILK0",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0021e79b-a950-48f2-bd6f-651d672c3f4d"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{(0, 0): 0,\n",
              " (0, 2): 1,\n",
              " (0, 4): 2,\n",
              " (0, 5): 3,\n",
              " (1, 1): 4,\n",
              " (1, 2): 5,\n",
              " (2, 0): 6,\n",
              " (2, 2): 7,\n",
              " (3, 0): 8,\n",
              " (3, 3): 9,\n",
              " (3, 5): 10,\n",
              " (4, 1): 11,\n",
              " (5, 1): 12,\n",
              " (5, 2): 13,\n",
              " (5, 5): 14}"
            ]
          },
          "metadata": {},
          "execution_count": 54
        }
      ],
      "source": [
        "n_points = 15\n",
        "range_points = 5\n",
        "\n",
        "points_dict = generate_points(n_points, range_points)\n",
        "points_dict"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xtrH2t0JM7VN"
      },
      "source": [
        "### Plot Functions"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 55,
      "metadata": {
        "id": "Uj5kcevGNdVa"
      },
      "outputs": [],
      "source": [
        "def plot_graph(points_dict, segments_dict={}, lines_dict={}):\n",
        "\n",
        "    x = [point[0] for point in points_dict]\n",
        "    y = [point[1] for point in points_dict]\n",
        "    labels = [label for label in points_dict.values()]\n",
        "\n",
        "    # Plot points\n",
        "    plt.scatter(x, y, color='red')\n",
        "    for i, label in enumerate(labels):\n",
        "        plt.annotate(label, (x[i], y[i]), (x[i] + 0.1, y[i] + 0.1), color='red')\n",
        "\n",
        "    if lines_dict != {}:\n",
        "\n",
        "        # Plot the solution\n",
        "        for label, segment in lines_dict.items():\n",
        "            x1, y1 = segment[0]\n",
        "            x2, y2 = segment[1]\n",
        "            plt.plot([x1, x2], [y1, y2], color='black')\n",
        "            if x1==x2:\n",
        "                plt.annotate(label, ((x1+x2)/2 + 0.1, (y1+y2)/2 - 0.1), color='black')\n",
        "            else:\n",
        "                plt.annotate(label, ((x1+x2)/2 - 0.1, (y1+y2)/2 + 0.1), color='black')\n",
        "\n",
        "    else:\n",
        "\n",
        "        # Plot all possible horizontal and vertical segments\n",
        "        for label, segment in segments_dict.items():\n",
        "            x1, y1 = segment[0]\n",
        "            x2, y2 = segment[1]\n",
        "            plt.plot([x1, x2], [y1, y2], color='black', linestyle='dashed')\n",
        "            if x1==x2:\n",
        "                plt.annotate(label, ((x1+x2)/2 + 0.1, (y1+y2)/2 - 0.1), color='black')\n",
        "            else:\n",
        "                plt.annotate(label, ((x1+x2)/2 - 0.1, (y1+y2)/2 + 0.1), color='black')\n",
        "\n",
        "    plt.xlim(-1, range_points+1)\n",
        "    plt.ylim(-1, range_points+1)\n",
        "    plt.gca().set_aspect('equal')\n",
        "\n",
        "    plt.xticks(range(0, range_points+1))\n",
        "    plt.yticks(range(0, range_points+1))\n",
        "    plt.grid(True)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 56,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "6vMw6ZpgPG5T",
        "outputId": "adb421c2-651c-4425-fd92-1624b10e44a9"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "plot_graph(points_dict)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def sat_plots(points_dict, segments_dict, sat_solution):\n",
        "\n",
        "    plt.subplot(1, 3, 1)\n",
        "    plot_graph(points_dict)\n",
        "    plt.title(\"Points\")\n",
        "\n",
        "    plt.subplot(1, 3, 2)\n",
        "    plot_graph(points_dict, segments_dict)\n",
        "    plt.title(\"Possible Segments\")\n",
        "\n",
        "    plt.subplot(1, 3, 3)\n",
        "    plot_graph(points_dict, {}, sat_solution)\n",
        "    plt.title(\"SAT Solution\")\n",
        "\n",
        "    plt.tight_layout()\n",
        "\n",
        "    plt.show()"
      ],
      "metadata": {
        "id": "8fnEUHODCVb9"
      },
      "execution_count": 57,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def max_sat_plots(points_dict, segments_dict, sat_solution, max_sat_solution):\n",
        "\n",
        "    plt.subplot(1, 3, 1)\n",
