half_chess_board.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/OptimizationExpert/Pyomo/blob/main/half_chess_board.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Developed by Alireza Soroudi\n",
        "alireza.soroudi@gmail.com\n",
        "\n",
        "Linkedin News letter : https://www.linkedin.com/newsletters/optimization-in-open-source-6874020019009859585/\n",
        "\n",
        "Git hub: https://github.com/OptimizationExpert/Pyomo"
      ],
      "metadata": {
        "id": "uAFN_QYBnmvs"
      }
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "w_3yuwV8XtMF",
        "outputId": "ec11f967-bf51-4592-f437-6b372679dfba",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "!pip install ortools\n",
        "from ortools.sat.python import cp_model # CP-SAT solver\n",
        "import numpy as np\n",
        "from random import randint\n",
        "import random\n",
        "from math import ceil\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt # Data visualization\n",
        "import time\n",
        "#plt.rcParams[\"figure.figsize\"] = (15,10)"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Requirement already satisfied: ortools in /usr/local/lib/python3.10/dist-packages (9.10.4067)\n",
            "Requirement already satisfied: absl-py>=2.0.0 in /usr/local/lib/python3.10/dist-packages (from ortools) (2.1.0)\n",
            "Requirement already satisfied: numpy>=1.13.3 in /usr/local/lib/python3.10/dist-packages (from ortools) (1.26.4)\n",
            "Requirement already satisfied: pandas>=2.0.0 in /usr/local/lib/python3.10/dist-packages (from ortools) (2.1.4)\n",
            "Requirement already satisfied: protobuf>=5.26.1 in /usr/local/lib/python3.10/dist-packages (from ortools) (5.28.0)\n",
            "Requirement already satisfied: immutabledict>=3.0.0 in /usr/local/lib/python3.10/dist-packages (from ortools) (4.2.0)\n",
            "Requirement already satisfied: python-dateutil>=2.8.2 in /usr/local/lib/python3.10/dist-packages (from pandas>=2.0.0->ortools) (2.8.2)\n",
            "Requirement already satisfied: pytz>=2020.1 in /usr/local/lib/python3.10/dist-packages (from pandas>=2.0.0->ortools) (2024.1)\n",
            "Requirement already satisfied: tzdata>=2022.1 in /usr/local/lib/python3.10/dist-packages (from pandas>=2.0.0->ortools) (2024.1)\n",
            "Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.10/dist-packages (from python-dateutil>=2.8.2->pandas>=2.0.0->ortools) (1.16.0)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "dic = {\n",
        "    (1, 1): 4, (1, 2): 4, (1, 3): 4, (1, 4): 4, (1, 5): 4, (1, 6): 4, (1, 7): 4, (1, 8): 4,\n",
        "    (2, 1): 4, (2, 2): 5, (2, 3): 4, (2, 4): 4, (2, 5): 4, (2, 6): 1, (2, 7): 1, (2, 8): 4,\n",
        "    (3, 1): 5, (3, 2): 5, (3, 3): 6, (3, 4): 6, (3, 5): 3, (3, 6): 3, (3, 7): 1, (3, 8): 1,\n",
        "    (4, 1): 5, (4, 2): 5, (4, 3): 5, (4, 4): 6, (4, 5): 3, (4, 6): 1, (4, 7): 1, (4, 8): 1,\n",
        "    (5, 1): 5, (5, 2): 8, (5, 3): 5, (5, 4): 7, (5, 5): 2, (5, 6): 1, (5, 7): 1, (5, 8): 1,\n",
        "    (6, 1): 8, (6, 2): 8, (6, 3): 7, (6, 4): 7, (6, 5): 2, (6, 6): 2, (6, 7): 2, (6, 8): 1,\n",
        "    (7, 1): 8, (7, 2): 8, (7, 3): 8, (7, 4): 8, (7, 5): 8, (7, 6): 8, (7, 7): 2, (7, 8): 1,\n",
        "    (8, 1): 8, (8, 2): 1, (8, 3): 1, (8, 4): 1, (8, 5): 1, (8, 6): 1, (8, 7): 1, (8, 8): 1\n",
        "}\n",
        "KOLORs = ['r','k','b','navy','gold','g','grey','brown','grey','orange']\n",
        "info = {}\n",
        "c= 0\n",
        "for (i,j),v in dic.items():\n",
        "  x,y = i,j\n",
        "  plt.scatter(1+y,8-x,s=100, c= KOLORs[v-1])\n",
        "  c+=1\n",
        "  info[c] = (1+y,8-x,v)\n",
        "plt.show()\n",
        "c"
      ],
      "metadata": {
        "id": "CFwTJ91NUzn9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        },