        "    plot_graph(points_dict, segments_dict)\n",
        "    plt.title(\"Possible Segments\")\n",
        "\n",
        "    plt.subplot(1, 3, 2)\n",
        "    plot_graph(points_dict, {}, sat_solution)\n",
        "    plt.title(\"SAT Solution\")\n",
        "\n",
        "    plt.subplot(1, 3, 3)\n",
        "    plot_graph(points_dict, {}, max_sat_solution)\n",
        "    plt.title(\"Minimum-length Solution\")\n",
        "\n",
        "    plt.tight_layout()\n",
        "\n",
        "    plt.show()"
      ],
      "metadata": {
        "id": "COHtCBd7CY_T"
      },
      "execution_count": 58,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qLHYjP5xT1sQ"
      },
      "source": [
        "### Find Segments\n",
        "\n",
        "Here we identify all the possible segments connecting the points in our game configuration."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 59,
      "metadata": {
        "id": "B7e9RWYrT1ez"
      },
      "outputs": [],
      "source": [
        "def find_segments(points_dict):\n",
        "\n",
        "    sorted_by_x = sorted(points_dict, key=lambda p: (p[0], p[1]))\n",
        "    sorted_by_y = sorted(points_dict, key=lambda p: (p[1], p[0]))\n",
        "\n",
        "    segments = []\n",
        "\n",
        "    # Vertical segments\n",
        "    for i in range(len(sorted_by_x) - 1):\n",
        "        if sorted_by_x[i][0] == sorted_by_x[i+1][0]:\n",
        "            segments.append((sorted_by_x[i], sorted_by_x[i+1]))\n",
        "\n",
        "    # Horizontal segments\n",
        "    for i in range(len(sorted_by_y) - 1):\n",
        "        if sorted_by_y[i][1] == sorted_by_y[i+1][1]:\n",
        "            segments.append((sorted_by_y[i], sorted_by_y[i+1]))\n",
        "\n",
        "    # Create Dictionary\n",
        "    segments_dict = {}\n",
        "    get_idx_dict = {}\n",
        "    for i in range(len(segments)):\n",
        "        segments_dict[i+1] = segments[i]\n",
        "        get_idx_dict[segments[i]] = i+1\n",
        "\n",
        "    return segments_dict, get_idx_dict"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 60,
      "metadata": {
        "id": "2sps7DB7Vd5J"
      },
      "outputs": [],
      "source": [
        "segments_dict, get_idx_dict = find_segments(points_dict)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 61,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rO69r9wvWF4Y",
        "outputId": "44adff33-aa62-4739-cf02-a08f36981f8f"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{1: ((0, 0), (0, 2)),\n",
              " 2: ((0, 2), (0, 4)),\n",
              " 3: ((0, 4), (0, 5)),\n",
              " 4: ((1, 1), (1, 2)),\n",
              " 5: ((2, 0), (2, 2)),\n",
              " 6: ((3, 0), (3, 3)),\n",
              " 7: ((3, 3), (3, 5)),\n",
              " 8: ((5, 1), (5, 2)),\n",
              " 9: ((5, 2), (5, 5)),\n",
              " 10: ((0, 0), (2, 0)),\n",
              " 11: ((2, 0), (3, 0)),\n",
              " 12: ((1, 1), (4, 1)),\n",
              " 13: ((4, 1), (5, 1)),\n",
              " 14: ((0, 2), (1, 2)),\n",
              " 15: ((1, 2), (2, 2)),\n",
              " 16: ((2, 2), (5, 2)),\n",
              " 17: ((0, 5), (3, 5)),\n",
              " 18: ((3, 5), (5, 5))}"
            ]
          },
          "metadata": {},
          "execution_count": 61
        }
      ],
      "source": [
        "segments_dict"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 62,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "1ip87gwvWI-5",
        "outputId": "724e025c-8d9f-4766-c9b4-f91b85d73781"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "plot_graph(points_dict, segments_dict)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "V6l5rMXAfm27"
      },
      "source": [
        "## Constraints\n",
        "\n",
        "I used the SAT encoding proposed in this [paper](https://www.cs.bu.edu/faculty/kfoury/UNI-Teaching/CS512/AK_Documents/Modeling-with-PL/main.pdf).  \n",
        "It uses the segments ids as variables and defines the game rules with the 3 following propositional formulas:\n",
        "\n",
        "$ϕ = ϕ_{no\\_crossing} \\land ϕ_{no\\_cycles} \\land ϕ_{tree}$\n",
        "\n",
        "The constraints that we are imposing are the following:\n",
        "\n",
        "1. $ϕ_{no\\_crossing}$ is satisfied by a truth-value assignment iff no two crossing segments are both present in the solution.\n",
        "2. $ϕ_{no\\_cycles}$ is satisfied by a truth-value assignment iff not all the segments that are part of a cycle are present in the solution.\n",
        "3. $ϕ_{tree}$ is satisfied by a truth-value assignment iff exactly (p - 1) segments are present in the solution."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9OKn9vBymYFT"
      },
      "source": [
        "### No Crossings\n",
        "\n",
        "If two segments are crossing, not both of them can be included in the solution.\n",
        "\n",
        "$\\phi_{no\\_crossing} = CNF(\\bigwedge_\\limits{\\substack{s_i, s_j, \\\\ s_i \\neq s_j, \\\\ are\\_crossing(s_i, s_j)}} \\overline{s_i \\land s_j}) = \\bigwedge_\\limits{\\substack{s_i,s_j, \\\\ s_i \\neq s_j, \\\\ are\\_crossing(s_i, s_j)}} (\\overline{s_i} \\lor \\overline{s_j})\n",
        "$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 63,
      "metadata": {
        "id": "IKv34CyutsDs"
      },
      "outputs": [],
      "source": [
        "def get_crossing_segments(segments, get_idx_dict):\n",
        "\n",
        "    def are_crossing(segment_1, segment_2):\n",
        "        (x1, y1), (x2, y2) = segment_1\n",
        "        (x3, y3), (x4, y4) = segment_2\n",
        "        return (\n",
        "            (min(x1, x2) < x3 < max(x1, x2) and min(y3, y4) < y1 < max(y3, y4)) or\n",
        "            (min(y1, y2) < y3 < max(y1, y2) and min(x3, x4) < x1 < max(x3, x4))\n",
        "        )\n",
        "\n",
        "    crossing_segments = []\n",
        "    for i in segments:\n",
        "        for j in segments:\n",
        "            if i != j:\n",
        "                if are_crossing(i, j):\n",
        "                    new_cross = sorted((get_idx_dict[i], get_idx_dict[j]))\n",
        "                    if new_cross not in crossing_segments:\n",
        "                        crossing_segments.append(new_cross)\n",
        "\n",
        "    return crossing_segments"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 64,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SKiZIRVz1hLL",
        "outputId": "e6daef99-fd21-4fa8-c9b3-4756018a9bb1"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[[5, 12], [6, 12], [6, 16]]"
            ]
          },
          "metadata": {},
          "execution_count": 64
        }
      ],
      "source": [
        "crossings = get_crossing_segments(segments_dict.values(), get_idx_dict)\n",
        "crossings"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iELbzMXelxOf"
      },
      "source": [
        "### No Cycles\n",
        "\n",
        "In this section we identify the cycles that are present in the graph formed by all the possible segments connecting our points, after that we impose that not all the segments that are part of a cycle are present in our final solution.\n",
        "\n",
        "$\\phi_{no\\_cycles} = CNF(\\bigwedge_\\limits{c \\in cycles} \\overline{\\bigwedge_\\limits{s \\in c} s}) = \\bigwedge_\\limits{c \\in cycles} \\bigvee_\\limits{s \\in c} \\overline{s}$\n",
        "\n",
        "We identify the cycles with the following procedure:\n",
        "- we create an adjacency list as a dictionary, with the points as keys and as values all the segmants that are adjecent to the respective point.\n",
        "- we perform a depth first search exploiting the adjecency list, obtaining in this way a list of all the cycles present in the graph."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 65,
      "metadata": {
        "id": "Y1JZrRdsfLdq"
      },
      "outputs": [],
      "source": [
        "def generate_adjacency_list(segments_dict):\n",
        "    adjacency_list = {}\n",
        "\n",
        "    for label, segment in segments_dict.items():\n",
        "        start, end = segment\n",
        "\n",
        "        if start in adjacency_list:\n",
        "            adjacency_list[start].append(end)\n",
        "        else:\n",
        "            adjacency_list[start] = [end]\n",
        "\n",
        "        if end in adjacency_list:\n",
        "            adjacency_list[end].append(start)\n",
        "        else:\n",
        "            adjacency_list[end] = [start]\n",
        "\n",
        "    return adjacency_list"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 66,