        "outputId": "3888bf39-1f48-49e2-9af1-89f11ade160b"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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PxjHT/5xsZll8Mk7b7jbC/cpfaMJhaGuDeNx9L33rj0gzy+Jxd71wgbXA9vyAmpCj+VM6Y/GVr3yFr371q6csW7ZsGS+//HLSTzjvMxZTEehvnD6gJpLYIABOEJYOQVFt6s+XiyzvQeR4hMa7G4lPxkkkkT9AgGBJkKHbhqgtr818gRlme35wz+w2Nrrvl4kkXgKBAASDMDQEtbWZri7zbM8PqAlZyJ+xMxYXXXQRv//972cf+/btS6vAtEW7p0/9J3NAxV3PjEF0Vyar8pflPeju62ZsciypgypAggRjk2Ps2q/8haK72z3zm8z7KbjrjY3BrgJpge35ATUhh/OnPFgUFxdzzjnnzD7e8Y53ZKKut2cMHO1Kb9ujO04/TZSPLO+BMYauZ9PLv+OZHfh8SZHnbM8P7i7cleZLYEf+vwSszw+oCTmeP+XB4sCBAyxevJjm5mY2bdrE66+/ftb1x8fHGRkZOeWRtqlhmBzg9OsJ5mLc7RJH0n/uXGF5D4bjwwwcHTjtmoK5GAwDRwc4Elf+fDc8DAMDqb83GuNudyTPW2B7fkBNyPH8KQ0WK1eu5Lvf/S4//OEP2blzJ6+99hrvf//7GR0dPeM2W7dupaamZvbR1NSUfrWJWPrbAkyduc68YXkPYhPzyz86ofz5LjbPl8BZ3q7ygu35ATUhx/OnNFisXbuW66+/nksuuYTW1lb27NlDJBLh0UcfPeM2W7ZsIRqNzj4GBwfnUW1l+tsCFFXNb/tcYHkPKkvnl7+qVPnzXeU8XwJVed4C2/MDakKO55/Xr5vW1tZywQUX0N/ff8Z1ysrKqK6uPuWRtqIGKAkxe4+GpDnudoH69J87V1jeg4ZgA6G60Ox9GpLl4BCqC1EfVP5819AAoVDqNxR0HHe7+jxvge35ATUhx/PPa7CIxWIMDAxw7rnnelXP2TkO1HWkt21dZ2Hc2tXyHjiOQ8eK9PJ3ruzM+9tc254f3F24I82XQGf+vwSszw+oCTmeP6X7WHzhC1/guuuu4/zzz+fw4cPccccd9PX18dJLL7Fw4cKk/gzdx8IDlvcg5fs4OAGCxYVzHwfb84NuYWB7fkBNKJT7WAwNDfGxj32MZcuWsWHDBhoaGvj5z3+e9FDhiaJa9xbVOMxdfsBdr7G3IA6osyzvQW15LT0benAch8Ac+QMEcHDo3dhbMAdV2/OD+77Y0+P+4BWY4yUQCLjr9fYWxvEElB9QE3I4f+F/V0hjLyxYk/7z5DLLe5Dsd2X0buxlTUj5C1GyX5PQ2wtrCrAFtucH1AQf8xf2d4WA+6VaS4dg0TYoaT71/5U0u8uXHirIA+osy3vQurSVoduG2PYX22iuOzV/c10z2/5iG4duO1SwB1Xb84P7nUpDQ7BtGzS/5SXQ3OwuP3SoMI8noPyAmpCD+fP3jMXJjHFv/DQ16v46ZaA+/y/OSZXlPTDGcCR+hNGJUapKq6gP1hfEhYrJsj0/uC+BI0fcX9GvqnIvfLepBbbnB9SEDOdP9vhdGIOFiIiIZFThfxQiIiIiOUeDhYiIiHhGg4WIiIh4RoOFiIiIeEaDhYiIiHhGg4WIiIh4RoOFiIiIeEaDhYiIiHhGg4WIiIh4RoOFiIiIeEaDhYiIiHhGg4WIiIh4RoOFiIiIeEaDhYiIiHhGg4WIiIh4RoOFiIiIeEaDhYiIiHhGg4WIiIh4RoOFiIiIeEaDhYiIiHhGg4WIiIh4RoOFiIiIeEaDhYiIiHhGg4WIiIh4RoOFiIiIeEaDhYiIiHhGg4WIiIh4RoOFiIiIeEaDhYiIiHhGg4WIiIh4pjjbBXjCGJgahkQMApVQ1ACOk+2q/GV7DyzPb4xhOD5MbCJGZWklDcEGHIvyg7sLDA9DLAaVldBg1y6gBoB6kCP58/uMxVQEjmyHgy3QvxAOLpn+d4u7fCqS7Qozz/YeWJ4/cjzC9p9vp6WrhYV3LWTJ9iUsvGshLV0tbP/5diLHI9kuMeMiEdi+HVpaYOFCWLLE/XdLi7s8Esl2hRlmfQNQD3Isv2OMMX4+4cjICDU1NUSjUaqrq9P/g2JhOLQezNj0gpNjTE9oTgW8qwcqW9N/nlxmew8szx/uD7P+0fWMTbr5zUn5nen8FSUV9GzooXVp4eUHCIdh/XoYm94FTn43m/lBraICenqgtRBbYH0DUA98zJ/s8Ts/z1jEwjDUBiaOezB562w0vczE3fViYf9rzDTbe2B5/nB/mLbdbcQn45jpf042syw+Gadtdxvh/sLKD+77aVsbxOPue+lbf0SaWRaPu+uFC60F1jcA9SBH88/rjMWdd97Jli1buOWWW9i2bVtS28z7jMVUBPobpw8oiSQ2CIAThKVDUFSb+vPlItt7YHn+yPEIjXc3Ep+Mk0gif4AAwZIgQ7cNUVtem/kCfRCJQGOj+36ZSGIXCAQgGIShIaitzXR1PrC+AagHWcif8TMWzz33HPfccw+XXHJJun9EeqLd06e+kzmg4K5nxiC6K5NV+cv2Hliev7uvm7HJsaSGCoAECcYmx9i1vzDyA3R3u2d+k3k/BXe9sTHYVSgtsL4BqAc5nD+twSIWi7Fp0ya+853vUFdX53VNZ2YMHO1Kb9ujO04/TZSPbO+B5fmNMXQ9m17+Hc/swOdLqjLCGOhKcxfYkf+7gBoA6kGO509rsNi8eTNtbW1ce+21c647Pj7OyMjIKY+0TQ3D5ACnf54+F+NulziS/nPnCtt7YHn+4fgwA0cHTrumYi4Gw8DRAY7E8zs/uL9NNzCQ+nujMe52R/K9BdY3APUgx/OnPFg8/PDD/OIXv2Dr1q1Jrb9161ZqampmH01NTSkXOSsRS39bgKnR+W2fC2zvgeX5YxPzyz86kd/5wf0V/fkYzfcWWN8A1IMcz5/SYDE4OMgtt9zCgw8+SHl5eVLbbNmyhWg0OvsYHBxMq1DAvfHRfBRVzW/7XGB7DyzPX1k6v/xVpfmdH9z7/sxHVb63wPoGoB7keP6UBosXXniBN998k/e+970UFxdTXFzM3r172bFjB8XFxUxNTZ22TVlZGdXV1ac80lbUACUhZu9RkDTH3S5Qn/5z5wrbe2B5/oZgA6G60Ox9KpLl4BCqC1EfzO/84N5MMBRK/YaCjuNuV5/vLbC+AagHOZ4/pcHimmuu4cUXX6Svr2/2cfnll7Np0yb6+vooKirKVJ0ux4G6jvS2ressjFu72t4Dy/M7jkPHivTyd67sLIjbfDsOdKS5C3Tm/y6gBoB6kOP5533nzQ9+8INceumluo+Fn2zvgeX5U76PhRMgWKz7WBTSLQzUANSDQryPRdYU1bq3aMZh7vID7nqNvQVxQJllew8sz19bXkvPhh4cxyEwR/4AARwcejf2FsxQAe77Yk+P+4NXYI5dIBBw1+vtLYzjCaAGgHqQw/nnPVj89Kc/TfpshWcqW6HxSfenUBxO/7x9epkThKY9sGCNv/X5wfYeWJ6/dWkrT378SYIlQZzpf042syxYEmTPpj2sCRVWfnC/9uDJJ90fwhzn9LO7M8uCQdizB9YUWgusbwDqQY7mz78zFjMqW91T24u2QUnzqf+vpNldvvRQwR1QTmF7DyzP37q0laHbhtj2F9torjs1f3NdM9v+YhuHbjtUkEPFjNZW98zutm3Q/JZdoLnZXX7oUOEdT2ZZ3wDUgxzMn7/fbnoyY9wbH02Nur9OGKjP/4tzUmV7DyzPb4zhSPwIoxOjVJVWUR+sL4gLNVNhjHvfn9FR97fp6u3aBdQAUA8ynD/Z43dhDBYiIiKSUYV78aaIiIjkLA0WIiIi4hkNFiIiIuIZDRYiIiLiGQ0WIiIi4hkNFiIiIuIZDRYiIiLiGQ0WIiIi4hkNFiIiIuIZDRYiIiLiGQ0WIiIi4hkNFiIiIuIZDRYiIiLiGQ0WIiIi4hkNFiIiIuIZDRYiIiLiGQ0WIiIi4hkNFiIiIuIZDRYiIiLiGQ0WIiIi4hkNFiIiIuIZDRYiIiLiGQ0WIiIi4hkNFiIiIuIZDRYiIiLiGQ0WIiIi4hkNFiIiIuIZDRYiIiLiGQ0WIiIi4hkNFiIiIuKZ4mwX4AljYGoYEjEIVEJRAzhOtqvylTGG8UiEE2NjFFdUUFZbi2NTDyzfB4wxxONxJiYmKC0tJRgM2vX3j9uD4eFhYrEYlZWVNDQ02NUDY2B4GGIxqKyEBrteA4B6kCP583uwmIpAtBuOdsHkwB+Xl4SgrgNq2qGoNlvV+WJiZISDjz/Oqw8+SGxwcHZ5ZVMTF2zaRPO6dZRWV2exwgyzfB84fvw4fX19PPvssxw9enR2eV1dHStWrODSSy+lvLw8ixVmXiQSobu7m66uLgYG/rgPhEIhOjo6aG9vp7a2NnsFZlokAt3d0NUFJ+UnFIKODmhvh0LOD+pBjuV3jDHGt2cDRkZGqKmpIRqNUj2fA14sDIfWgxmbXnByjOkJzamAd/VAZWv6z5PDDu/bx75bb+XE8ePugpP/Kqen1OLyclZv28bi1auzUGGGWb4P9Pf38+ijjzI5OXnGdUpKStiwYQNLly71sTL/hMNh1q9fz9iYuw+c/HY2c7aioqKCnp4eWlsLbx8gHIb162E6/9u9B1BRAT09UIj5QT3wMX+yx+/8vMYiFoahNjBx3IPJW2ej6WUm7q4XC/tfY4Yd3rePvTff7A4Vxpy6M8HsshPHj7P35ps5vG9fdgrNFMv3gf7+fnbv3n3WoQJgcnKS3bt309/f71Nl/gmHw7S1tRGPxzHG8NafkWaWxeNx2traCIcLax8gHIa2NojHz/oeQDzurldo+UE9yNH8KZ2x2LlzJzt37uS3v/0tABdddBFf/vKXWbt2bdJPOO