      "metadata": {
        "id": "UVWYZMoejaDd",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8b59a429-ee56-4e65-af4e-26403adb7e0c"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{(0, 0): [(0, 2), (2, 0)],\n",
              " (0, 2): [(0, 0), (0, 4), (1, 2)],\n",
              " (0, 4): [(0, 2), (0, 5)],\n",
              " (0, 5): [(0, 4), (3, 5)],\n",
              " (1, 1): [(1, 2), (4, 1)],\n",
              " (1, 2): [(1, 1), (0, 2), (2, 2)],\n",
              " (2, 0): [(2, 2), (0, 0), (3, 0)],\n",
              " (2, 2): [(2, 0), (1, 2), (5, 2)],\n",
              " (3, 0): [(3, 3), (2, 0)],\n",
              " (3, 3): [(3, 0), (3, 5)],\n",
              " (3, 5): [(3, 3), (0, 5), (5, 5)],\n",
              " (5, 1): [(5, 2), (4, 1)],\n",
              " (5, 2): [(5, 1), (5, 5), (2, 2)],\n",
              " (5, 5): [(5, 2), (3, 5)],\n",
              " (4, 1): [(1, 1), (5, 1)]}"
            ]
          },
          "metadata": {},
          "execution_count": 66
        }
      ],
      "source": [
        "adjacency_list = generate_adjacency_list(segments_dict)\n",
        "adjacency_list"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 67,
      "metadata": {
        "id": "cyXUiz5ijlhJ"
      },
      "outputs": [],
      "source": [
        "def find_cycles(adjacency_list):\n",
        "\n",
        "    def depth_first_search(current, start, path):\n",
        "        nonlocal cycles, sorted_cycles\n",
        "        visited[current] = True\n",
        "        path.append(current)\n",
        "        for neighbor in adjacency_list[current]:\n",
        "            if not visited[neighbor]:\n",
        "                depth_first_search(neighbor, start, path)\n",
        "            elif neighbor == start and len(path) > 2:\n",
        "                new_cycle = path[:]\n",
        "                sorted_cycle = sorted(path[:])\n",
        "                if sorted_cycle not in sorted_cycles:\n",
        "                    cycles.append(new_cycle)\n",
        "                    sorted_cycles.append(sorted_cycle)\n",
        "        path.pop()\n",
        "        visited[current] = False\n",
        "\n",
        "\n",
        "    nodes = adjacency_list.keys()\n",
        "    visited = {}\n",
        "    for node in nodes:\n",
        "        visited[node] = False\n",
        "    cycles, sorted_cycles = [], []\n",
        "\n",
        "    for node in nodes:\n",
        "        depth_first_search(node, node, [])\n",
        "\n",
        "    return cycles"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 68,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "I8tiWYrSouiI",
        "outputId": "71db689b-e05b-45f2-d3e0-b4f1bdb5bc07"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[(0, 0), (0, 2), (0, 4), (0, 5), (3, 5), (3, 3), (3, 0), (2, 0)]\n",
            "[(0, 0), (0, 2), (0, 4), (0, 5), (3, 5), (5, 5), (5, 2), (5, 1), (4, 1), (1, 1), (1, 2), (2, 2), (2, 0)]\n",
            "[(0, 0), (0, 2), (0, 4), (0, 5), (3, 5), (5, 5), (5, 2), (2, 2), (2, 0)]\n",
            "[(0, 0), (0, 2), (1, 2), (1, 1), (4, 1), (5, 1), (5, 2), (5, 5), (3, 5), (3, 3), (3, 0), (2, 0)]\n",
            "[(0, 0), (0, 2), (1, 2), (1, 1), (4, 1), (5, 1), (5, 2), (2, 2), (2, 0)]\n",
            "[(0, 0), (0, 2), (1, 2), (2, 2), (2, 0)]\n",
            "[(0, 0), (0, 2), (1, 2), (2, 2), (5, 2), (5, 5), (3, 5), (3, 3), (3, 0), (2, 0)]\n",
            "[(0, 2), (0, 4), (0, 5), (3, 5), (3, 3), (3, 0), (2, 0), (2, 2), (1, 2)]\n",
            "[(0, 2), (0, 4), (0, 5), (3, 5), (3, 3), (3, 0), (2, 0), (2, 2), (5, 2), (5, 1), (4, 1), (1, 1), (1, 2)]\n",
            "[(0, 2), (0, 4), (0, 5), (3, 5), (5, 5), (5, 2), (5, 1), (4, 1), (1, 1), (1, 2)]\n",
            "[(0, 2), (0, 4), (0, 5), (3, 5), (5, 5), (5, 2), (2, 2), (1, 2)]\n",
            "[(1, 1), (1, 2), (2, 2), (2, 0), (3, 0), (3, 3), (3, 5), (5, 5), (5, 2), (5, 1), (4, 1)]\n",
            "[(1, 1), (1, 2), (2, 2), (5, 2), (5, 1), (4, 1)]\n",
            "[(2, 0), (2, 2), (5, 2), (5, 5), (3, 5), (3, 3), (3, 0)]\n"
          ]
        }
      ],
      "source": [
        "cycles = find_cycles(adjacency_list)\n",
        "\n",
        "for cycle in cycles:\n",
        "    print(cycle)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 69,
      "metadata": {
        "id": "mS11JD39msO3"
      },
      "outputs": [],
      "source": [
        "def convert_cycles_into_segment_list(cycles):\n",
        "\n",
        "    cycles_segments = []\n",
        "\n",
        "    for cycle in cycles:\n",
        "        segments_list = []\n",
        "\n",
        "        # Get the name of the segment connecting point i and point i+1 in the cycle list\n",
        "        for i in range(len(cycle)-1):\n",
        "            cyc = get_idx_dict[tuple(sorted((cycle[i], cycle[i+1]), key=lambda p: (p[0], p[1])))]\n",
        "            segments_list.append(cyc)\n",
        "\n",
        "        # Repeat the procedure also for the segment connecting the first and last point in the list\n",
        "        cyc = get_idx_dict[tuple(sorted((cycle[0], cycle[len(cycle)-1]), key=lambda p: (p[0], p[1])))]\n",
        "        segments_list.append(cyc)\n",
        "\n",
        "        cycles_segments.append(segments_list)\n",
        "\n",
        "    return cycles_segments\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 70,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8o0GRTuQmbdu",
        "outputId": "5591941f-54e6-4ebe-97f8-62eda503a3d9"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[[1, 2, 3, 17, 7, 6, 11, 10],\n",
              " [1, 2, 3, 17, 18, 9, 8, 13, 12, 4, 15, 5, 10],\n",
              " [1, 2, 3, 17, 18, 9, 16, 5, 10],\n",
              " [1, 14, 4, 12, 13, 8, 9, 18, 7, 6, 11, 10],\n",
              " [1, 14, 4, 12, 13, 8, 16, 5, 10],\n",
              " [1, 14, 15, 5, 10],\n",
              " [1, 14, 15, 16, 9, 18, 7, 6, 11, 10],\n",
              " [2, 3, 17, 7, 6, 11, 5, 15, 14],\n",
              " [2, 3, 17, 7, 6, 11, 5, 16, 8, 13, 12, 4, 14],\n",
              " [2, 3, 17, 18, 9, 8, 13, 12, 4, 14],\n",
              " [2, 3, 17, 18, 9, 16, 15, 14],\n",
              " [4, 15, 5, 11, 6, 7, 18, 9, 8, 13, 12],\n",
              " [4, 15, 16, 8, 13, 12],\n",
              " [5, 16, 9, 18, 7, 6, 11]]"
            ]
          },
          "metadata": {},
          "execution_count": 70
        }
      ],
      "source": [
        "cycles_segments = convert_cycles_into_segment_list(cycles)\n",
        "cycles_segments"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Xj4y_2JSmcgY"
      },
      "source": [
        "### Tree\n",
        "\n",
        "\n",
        "We must guarantee that exactly (p - 1) segments are present in the solution.  \n",
        "We know from _Graph Theory_ that a minimum spanning tree has precisely p-1 edges, where p is the number of vertices in the graph.\n",
        "\n",
        "\\\n",
        "\n",
        "The constraint \"exactly k\" is the conjunction of \"at least k\" and \"at most k\"\n",
        "\n",
        "\n",
        "\n",
        "$\\phi_{tree} = (\\bigwedge_\\limits{\\substack{I \\subseteq [n] \\\\ |I|=n-k+1}} \\bigvee_\\limits{i \\in I} s_i) \\land (\\bigwedge_\\limits{\\substack{I \\subseteq [n] \\\\ |I|=k+1}} \\bigvee_\\limits{i \\in I} \\bar{s_i})$\n",
        "\n",
        "with:\n",
        "- $k =$ number of points $ - 1$\n",
        "- $n =$ number of segments\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def exactly_k(segments, k):\n",
        "\n",
        "    formulas = WCNF()\n",
        "    n = len(segments)\n",
        "\n",
        "    # at least k\n",
        "    for sub_lists in itertools.combinations(segments, n-k+1):\n",
        "        formulas.append(list(sub_lists))\n",
        "\n",
        "    # at most k\n",
        "    for sub_lists in itertools.combinations(segments, k+1):\n",
        "        tmp = [-i for i in list(sub_lists)]\n",
        "        formulas.append(tmp)\n",
        "\n",
        "    return formulas"
      ],
      "metadata": {
        "id": "c0l5OBrQTz0L"
      },
      "execution_count": 71,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "k = len(points_dict) - 1\n",
        "ex_k = exactly_k(segments_dict.keys(), k)"
      ],
      "metadata": {
        "id": "CD9ImW_TUna5"
      },
      "execution_count": 72,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Minimum-Lenght\n",
        "\n",
        "Here we generate the __soft constraints__ that are used to determine the minimum-length solution.  \n",
        "Each segment is associated with a weight that corresponds to the negative of his length, which is computed as an euclidean distance."