8zFlMR6G+cPqAkktggAE4Qlg4VzCnxiZERvvehD/1xqJiL41BcXs5Hn366MD4WsXwfOH78OHffffecQ8XJSkpKuO222wrmY5FIJEJjYyPxeJxEYu59IBAIEAwGGRoaKoyPRSIRaGx0DxhJ5CcQgGAQhoYK5yMB23uQhfwZOWPR2NjInXfeyQsvvMDzzz/Phz70IdatW8dvfvObtIpMS7R7+tR3MgcU3PXMGER3ZbIqXx18/PHkhwqYPXPx2hNPZLYwv1i+D/T19aU0VIB75mL//v0Zqsh/3d3djI2NJTVUACQSCcbGxti1qzD2Abq73VPfSeYnkXDXL5T8oB7kcP55X2NRX1/PXXfdxac+9amk1p/XGQtj4GALTB7k9FPfZ+NASTM0H8j7K4SNMXx/7VpiQ0PJDxYAjkNlYyPXPfVUfl8pb/k+YIyhq6vrlAs1k1VXV0dHR0d+//3j9qClpYWDBw+e9vHH2TiOQ3NzMwcOHMjvHhgDLS1w8GDK7wE0N8OB/H4NAOpBlvJn/BqLqakpHn74YY4dO8aVV155xvXGx8cZGRk55ZG2qeHpK/9TnYWMu13iSPrPnSPGIxH3tz9SnQeNITY4yEQ0mpnC/GL5PhCPx9MaKgCOHj1KPB73uCL/DQ8PMzAwkNJQAe5AMjAwwJEj+b0PMDzsXvmfxnsAAwOQ7/lBPcjx/CkPFi+++CKVlZWUlZXxuc99jscee4z3vOc9Z1x/69at1NTUzD6amprSrzYRS39bgKnR+W2fA07MXPmbpsljxzyqJEss3wcmJiayun0uiMXmtw+Mjub3PsA885Pv+UE9yPH8KQ8Wy5Yto6+vj2eeeYabb76Z9vZ2XnrppTOuv2XLFqLR6Oxj8KR7LaRebWX62wIUVc1v+xxQXFExr+1LFizwqJIssXwfKC0tzer2uaCycn77QFVVfu8DzDM/+Z4f1IMcz5/yYFFaWsrSpUt53/vex9atW1m+fDnbt28/4/plZWVUV1ef8khbUYN74yNS/WzIcbcL1Kf/3DmirLaWyqam1D8fcxwqm5ooranJTGF+sXwfCAaD1NXVpbVtXV0dwWDQ44r819DQQCgUSvk6CcdxCIVC1Nfn9z5AQ4N746M03gMIhSDf84N6kOP5530fi0Qiwfj4uBe1zM1x3LsppqOuM78v1pnmOA4XbNqU1rbLbrghvy9aA+v3AcdxWLFiRVrbrly5Mv///nF70NGR3j7Q2dmZ/z1wHPduiunozP/XAKAe5Hj+lAaLLVu28LOf/Yzf/va3vPjii2zZsoWf/vSnbErzQJeWmnb3bopJlx5w16+5MZNV+ap53TqKy8uT3zkCAYrLy1nykY9ktjC/WL4PXHrppZSUlCS9vuM4lJSUsHz58gxW5a/29nYqKioIBJLbBwKBABUVFdx4Y2HsA7S3u3dTTDI/gYC7fqHkB/Ugh/OnNFi8+eab3HjjjSxbtoxrrrmG5557jnA4zIc//OFM1Xe6olr3Fs04zF1+wF2vsbcgbow0o7S6mtXbtrk/ec01XDgODvD+7dsL4+ZYYP0+UF5ezoYNG1L6yXvjxo0Fc3MsgNraWnp6enAcZ87hIhAI4DgOvb29hXFzLHBvcNTT477+5zqwBALuer29hXFjqBm29yCH8xf+d4U09sKCNek/Tw5L9rtC3r99O+euWpWFCjPM8n0g2e8K2bhxI6FQyMfK/JPsd4X09vayZk3h7QNJf09Eby8UYn5QD3zMn+zxO38HC5j+ZstdcHTH23yzZef0N1vm+cWKc5gYGeG1J57glQceOO3bTZfdcANL1q2jNN+vgD4by/eB48ePs3//fp555pnTvt105cqVLF++vKDOVLydSCTCrl272LFjx2nfbtrZ2Ul7ezs1+X7R8tlEIu7dFHfsOP2bLTs73VPmhZwf1AOf8tsxWMwwxr3x0dSo++uEgfr8vzgnRcYYJqJRJo8do2TBAkpravL/IrVUWL4PzHzZ1sTEBKWlpQSDQbv+/nF7cOTIEUZHR6mqqqK+vt6uHhjj3vhodNT9dcJ6u14DgHqQ4fx2DRYiIiKSUYX9tekiIiKSkzRYiIiIiGc0WIiIiIhnNFiIiIiIZzRYiIiIiGc0WIiIiIhnNFiIiIiIZzRYiIiIiGc0WIiIiIhnNFiIiIiIZzRYiIiIiGc0WIiIiIhnNFiIiIiIZzRYiIiIiGc0WIiIiIhnNFiIiIiIZzRYiIiIiGc0WIiIiIhnNFiIiIiIZzRYiIiIiGc0WIiIiIhnNFiIiIiIZzRYiIiIiGc0WIiIiIhnNFiIiIiIZzRYiIiIiGc0WIiIiIhnNFiIiIiIZzRYiIiIiGc0WIiIiIhnirNdgBeMMYxHIpwYG6O4ooKy2locx8l2Wb6yvQfGGOLxOBMTE5SWlhIMBpXfovzg9mB4eJhYLEZlZSUNDQ1W9cD2/KAeYAwMD0MsBpWV0NAAWcif14PFxMgIBx9/nFcffJDY4ODs8sqmJi7YtInmdesora7OYoWZZ3sPjh8/Tl9fH88++yxHjx6dXV5XV8eKFSu49NJLKS8vz2KFmWV7foBIJEJ3dzddXV0MDAzMLg+FQnR0dNDe3k5tbW32Csww2/ODekAkAt3d0NUFJ+UnFIKODmhvBx/zO8YY49uzASMjI9TU1BCNRqmexwHv8L597Lv1Vk4cP+4uODnG9IRWXF7O6m3bWLx69XxKzlm296C/v59HH32UycnJM65TUlLChg0bWLp0qY+V+cP2/ADhcJj169czNjYGuD+xzpj5SbWiooKenh5aW1uzUmMm2Z4f1APCYVi/Hqbzv91xgIoK6OmBeeZP9vidl9dYHN63j7033+weUI05tZEwu+zE8ePsvflmDu/bl51CM8j2HvT397N79+6zHlQBJicn2b17N/39/T5V5g/b84N7QGlrayMej2OM4a0/I80si8fjtLW1EQ6Hs1RpZtieH9QDwmFoa4N4/KzHAeJxdz2f8qd0xmLr1q309vby8ssvEwwGueqqq/jGN77BsmXLkn7C+Z6xmBgZ4Xsf+tAfD6hzcRyKy8v56NNPF8xHArb34Pjx49x9991zHlRPVlJSwm233VYQHwvYnh/cU9+NjY3E43ESicSc6wcCAYLBIENDQwVxStz2/KAeEIlAY6M7NCSRn0AAgkEYGkr7Y5GMnLHYu3cvmzdv5uc//zk/+tGPmJycZM2aNRw7diytItNx8PHHkz+gwuxP7a898URmC/OR7T3o6+tL6aAK7k/u+/fvz1BF/rI9P0B3dzdjY2NJHVAAEokEY2Nj7Nq1K8OV+cP2/KAe0N3tfvyRZH4SCXd9H/LP6xqL//3f/2XRokXs3buXD3zgA0ltM58zFsYYvr92LbGhoeQPqgCOQ2VjI9c99VTeXyFsew+MMXR1dZ1yoWKy6urq6OjoUP48zg9uD1paWjh48OBpp77PxnEcmpubOXDgQF73wPb8oB5gDLS0wMGDKR8HaG6GAwfS+m0RX66xiEajANTX159xnfHxcUZGRk55pGs8EnF/8yHVWcgYYoODTEzXm89s70E8Hk/roApw9OhR4vG4xxX5y/b8AMPDwwwMDKR0QAH3YDQwMMCRI0cyVJk/bM8P6gHDw+5vf6RxHGBgADKcP+3BIpFIcOutt7Jq1SouvvjiM663detWampqZh9NTU3pPiUnZq56TdOkjx/ZZIrtPZiYmMjq9tlme36AWCw2r+1HR0c9qiQ7bM8P6gHzzE+G86c9WGzevJlf//rXPPzww2ddb8uWLUSj0dnH4En3WkhVcUVF2tsClCxYMK/tc4HtPSgtLc3q9tlme36AysrKeW1fVVXlUSXZYXt+UA+YZ34ynD+tweLzn/88P/jBD/jP//xPGhsbz7puWVkZ1dXVpzzSVVZbS2VTU+qfDTkOlU1NlNbUpP3cucL2HgSDQerq6tLatq6ujmAw6HFF/rI9P0BDQwOhUCjlz8gdxyEUCp31o9t8YHt+UA9oaHBvfpXGcYBQCDKcP6XBwhjD5z//eR577DGefvpplixZkqm63pbjOFywaVNa2y674Yb8vlhnmu09cByHFStWpLXtypUrlT/P84Pbg46OjrS27ezszPse2J4f1AMcx72jZjo6OzN+m++UBovNmzfzwAMPsHv3bqqqqnjjjTd44403fL0grHndOorLy5NvTCBAcXk5Sz7ykcwW5iPbe3DppZdSUlKS9PqO41BSUsLy5cszWJV/bM8P0N7eTkVFBYFAcm9hgUCAiooKbrzxxgxX5g/b84N6QHu7e0fNJPMTCLjr+5A/pcFi586dRKNRPvjBD3LuuefOPh555JFM1Xea0upqVm/b5k6ccx1YHQcHeP/27QVxY6gZtvegvLycDRs2pPRTx8aNGwvm5lC25weora2lp6cHx3HmPLAEAgEcx6G3t7cwboyE8oN6QG2te5tux5l7uAgE3PV6e335zpCUPwp5u8cnPvGJDJX39havXs3VO3f+8af2t77BTi8rLi/ng9/+NueuWuVrfX6wvQdLly7l4x//+Jw/uZeUlLBp0yZCoZBPlfnD9vwAra2tPPnkk7Pf5PrWQWtmWTAYZM+ePaxZsyZLlWaG7flBPaC1FZ580r2j5lmOAwSDsGcP+JQ/b7+EDNxbW7/2xBO88sADp32z57IbbmDJunWU5vvVv3OwvQfHjx9n//79PPPMM6d9u+fKlStZvnx5Qf2k/la25wf31s67du1ix44dp32zZWdnJ+3t7dTk+UXLZ2N7flAPiETcO2ru2HH6t5t2drofm3iQP9njd14PFjOMMUxEo0weO0bJggWU1tTk/8U5KbK9BzNfNDQxMUFpaensTzC2sD0/uD04cuQIo6OjVFVVUV9fb1UPbM8P6gHGuDe/Gh11f6W0vt7TCzWtGixEREQkswr6a9NFREQkN2mwEBEREc9osBARERHPaLAQERERz2iwEBEREc9osBARERHPaLAQERERz2iwEBEREc9osBARERHPaLAQERERz2iwEBEREc9osBARERHPaLAQERERz2iwEBEREc9osBARERHPaLAQERERz2iwEBEREc9osBARERHPaLAQERERz2iwEBEREc9osBARERHPaLAQERERz2iwEBEREc9osBARERHPaLAQERERz2iwEBEREc9osBARERHPaLAQERERz2iwEBEREc9osBARERHPFGe7AC8YYxiPRDgxNkZxRQVltbU4jpPtsnxlew+U3+78oB7Ynh/cHgwPDxOLxaisrKShocGuHhgDw8MQi0FlJTQ0QBby5/VgMTEywsHHH+fVBx8kNjg4u7yyqYkLNm2ied06Squrs1hh5tneA+W3Oz+oB7bnB4hEInR3d9PV1cXAwMDs8lAoREdHB+3t7dTW1mavwEyLRKC7G7q64KT8hELQ0QHt7eBjfscYY3x7NmBkZISamhqi0SjV89jZD+/bx75bb+XE8ePugpNjTE9oxeXlrN62jcWrV8+n5Jxlew+U3+78oB7Ynh8gHA6zfv16xsbGAPesxYyZsxUVFRX09PTQ2tqalRozKhyG9ethOv/b7QNUVEBPD8wzf7LH77y8xuLwvn3svflm98VkzKmNhNllJ44fZ+/NN3N4377sFJpBtvdA+e3OD+qB7fnBHSra2tqIx+MYY3jrz8kzy+LxOG1tbYTD4SxVmiHhMLS1QTx+1n2AeNxdz6f8KZ+x+NnPfsZdd93FCy+8wO9//3see+wxPvrRjya9/XzPWEyMjPC9D33ojy+muTgOxeXlfPTppwvmdKDtPVB+u/ODemB7fnA//mhsbCQej5NIJOZcPxAIEAwGGRoaKoyPRSIRaGx0h4Yk8hMIQDAIQ0NpfyySsTMWx44dY/ny5XzrW99Kq7D5Ovj448m/mGB2Yn/tiScyW5iPbO+B8tudH9QD2/MDdHd3MzY2ltRQAZBIJBgbG2PXrl0Zrswn3d3uxx9J5ieRcNf3IX/Kg8XatWv5p3/6J/76r/86E/WclTGGVx98MK1tX3nggdNOk+Uj23ug/HbnB/XA9vzg9qCrqyutbXfs2JH/PTDGvVAzHTt2JD+Qpinj11iMj48zMjJyyiPtPysSca96TrUpxhAbHGQiGk37uXOF7T1Qfrvzg3pge36A4eFhBgYGUh4QjDEMDAxw5MiRDFXmk+Fh97c/0tgHGBiADOfP+GCxdetWampqZh9NTU1p/1knZq56TdPksWPz2j4X2N4D5bc7P6gHtucHiMVi89p+dHTUo0qyZJ75yXD+jA8WW7ZsIRqNzj4GT/o961QVV1TMq5aSBQvmtX0usL0Hym93flAPbM8PUFlZOa/tq6qqPKokS+aZnwznz/hgUVZWRnV19SmPtP+s2loqm5pSv5OY41DZ1ERpTU3az50rbO+B8tudH9QD2/MDNDQ0EAqFUr6rpuM4hEIh6uvrM1SZTxoa3JtfpbEPEApBhvPn1X0sHMfhgk2b0tp22Q03FMStXW3vgfLbnR/UA9vzg9uDjo6OtLbt7OzM/x44jntHzXR0dmb8Nt8pDxaxWIy+vj76+voAeO211+jr6+P111/3ura31bxuHcXl5ck3JhCguLycJR/5SGYL85HtPVB+u/ODemB7foD29nYqKioIBJI7jAUCASoqKrjxxhszXJlP2tvdO2ommZ9AwF3fh/wpDxbPP/88l112GZdddhkAt912G5dddhlf/vKXPS/u7ZRWV7N62zZ34pzrReU4OMD7t28vmJvCgHqg/HbnB/XA9vwAtbW19PT04DjOnMNFIBDAcRx6e3sL4+ZY4N7kqqfH/fufa7gIBNz1ent9+c6QlAeLD37wg7O3ST358d3vfjcD5b29xatXc/XOnX+c2N/6wppeVlxezge//W3OXbXKt9r8YnsPlN/u/KAe2J4foLW1lSeffJJgMIjjOKd9xDGzLBgMsmfPHtasWZOlSjOktRWefNK9o+ZZ9gGCQdizB3zKn7dfQgbubW1fe+IJXnnggdO+1W/ZDTewZN06SvP96t852N4D5bc7P6gHtucH9/beu3btYseOHad9u2lnZyft7e3UFMBFq2cUibh31Nyx4/RvN+3sdD828SB/ssfvvB4sZhhjmIhGmTx2jJIFCyitqcn/i3NSZHsPlN/u/KAe2J4f3B4cOXKE0dFRqqqqqK+vt6sHxrg3vxoddX+ltL7e0ws1rRosREREJLMK+mvTRUREJDdpsBARERHPaLAQERERz2iwEBEREc9osBARERHPaLAQERERz2iwEBEREc9osBARERHPaLAQERERz2iwEBEREc9osBARERHPaLAQERERz2iwEBEREc9osBARERHPaLAQERERz2iwEBEREc9osBARERHPaLAQERERz2iwEBEREc9osBARERHPaLAQERERz2iwEBEREc9osBARERHPaLAQERERz2iwEBEREc9osBARERHPaLAQERERz2iwEBEREc9osBARERHPaLAQERERzxRnuwAvGGMYj0Q4MTZGcUUFZbW1OI6T7bL8ZQwMD0MsBpWV0NAANvVA+e3OD+qB7flBPciR/Hl9xmJiZISX77+f769dS+/q1TyxZg29q1fz/bVrefn++5kYGcl2iZkXicD27dDSAgsXwpIl7r9bWtzlkUi2K8ws5bc7P6gHtucH9SDH8jvGGOPnE46MjFBTU0M0GqW6ujrtP+fwvn3su/VWThw/7i44Ocb0hFZcXs7qbdtYvHr1fErOXeEwrF8PY2Puf79ND6iogJ4eaG31v75MU36784N6YHt+UA98zJ/s8Tsvz1gc3rePvTff7A4VxpzaSJhdduL4cfbefDOH9+3LTqGZFA5DWxvE42ftAfG4u144nJ06M0X57c4P6oHt+UE9yNH8aZ2x+Na3vsVdd93FG2+8wfLly+nq6mLFihVJbTvfMxYTIyN870Mf+uNQMRfHobi8nI8+/TSl8zhDklMiEWhsdHeWRGLu9QMBCAZhaAhqazNdXeYpv935QT2wPT+oB1nIn7EzFo888gi33XYbd9xxB7/4xS9Yvnw5ra2tvPnmm2kVmqqDjz+e/FABs2cuXnviicwW5qfubve0VzI7E7jrjY3Brl2Zrcsvym93flAPbM8P6kEO50/5jMXKlSu54oor+OY3vwlAIpGgqamJjo4Obr/99jm3n88ZC2MM31+7ltjQUPKDBYDjUNnYyHVPPZX/vy1ijHtBzsGDKfeA5mY4cCC/r5JWfrvzg3pge35QD7KUPyNnLCYmJnjhhRe49tpr//gHBAJce+21/M///M/bbjM+Ps7IyMgpj3SNRyLEBgdTaySAMcQGB5mIRtN+7pwxPAwDA2n1gIEBOHIkM3X5Rfntzg/qge35QT3I8fwpDRb/93//x9TUFO985ztPWf7Od76TN95442232bp1KzU1NbOPpqamtIs9MXPVa5omjx2b1/Y5IRab3/ajo97UkS3KP7/t8z0/qAe25wf1IMfzZ/y3QrZs2UI0Gp19DA4Opv1nFVdUzKuWkgUL5rV9TqisnN/2VVXe1JEtyj+/7fM9P6gHtucH9SDH86c0WLzjHe+gqKiIP/zhD6cs/8Mf/sA555zzttuUlZVRXV19yiNdZbW1VDY1pf7ZkONQ2dREaU1N2s+dMxoaIBRKqweEQlBfn5m6/KL8ducH9cD2/KAe5Hj+lAaL0tJS3ve+9/GTn/xkdlkikeAnP/kJV155pefFvZXjOFywaVNa2y674Yb8v3AT3B2joyO9bTs78/uCJVB+2/ODemB7flAPcjx/yr8V8sgjj9De3s4999zDihUr2LZtG48++igvv/zyaddevB3f72MRCFBcVqb7WOj3t5W/UPKDemB7flAPCuk+Fhs3buSf//mf+fKXv8yll15KX18fP/zhD5MaKrxQWl3N6m3b3LMPc01djoMDvH/79sIZKsDdKXp63PyBOf4KAwF3vd7ewngxgfLbnh/UA9vzg3qQw/kL/rtC3r99O+euWjWfknNXsveI7+2FNWv8ry/TlN/u/KAe2J4f1AMf8yd9/DY+i0ajBjDRaHTef9Z4NGpevv9+83hrq3nwPe+ZfTze2mpevv9+Mz4y4kHFOe7oUWO2bzcmFJq5K7z7CIXc5ZFItivMLOW3O78x6oHt+Y1RD3zKn+zxO2/PWJzMGMNENMrksWOULFhAaU1NYVyomQpj3JuejI66v0pUX5//FyilQvntzg/qge35QT3IcP5kj98FMViIiIhIZhX016aLiIhIbtJgISIiIp7RYCEiIiKe0WAhIiIintFgISIiIp7RYCEiIiKeKfb7CWd+u3VkZMTvpxYREZE0zRy357pLhe+DxejoKABNTU1+P7WIiIjM0+joKDU1NWf8/77fICuRSHD48GGqqqo8vTvmyMgITU1NDA4OWnvjLdt7oPx25wf1wPb8oB5kMr8xhtHRURYvXkzgLF985vsZi0AgQGNjY8b+/Orqait3ppPZ3gPltzs/qAe25wf1IFP5z3amYoYu3hQRERHPaLAQERERzxTMYFFWVsYdd9xBWVlZtkvJGtt7oPx25wf1wPb8oB7kQn7fL94UERGRwlUwZyxEREQk+zRYiIiIiGc0WIiIiIhnNFiIiIiIZ/J+sNi6dStXXHEFVVVVLFq0iI9+9KO88sor2S7LNzt37uSSSy6ZvRnKlVdeyVNPPZXtsrLmzjvvxHEcbr311myX4puvfOUrOI5zyuPCCy/Mdlm+OnToEDfccAMNDQ0Eg0H+9E//lOeffz7bZfnm3e9+92n7gOM4bN68Odul+WJqaop//Md/ZMmSJQSDQUKhEF/72tfm/E6LQjI6Osqtt97K+eefTzAY5KqrruK5557LSi2+33nTa3v37mXz5s1cccUVnDhxgn/4h39gzZo1vPTSSyxYsCDb5WVcY2Mjd955Jy0tLRhj6O7uZt26dfzyl7/koosuynZ5vnruuee45557uOSSS7Jdiu8uuugifvzjH8/+d3Fx3r+0k3b06FFWrVrFn//5n/PUU0+xcOFCDhw4QF1dXbZL881zzz3H1NTU7H//+te/5sMf/jDXX399Fqvyzze+8Q127txJd3c3F110Ec8//zyf/OQnqampobOzM9vl+eLTn/40v/71r7n//vtZvHgxDzzwANdeey0vvfQS73rXu/wtxhSYN9980wBm79692S4la+rq6sy//du/ZbsMX42OjpqWlhbzox/9yFx99dXmlltuyXZJvrnjjjvM8uXLs11G1nzxi180q1evznYZOeWWW24xoVDIJBKJbJfii7a2NnPTTTedsuxv/uZvzKZNm7JUkb/GxsZMUVGR+cEPfnDK8ve+973mS1/6ku/15P1HIW8VjUYBqK+vz3Il/puamuLhhx/m2LFjXHnlldkux1ebN2+mra2Na6+9NtulZMWBAwdYvHgxzc3NbNq0iddffz3bJfnmiSee4PLLL+f6669n0aJFXHbZZXznO9/JdllZMzExwQMPPMBNN93k6Rc95rKrrrqKn/zkJ7z66qsA7N+/n3379rF27dosV+aPEydOMDU1RXl5+SnLg8Eg+/bt878g30eZDJqamjJtbW1m1apV2S7FV7/61a/MggULTFFRkampqTFPPvlktkvy1UMPPWQuvvhiE4/HjTHGujMWe/bsMY8++qjZv3+/+eEPf2iuvPJKc95555mRkZFsl+aLsrIyU1ZWZrZs2WJ+8YtfmHvuuceUl5eb7373u9kuLSseeeQRU1RUZA4dOpTtUnwzNTVlvvjFLxrHcUxxcbFxHMd8/etfz3ZZvrryyivN1VdfbQ4dOmROnDhh7r//fhMIBMwFF1zgey0FNVh87nOfM+eff74ZHBzMdim+Gh8fNwcOHDDPP/+8uf3228073vEO85vf/CbbZfni9ddfN4sWLTL79++fXWbbYPFWR48eNdXV1dZ8HFZSUmKuvPLKU5Z1dHSYP/uzP8tSRdm1Zs0a81d/9VfZLsNXDz30kGlsbDQPPfSQ+dWvfmV27dpl6uvrrRou+/v7zQc+8AEDmKKiInPFFVeYTZs2mQsvvND3WgpmsNi8ebNpbGw0Bw8ezHYpWXfNNdeYz372s9kuwxePPfbY7Atp5gEYx3FMUVGROXHiRLZLzIrLL7/c3H777dkuwxfnnXee+dSnPnXKsn/91381ixcvzlJF2fPb3/7WBAIB873vfS/bpfiqsbHRfPOb3zxl2de+9jWzbNmyLFWUPbFYzBw+fNgYY8yGDRvMX/7lX/peQ95fY2GM4fOf/zyPPfYYTz/9NEuWLMl2SVmXSCQYHx/Pdhm+uOaaa3jxxRfp6+ubfVx++eVs2rSJvr4+ioqKsl2i72KxGAMDA5x77rnZLsUXq1atOu1XzF999VXOP//8LFWUPffddx+LFi2ira0t26X4amxsjEDg1MNZUVERiUQiSxVlz4IFCzj33HM5evQo4XCYdevW+V5D3v9O2ubNm9m9ezePP/44VVVVvPHGGwDU1NQQDAazXF3mbdmyhbVr13LeeecxOjrK7t27+elPf0o4HM52ab6oqqri4osvPmXZggULaGhoOG15ofrCF77Addddx/nnn8/hw4e54447KCoq4mMf+1i2S/PF3/3d33HVVVfx9a9/nQ0bNvDss89y7733cu+992a7NF8lEgnuu+8+2tvbrfp1Y4DrrruO//f//h/nnXceF110Eb/85S+5++67uemmm7Jdmm/C4TDGGJYtW0Z/fz9///d/z4UXXsgnP/lJ/4vx/RyJx4C3fdx3333ZLs0XN910kzn//PNNaWmpWbhwobnmmmvMf/zHf2S7rKyy7RqLjRs3mnPPPdeUlpaad73rXWbjxo2mv78/22X56vvf/765+OKLTVlZmbnwwgvNvffem+2SfBcOhw1gXnnllWyX4ruRkRFzyy23mPPOO8+Ul5eb5uZm86UvfcmMj49nuzTfPPLII6a5udmUlpaac845x2zevNlEIpGs1KKvTRcRERHP5P01FiIiIpI7NFiIiIiIZzRYiIiIiGc0WIiIiIhnNFiIiIiIZzRYiIiIiGc0WIiIiIhnNFiIiIiIZzRYiIiIiGc0WIiIiIhnNFiIiIiIZzRYiIiIiGf+P70WX4NY4/q1AAAAAElFTkSuQmCC\n"
          },
          "metadata": {}
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "64"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "N = len(dic)\n",
        "info_color = {}\n",
        "for c,(x,y,v) in info.items():\n",
        "  info_color[v] = info_color.get(v,[])+[c]\n",
        "X= {x for (x,y,c) in info.values()}\n",
        "Y= {y for (x,y,c) in info.values()}\n",
        "\n",
        "sorted_y = sorted(Y)\n",
        "X,Y,sorted_y"
      ],
      "metadata": {
        "id": "yU46bQJO2WvI",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e56a1c32-e737-4c72-dbd9-06405fbdc0a8"
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "({2, 3, 4, 5, 6, 7, 8, 9}, {0, 1, 2, 3, 4, 5, 6, 7}, [0, 1, 2, 3, 4, 5, 6, 7])"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yyF-IzKMcyrj",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "49ec35e0-ce4e-476d-9ee6-38eaca1247d6"
      },
      "source": [
        "def dist(i,j):\n",
        "  return int((info[i][0]-info[j][0])**2+(info[i][1]-info[j][1])**2)\n",
        "class VarArraySolutionPrinter(cp_model.CpSolverSolutionCallback):\n",
        "    \"\"\"Print intermediate solutions.\"\"\"\n",
        "\n",