      ],
      "metadata": {
        "id": "jmYUKtfdbRfm"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def euclidean_distance(segment):\n",
        "    x1, y1 = segment[0]\n",
        "    x2, y2 = segment[1]\n",
        "    return math.sqrt((x1 - x2) ** 2 + (y1 - y2) ** 2)\n",
        "\n",
        "\n",
        "def get_minimum_lenght_constraint(segments_dict):\n",
        "    formulas = WCNF()\n",
        "    for idx, segment in segments_dict.items():\n",
        "        weight = -euclidean_distance(segment)\n",
        "        formulas.append([idx], weight)\n",
        "    return formulas"
      ],
      "metadata": {
        "id": "m8pi2sqEp2bc"
      },
      "execution_count": 73,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Solver"
      ],
      "metadata": {
        "id": "9Eydp3CqVShk"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### SAT Solver\n",
        "\n",
        "Decide if there is a solution. If there is one, return one solution.\n",
        "\n",
        "For this point we use a SAT Solver (_Minisat22_). We create a WCNF (weighted CNF) object containing all the hard constraints and pass it to the SAT Solver.\n",
        "If the solver determines that there is a solution, that solution will be returned and plotted."
      ],
      "metadata": {
        "id": "eN4_KDVNM58A"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def find_solution(points_dict, segments_dict, get_idx_dict):\n",
        "\n",
        "    wcnf = WCNF()\n",
        "\n",
        "    # No Crossing Constraint\n",
        "\n",
        "    crossings = get_crossing_segments(segments_dict.values(), get_idx_dict)\n",
        "\n",
        "    for crossing in crossings:\n",
        "        clause = [i * -1 for i in crossing]\n",
        "        wcnf.append(clause)\n",
        "\n",
        "    # Cycle Constraint\n",
        "\n",
        "    adjacency_list = generate_adjacency_list(segments_dict)\n",
        "    cycles = find_cycles(adjacency_list)\n",
        "    cycles_segments = convert_cycles_into_segment_list(cycles)\n",
        "\n",
        "    for cycle in cycles_segments:\n",
        "        clause = [i * -1 for i in cycle]\n",
        "        wcnf.append(clause)\n",
        "\n",
        "    # Tree (Exactly p-1)\n",
        "\n",
        "    k = len(points_dict) - 1\n",
        "\n",
        "    if (k) > len(segments_dict.keys()):\n",
        "        print('No solution: the number of possible segments present in the graph in not sufficient to connect all the points')\n",
        "        return\n",
        "\n",
        "    ex_k = exactly_k(segments_dict.keys(), k)\n",
        "\n",
        "    wcnf.extend(ex_k.hard)\n",
        "\n",
        "\n",
        "\n",
        "    # SAT Solver\n",
        "\n",
        "    solver = Minisat22()\n",
        "    solver.append_formula(wcnf.hard)\n",
        "    solution = solver.solve()\n",
        "\n",
        "    if solution:\n",
        "\n",
        "        model = solver.get_model()\n",
        "        sat_solution = {x: segments_dict[x] for x in model if x > 0}\n",
        "\n",
        "        print('Model: ', model, '\\n')\n",
        "\n",
        "        figure(figsize=(15, 15), dpi=80)\n",
        "        sat_plots(points_dict, segments_dict, sat_solution)\n",
        "\n",
        "    else:\n",
        "        print('No solution for this instance')"
      ],
      "metadata": {
        "id": "YIktLm25fL83"
      },
      "execution_count": 74,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### MaxSAT\n",
        "\n",
        "Decide if there is a solution for G. If there is one, return a __minimum-length__ solution.  \n",
        "\n",
        "For this point we use a FM Solver (based on the _Fu&Malik MaxSAT algorithm_). We create a WCNF (weighted CNF) object containing all the hard constraints and the soft constraints and pass it to the MaxSAT Solver.\n",
        "If there is a solution, the solver will return and plot the minimum-length solution."