        "    def __init__(self, variables):\n",
        "        cp_model.CpSolverSolutionCallback.__init__(self)\n",
        "        self.__variables = variables\n",
        "        self.__solution_count = 0\n",
        "        self.__save_solution = {}\n",
        "\n",
        "\n",
        "\n",
        "    def on_solution_callback(self):\n",
        "        self.__solution_count += 1\n",
        "        #print(self.__solution_count , [self.Value(self.__variables[i]) for i in self.__variables])\n",
        "        self.__save_solution[self.__solution_count] = {i:self.Value(self.__variables[i]) for i in self.__variables}\n",
        "        if self.__solution_count == 7:\n",
        "          self.StopSearch()\n",
        "\n",
        "    def solution_count(self):\n",
        "        return self.__solution_count\n",
        "    def solution_save(self):\n",
        "        return self.__save_solution\n",
        "\n",
        "\n",
        "model = cp_model.CpModel()\n",
        "solver = cp_model.CpSolver()\n",
        "nodes = range(1,N+1)\n",
        "U = {c:model.NewBoolVar(f\"blackcell_{c}\") for c in nodes}\n",
        "Z = {(i,j):model.NewBoolVar(f\"Z_{i}_{j}\") for i in nodes for j in nodes if dist(i,j) == 1}\n",
        "flow = {(i,j):model.NewIntVar(0,int(N/2), f\"flow_{i}_{j}\") for i in nodes for j in nodes if dist(i,j) == 1}\n",
        "\n",
        "\n",
        "W = {(i,j):model.NewBoolVar(f\"W_{i}_{j}\") for i in nodes for j in nodes if dist(i,j) == 1}\n",
        "flowW = {(i,j):model.NewIntVar(0,int(N/2), f\"flowW_{i}_{j}\") for i in nodes for j in nodes if dist(i,j) == 1}\n",
        "\n",
        "blacks = {c:model.NewBoolVar(f\"blacks_{c}\") for c in nodes}\n",
        "whites = {c:model.NewBoolVar(f\"whites_{c}\") for c in nodes}\n",
        "\n",
        "colors = info_color.keys()\n",
        "\n",
        "for (i,j),v in Z.items():\n",
        "  model.Add(v<=U[i])\n",
        "  model.Add(v<=U[j])\n",
        "\n",
        "for (i,j),vw in W.items():\n",
        "  model.Add(vw<=1-U[i])\n",
        "  model.Add(vw<=1-U[j])\n",
        "  model.AddAtMostOne([vw, Z[i,j]])\n",
        "\n",
        "for i in nodes:\n",
        "  model.Add(int(N/2)*blacks[i] - U[i] == sum(flow[i,j]-flow[j,i] for j in nodes if (i,j) in flow) )\n",
        "\n",
        "for i in nodes:\n",
        "  model.Add(int(N/2)*whites[i] - (1-U[i]) == sum(flowW[i,j]-flowW[j,i] for j in nodes if (i,j) in flowW) )\n",
        "\n",
        "for i in nodes:\n",
        "  model.Add(blacks[i] + whites[i] <= 1)\n",
        "  model.Add(blacks[i]  <= U[i])\n",
        "  model.Add(whites[i]  <= 1-U[i])\n",
        "\n",
        "\n",
        "expressions = [blacks[n] for n in nodes ]\n",
        "model.AddExactlyOne(expressions)\n",
        "\n",
        "expressions = [whites[n] for n in nodes ]\n",
        "model.AddExactlyOne(expressions)\n",
        "\n",
        "for (i,j),v in Z.items():\n",
        "  model.Add(flow[i,j] == 0).OnlyEnforceIf(v.Not())\n",
        "\n",
        "for (i,j),vw in W.items():\n",
        "  model.Add(flowW[i,j] == 0).OnlyEnforceIf(vw.Not())\n",
        "\n",
        "\n",
        "expressions_up = [U[n] for n in nodes if info[n][1] >= 0.5*(max(Y)+min(Y))]\n",
        "expressions_down = [U[n] for n in nodes if info[n][1] < 0.5*(max(Y)+min(Y))]\n",
        "model.Add(sum(expressions_up) >= sum(expressions_down) )\n",
        "\n",
        "\n",
        "expressions = [U[n] for n in nodes ]\n",
        "model.Add(sum(expressions) == int(N/2) )\n",
        "\n",
        "solver.parameters.enumerate_all_solutions = False\n",
        "solution_printer = VarArraySolutionPrinter(U)\n",
        "\n",
        "\n",
        "st = time.time()\n",
        "status = solver.Solve(model, solution_printer)\n",
        "\n",
        "et = time.time()\n",
        "print(f\"time = {et-st}\")\n",
        "print(f\"status = {solver.StatusName(status)}\")\n",
        "print(f\"Number of solutions found: {solution_printer.solution_count()}\")"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "time = 0.07570934295654297\n",
            "status = OPTIMAL\n",
            "Number of solutions found: 1\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "for c,(x,y,v) in info.items():\n",
        "  plt.scatter(x,y,s=400, c= 'grey', alpha= 0.6)\n",
        "\n",
        "for i in nodes:\n",
        "  plt.text(info[i][0]-0.1,info[i][1],s=str(i), c= 'r', fontsize=14)\n",
        "  if solver.Value(blacks[i]):\n",
        "    print(\"Black\",i)\n",
        "  if solver.Value(whites[i]):\n",
        "    print(\"whites\",i)\n",
        "\n",
        "\n",
        "for i ,v in U.items():\n",
        "  if solver.Value(v):\n",
        "    plt.scatter(info[i][0],info[i][1],s=400, c= 'k')\n",
        "\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 465
        },
        "id": "aw7I7Iy-i4Dc",
        "outputId": "cd7c2c2a-9a77-4145-c14f-3e1144ec1662"
      },
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "whites 1\n",
            "Black 2\n"
          ]
        },
        {
          "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": [
        "\n"
      ],
      "metadata": {
        "id": "o-b7kzmAmVnL"
      },
      "execution_count": 15,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "for i , dic in solution_printer.solution_save().items():\n",
        "  plt.figure(figsize=(5,5))\n",
        "  print(i, dic)\n",
        "  for c,v in dic.items():\n",
        "    if v:\n",
        "      plt.scatter(info[c][0],info[c][1],s=500, marker = 's', c= 'k')\n",
        "    else:\n",
        "      plt.scatter(info[c][0],info[c][1],s=500, marker = 's', c= 'grey', alpha = 0.3)\n",
        "  plt.tight_layout()\n",
        "  plt.axis('off')\n",
        "  plt.show()\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 520
        },
        "id": "g_Hh-NjFOiLp",
        "outputId": "297d84ff-842c-4fa9-9bcc-b4deab502af3"
      },
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1 {1: 0, 2: 1, 3: 1, 4: 1, 5: 1, 6: 1, 7: 1, 8: 1, 9: 1, 10: 1, 11: 1, 12: 1, 13: 1, 14: 1, 15: 1, 16: 1, 17: 1, 18: 1, 19: 1, 20: 1, 21: 1, 22: 1, 23: 1, 24: 1, 25: 1, 26: 1, 27: 1, 28: 1, 29: 1, 30: 1, 31: 1, 32: 1, 33: 1, 34: 0, 35: 0, 36: 0, 37: 0, 38: 0, 39: 0, 40: 0, 41: 0, 42: 0, 43: 0, 44: 0, 45: 0, 46: 0, 47: 0, 48: 0, 49: 0, 50: 0, 51: 0, 52: 0, 53: 0, 54: 0, 55: 0, 56: 0, 57: 0, 58: 0, 59: 0, 60: 0, 61: 0, 62: 0, 63: 0, 64: 0}\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": 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376xb34orAPArX2gCgDBxBYAwcQWAMHEFgDBxBYAwcQWAMHEFgDBxBYAwcQWAMHEFgDBxBYCw/wOE27/LIVocfgAAAABJRU5ErkJggg==\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "for i , dic in solution_printer.solution_save().items():\n",
        "  plt.figure(figsize=(5,5))\n",
        "  print(i, dic)\n",
        "  for c,v in dic.items():\n",
        "    if v:\n",
        "      plt.scatter(info[c][0],info[c][1],s=500, marker = 's', c= 'k')\n",
        "    else:\n",
        "      plt.scatter(info[c][0],info[c][1],s=500, marker = 's', c= 'grey', alpha = 0.3)\n",
        "\n",
        "  for i in nodes:\n",
        "    if solver.Value(blacks[i]):\n",
        "      plt.scatter(info[i][0],info[i][1],s=200, marker = 'o', c= 'r')\n",
        "      print(\"Black\",i)\n",
        "    if solver.Value(whites[i]):\n",
        "      plt.scatter(info[i][0],info[i][1],s=200, marker = 'o', c= 'b')\n",
        "\n",
        "  for (i,j), vz in Z.items():\n",
        "    if solver.Value(vz):\n",
        "      plt.plot([info[i][0],info[j][0]],[info[i][1],info[j][1]],c= 'r')\n",
        "  for (i,j), vw in W.items():\n",
        "    if solver.Value(vw):\n",
        "      plt.plot([info[i][0],info[j][0]],[info[i][1],info[j][1]],c= 'b')\n",
        "  plt.tight_layout()\n",
        "  plt.axis('off')\n",
        "  plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 538
        },
        "id": "8476QEFTGkXL",
        "outputId": "01d7f5d3-9fc9-4542-aee3-492de9c6256a"
      },
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1 {1: 0, 2: 1, 3: 1, 4: 1, 5: 1, 6: 1, 7: 1, 8: 1, 9: 1, 10: 1, 11: 1, 12: 1, 13: 1, 14: 1, 15: 1, 16: 1, 17: 1, 18: 1, 19: 1, 20: 1, 21: 1, 22: 1, 23: 1, 24: 1, 25: 1, 26: 1, 27: 1, 28: 1, 29: 1, 30: 1, 31: 1, 32: 1, 33: 1, 34: 0, 35: 0, 36: 0, 37: 0, 38: 0, 39: 0, 40: 0, 41: 0, 42: 0, 43: 0, 44: 0, 45: 0, 46: 0, 47: 0, 48: 0, 49: 0, 50: 0, 51: 0, 52: 0, 53: 0, 54: 0, 55: 0, 56: 0, 57: 0, 58: 0, 59: 0, 60: 0, 61: 0, 62: 0, 63: 0, 64: 0}\n",