      ],
      "metadata": {
        "id": "wG2DjnvENFpc"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def find_min_length_solution(points_dict, segments_dict, get_idx_dict):\n",
        "\n",
        "    wcnf = WCNF()\n",
        "\n",
        "    # No Crossing Constraint\n",
        "\n",
        "    crossings = get_crossing_segments(segments_dict.values(), get_idx_dict)\n",
        "\n",
        "    for crossing in crossings:\n",
        "        clause = [i * -1 for i in crossing]\n",
        "        wcnf.append(clause)\n",
        "\n",
        "    # Cycle Constraint\n",
        "\n",
        "    adjacency_list = generate_adjacency_list(segments_dict)\n",
        "    cycles = find_cycles(adjacency_list)\n",
        "    cycles_segments = convert_cycles_into_segment_list(cycles)\n",
        "\n",
        "    for cycle in cycles_segments:\n",
        "        clause = [i * -1 for i in cycle]\n",
        "        wcnf.append(clause)\n",
        "\n",
        "    # Tree (Exactly p-1)\n",
        "\n",
        "    k = len(points_dict) - 1\n",
        "\n",
        "    if (k) > len(segments_dict.keys()):\n",
        "        print('No solution: the number of possible segments present in the graph in not sufficient to connect all the points')\n",
        "        return\n",
        "\n",
        "    ex_k = exactly_k(segments_dict.keys(), k)\n",
        "\n",
        "    wcnf.extend(ex_k.hard)\n",
        "\n",
        "\n",
        "    # SAT Solver\n",
        "\n",
        "    solver = Minisat22()\n",
        "    solver.append_formula(wcnf.hard)\n",
        "    solution = solver.solve()\n",
        "\n",
        "    if solution:\n",
        "\n",
        "        model = solver.get_model()\n",
        "        sat_solution = {x: segments_dict[x] for x in model if x > 0}\n",
        "\n",
        "        # Minimum Lenght\n",
        "\n",
        "        minimum_lenght_constraint = get_minimum_lenght_constraint(segments_dict)\n",
        "\n",
        "        wcnf.extend(minimum_lenght_constraint.soft, weights=minimum_lenght_constraint.wght)\n",
        "\n",
        "        # MaxSAT Solver\n",
        "\n",
        "        solver = FM(wcnf, verbose=0)\n",
        "        solution = solver.compute()\n",
        "\n",
        "\n",
        "        print('Cost of the minimum-lenght solution: ', -sum(minimum_lenght_constraint.wght) + solver.cost)\n",
        "\n",
        "        model = solver.model\n",
        "        max_sat_solution = {x: segments_dict[x] for x in model if x > 0}\n",
        "\n",
        "        print('Model: ', model, '\\n')\n",
        "\n",
        "        figure(figsize=(15, 15), dpi=80)\n",
        "        max_sat_plots(points_dict, segments_dict, sat_solution, max_sat_solution)\n",
        "\n",
        "    else:\n",
        "        print('No solution for this instance')"
      ],
      "metadata": {
        "id": "WO54kG2VQCtu"
      },
      "execution_count": 75,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Examples"
      ],
      "metadata": {
        "id": "Uqfs8CZ0Tgg-"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Example 1"
      ],
      "metadata": {
        "id": "NIU5OrefsNFh"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "random.seed(3)\n",
        "n_points = 16\n",
        "range_points = 6\n",
        "\n",
        "points_dict = generate_points(n_points, range_points)\n",
        "segments_dict, get_idx_dict = find_segments(points_dict)\n",
        "\n",
        "plot_graph(points_dict, segments_dict)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "WPbt56IijBTY",
        "outputId": "b9d7f0be-daee-400a-8d96-d88bf02753b3"
      },
      "execution_count": 76,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "find_solution(points_dict, segments_dict, get_idx_dict)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "CXetw49QjLWY",
        "outputId": "1a5d8085-c2c0-4928-87c7-da44e0db1b9c"
      },
      "execution_count": 77,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model:  [1, 2, 3, 4, -5, 6, 7, 8, 9, 10, 11, 12, -13, 14, 15, 16, 17, -18, -19] \n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x1200 with 3 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "find_min_length_solution(points_dict, segments_dict, get_idx_dict)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 489
        },
        "id": "Wba4IUcPjLRa",
        "outputId": "152dbcf2-0c36-4872-e1f2-78e9ab8a0679"
      },
      "execution_count": 78,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Cost of the minimum-lenght solution:  24.0\n",
            "Model:  [1, 2, 3, 4, 5, -6, -7, 8, -9, 10, 11, 12, 13, 14, 15, 16, 17, -18, 19] \n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x1200 with 3 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Example 2"
      ],
      "metadata": {
        "id": "3O6CFNRIsu7j"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "random.seed(30)\n",
        "n_points = 15\n",
        "range_points = 5\n",
        "\n",
        "points_dict = generate_points(n_points, range_points)\n",
        "segments_dict, get_idx_dict = find_segments(points_dict)\n",
        "\n",
        "plot_graph(points_dict, segments_dict)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "PCBZeNIEtUzU",
        "outputId": "ec9d28cd-5870-48b9-cb56-de510072b828"
      },
      "execution_count": 79,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "find_solution(points_dict, segments_dict, get_idx_dict)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "Jgrrb8DXuoUb",
        "outputId": "9b7b8e08-bc92-41e3-ddfc-48930def5cd4"
      },
      "execution_count": 80,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model:  [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, -14, 15, -16, -17, -18, -19] \n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x1200 with 3 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "find_min_length_solution(points_dict, segments_dict, get_idx_dict)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 489
        },
        "id": "racQoKk9uqwj",
        "outputId": "acb3d297-3884-4fd5-b923-41385e1ccf75"
      },
      "execution_count": 81,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Cost of the minimum-lenght solution:  21.0\n",
            "Model:  [1, 2, 3, 4, -5, 6, 7, 8, 9, -10, 11, 12, 13, -14, 15, -16, 17, -18, 19] \n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x1200 with 3 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Example 3"
      ],
      "metadata": {
        "id": "3Z7tJctFurVz"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "random.seed(6)\n",
        "n_points = 25\n",
        "range_points = 11\n",
        "\n",
        "points_dict = generate_points(n_points, range_points)\n",
        "segments_dict, get_idx_dict = find_segments(points_dict)\n",
        "\n",
        "plot_graph(points_dict, segments_dict)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "Ha2yRJoFsl5a",
        "outputId": "e74db85c-519e-4254-fca2-8eda0bdb03db"
      },
      "execution_count": 82,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "find_solution(points_dict, segments_dict, get_idx_dict)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 465
        },
        "id": "BONnmFK1sxGS",
        "outputId": "5e2a6680-69dc-4b31-b662-5f77911297ee"
      },
      "execution_count": 83,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model:  [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, -18, 19, -20, 21, -22, 23, 24, 25, -26, 27, 28] \n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x1200 with 3 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "find_min_length_solution(points_dict, segments_dict, get_idx_dict)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 482
        },
        "id": "5z9kchvss4l9",
        "outputId": "304f2070-ae29-4591-a664-82e94fbe8beb"
      },
      "execution_count": 84,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Cost of the minimum-lenght solution:  68.0\n",
            "Model:  [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, -18, 19, -20, 21, -22, -23, 24, 25, 26, 27, 28] \n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x1200 with 3 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Example 4: No Solution - Graph Not Fully Connected"
      ],
      "metadata": {
        "id": "MROxHBF0VjU3"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "random.seed(42)\n",
        "n_points = 15\n",
        "range_points = 10\n",
        "\n",
        "points_dict = generate_points(n_points, range_points)\n",
        "segments_dict, get_idx_dict = find_segments(points_dict)"
      ],
      "metadata": {
        "id": "hMTuPxmQgGsA"
      },
      "execution_count": 85,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plot_graph(points_dict, segments_dict)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "k_kMT00RVzx9",
        "outputId": "166191d6-622c-4817-db36-ceb2abcfa9a6"
      },
      "execution_count": 86,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "find_solution(points_dict, segments_dict, get_idx_dict)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "u98vc-njVzpk",
        "outputId": "6d6916d1-b0ca-44c1-e6df-3ef4a830d37c"
      },
      "execution_count": 87,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "No solution: the number of possible segments present in the graph in not sufficient to connect all the points\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Example 5: No Solution - Fully Connected Graph with Crossing Segments"
      ],
      "metadata": {
        "id": "5ZwO72ofiRzs"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "random.seed(44)\n",
        "n_points = 15\n",
        "range_points = 6\n",
        "\n",
        "points_dict = generate_points(n_points, range_points)\n",
        "segments_dict, get_idx_dict = find_segments(points_dict)"
      ],
      "metadata": {
        "id": "AThknVdCiRTr"
      },
      "execution_count": 88,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plot_graph(points_dict, segments_dict)"
      ],
      "metadata": {
        "id": "awUC50jvQCqm",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "outputId": "cbe9dad7-1b41-4ce4-b5b6-5445a413094a"
      },
      "execution_count": 89,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "find_solution(points_dict, segments_dict, get_idx_dict)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "kRoNUz7IkVn1",
        "outputId": "d4a6e0ee-87aa-4efc-842b-b58ea6d82f8c"
      },
      "execution_count": 90,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "No solution for this instance\n"
          ]
        }
      ]
    }
  ],
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}