            "Black 2\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAdcAAAHSCAYAAAC+SYFyAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAAA9hAAAPYQGoP6dpAAAV9klEQVR4nO3dwY5j53km4LfYVFHVLcIwYAOelQJEJTSmbUy7pVWiTHIB1karCWYWY3g9y2SjbOVFcgtJvLGRWSkL5QYGac9KLRVgKSgUbcDOLGJMsjFK3SVSbHIWVTVWJHWbdfgdslj/8wCFZlfXOd//Ng/w8pCnyL3lcrkMAFBmsO0FAMBNo1wBoJhyBYBiyhUAiilXACimXAGgmHIFgGLKFQCKKVcAKKZcAaCYcgWAYsoVAIoN19l4NptlsVhUreXKBoNB9vf3e58zmUxyenra+5xnGY/HOTw83MisVrK2kjORdZMcv/V2NWvncp3NZjk+Ps50Ou26i7WNRqPcvXu314KdTCZ59dVXe9v/qk5OTno/mFvJ2krORNZtcPzW2eWsnct1sVhkOp1mOBxmOFzrBLiT+Xye6XTa+5nzNh8xfd4m1tFK1lZybmrGKmTdnf2vyn36fGu34nA43MhTs19lPp9vZS4API8LmgCgmHIFgGJbLdctXmi8UXvbXgAAG7XRK5E+/niUd9/9Wh49OsjPfz7KfL6X4XCZV16Z5rXXzvLWW7/JvXvbu/q4yneTfD/JHyX5j0n2k8yS/FOSf0zyoyQfbm11APRtI+X6q1+9kLff/lbef/92bt1a5unT357Lzed7OT5+MZPJKD/5ydfz+utP8s47v87LL3+2iaWV+v0kf5Pkj5N8luSFz/3bfpL7Se4l+R9J/leSHyT5xWaXCMAG9P608HvvjfPmm7+XDz88SJJ/V6yfd/n9Dz88yJtv/l7+4R/GfS+t1J8m+SjJH1z8/YVn/Nzl9//g4uf/S8/rAmDzej1zfe+9cf78z/9Dlstk1Vcenz7dy9OnyZ/92fl2b755PX7P6Xn+NMmPL26v+mjlhSS3kvwk5/8zf9fDugDYjt7OXH/5y/Ongq9SrL+1l+Uyefvtb+VXv3rWOeD18EqSv724fdX/zMuf/9ucP6UMwM3QW7n+xV986+Kp3q7Xyu7l6dO9vP32tyqXVe6vc34G2vU/cnCx/d+UrQiAbeulXD/6aJT337/9zNdXV/X06V7ef/92Pv54VLSyWg9yfvHSuufWL1zs57trrwiA66CXcv37v/9abt1aluzr1q1l3n33ayX7qvbfc35VcIXPcv7rOwDsvl4uaHr06GDts9ZLT5/u5YMPDkr2Ve2Psv5Z66UXkvznJLef8e+Ds7Pk8eOiac+e8az5q/jGxZ//VrCOPrO2kvNyhqyr2ZWsreS8nLFO1stt183axd5yuex0ivnpp5/mZz/7WV588cUvvXH/t7/9aubzuvclGg6X+eijk3/3vdlslk8//TTf+c538uKLL5bN+qIPPvggr7322lf+2zTnv78KwPX1zaxXsI8ePcqDBw+utE3508KLRUqLNTnf33V7q8S9KFYAvlr508KDwfmZZvWZ6+CafcTAMudvaVhZsLMkX3/Gv/304cPcv3+/cNqXHR0d5Q/feKPTtreT/OvF7W8mebLGOvrO2krORNZV7VLWVnImdVnXydlVL6+5vvLKNMfHdU/VHh5ez/cb/qecv6VhlY/z7INgcXCQ3LlTOO2rZ1QchE+y3sHcd9ZWcl7OkPVqrnvWVnJezthGMVbo5XzwtdfOSq8WfvDgrGRf1f4xtVcLPyzaFwDb1Uu5vvXWb0qvFn7rrd+U7Kvaj1J7tfCPivYFwHb1Uq737k3z+utP1j57vXVrmddff3JtP4buw5x/us26Z6+fXezHx9AB3Ay9XSb0zju/vijXrgW7zK1by7zzzq8rl1XuB0meJul6MfPiYvsflK0IgG3rrVxffvmz/PCHv87eXnL1gl1mby/54Q+v/+e6/iK/fWelqxbs5c9/Pz7XFeAm6fUXXL73vdP85V/+S/b3lys/RXzr1jL7+8v81V/9S773vev/cXNJ8j+T/Lec/yrNqg8FPrv4+f96sT0AN0fvvz365punee+9X+a73z2/4vdZJXv5/QcPzvLee7/cmWK99HdJvp3kf1/8/Vkle/n9n178vGIFuHl6/bD0Sy+//Fl+/OP/k48/HuXdd7+WR48O8vOfjzKf72U4XObwcJoHD87y1lu/ubYXL63iF0n+JOefbvP9nL9X8H+6+LdZzn+P9WHOrwp28RLAzbWRcr1079409+793///98Ui1+6dlyp8ePF1O8nl21p/Pdt5lxAANm+r1XYTixUA1BsAFFOuAFBs7ddc5/N5xTp2Zi4A/C6dy3UwGGQ0GmU6nW6t6EajUQY9v3A7Ho973f+qNrGOVrK2knNTM1Yh6+7sf1Xu0+fbWy6Xnd8AeDabZbHFTzEfDAbZ3+//I8snk0lOT6/+e7eDs7Pcv/gswqOHD88/oqmD8Xicw8PDTtteVStZW8mZyLqKXcvaSs5kd7OuVa78Do8fJy+9dH77k096/+zDrWolays5E1lvolZyJlvP6oImACimXAGgmHIFgGLKFQCKKVcAKKZcAaCYcgWAYsoVAIopVwAoplwBoJhyBYBiyhUAiilXACimXAGgmHIFgGLKFQCKKVcAKKZcAaCYcgWAYsoVAIopVwAoplwBoNhwnY0nk0lOT0+r1nJl4/E4h4eHvc/pmnNwdpb7F7ePjo6yODjoNH9TOZN2sraSM5F1FbuWtZWcyQ5nXXZ0cnKyTLL1r5OTk64Res95O1kuL75uX/OcLWVtJaesNzNrKzl3PWvnp4W3ecb6eX2vo5Wcm5qxCvfpbs1Yhay7s/9VuU+fz2uuAFBMuQJAMeUKAMWUKwAUU64AUEy5AkAx5QoAxZQrABRTrgBQTLkCQDHlCgDFlCsAFFvrI+fW8Y2LP5+suZ/B2Vny+PG6y3nu/m933LbrdgDstq2U6zeS/GvVzt54o2pPX+l+korq/kaSfy7Yz3V1+wu3133QdF21kjOR9SZqJWey/ayeFgaAYls5c/38I4hvZr1HFD99+DD3799fb0HPcXR0lD/seHZ8O789Q/+3shVdT0+ecfumaSVnIutN1ErOZPtZt/aa66UnWS/44uAguXOnajlfuf+bfhACUMvTwgBQTLkCQDHlCgDFlCsAFFOuAFBMuQJAMeUKAMWUKwAUU64AUEy5AkAx5QoAxZQrABRTrgBQrHO5jsfjynV01vc6Wsm5qRmrcJ/u1oxVyLo7+1+V+/T59pbL5bLrwMlkktPT0ytvNzg7y/2Lz0g9evjw/GPjOhiPxzk8POy07VW0kjNpJ2srORNZV7FrWVvJmexu1rXKtbPHj5OXXjq//cknvX4e61a1kjNpJ2srORNZb6JWciZbz+o1VwAoplwBoJhyBYBiyhUAiilXACimXAGgmHIFgGLKFQCKKVcAKKZcAaCYcgWAYsoVAIopVwAoplwBoJhyBYBiyhUAiilXACimXAGgmHIFgGLKFQCKKVcAKKZcAaDYcJ2NJ5NJTk9Pr7zd4Ows9y9uHx0dZXFw0Gn+eDzO4eFhp22vopWcSTtZW8mZyLqKXcvaSs5kh7MuOzo5OVkm6fR1O1kuL75ud9zH5dfJyUnXCHI2mrWVnLLezKyt5Nz1rJ2fFu7ySKIPfa+jlZybmrEK9+luzViFrLuz/1W5T5/Pa64AUEy5AkAx5QoAxZQrABRTrgBQTLkCQDHlCgDFlCsAFFOuAFBMuQJAMeUKAMWUKwAUU64AUGwr5Xr7GbdvmlZyJu1kbSVnIutN1ErOZPtZnbkCQLGtlOuTZ9y+aVrJmbSTtZWciaw3USs5k+1ndeYKAMWUKwAUU64AUEy5AkAx5QoAxZQrABRTrgBQTLkCQDHlCgDFlCsAFFOuAFBMuQJAMeUKAMWUKwAU61yu4/G4ch2d9b2OVnJuasYq3Ke7NWMVsu7O/lflPn2+veVyuew6cDKZ5PT09MrbDc7Ocv+NN5IkRw8fZnFw0Gn+eDzO4eFhp22vopWcSTtZW8mZyLqKXcvaSs5kd7OuVa6dPX6cvPTS+e1PPknu3Nn4EjailZxJO1lbyZnIehO1kjPZelavuQJAMeUKAMWUKwAUU64AUEy5AkAx5QoAxZQrABRTrgBQTLkCQDHlCgDFlCsAFFOuAFBMuQJAMeUKAMWUKwAUU64AUEy5AkAx5QoAxZQrABRTrgBQTLkCQDHlCgDFhutsPJlMcnp6euXtBmdnuX9x++joKIuDg07zx+NxDg8PO217Fa3kTNrJ2krORNZV7FrWVnImO5x12dHJyckySaev28lyefF1u+M+Lr9OTk66RpCz0ayt5JT1ZmZtJeeuZ+38tHCXRxJ96HsdreTc1IxVuE93a8YqZN2d/a/Kffp8XnMFgGLKFQCKKVcAKKZcAaCYcgWAYsoVAIopVwAoplwBoJhyBYBiyhUAiilXACimXAGgmHIFgGJbKdfbz7gNADeBM1cAKDbcxtAnz7h90zxJcudzt2+yVrK2kjOR9SZqJWey/axbKdeW3PQD+PNaydpKzkTWm6iVnMl2s3paGACKKVcAKKZcAaCYcgWAYsoVAIopVwAoplwBoJhyBYBiyhUAiilXACimXAGgmHIFgGLKFQCKdS7X8XhcuY7O+l5HKzk3NWMV7tPdmrEKWXdn/6tynz7f3nK5XHYdOJlMcnp6euXtBmdnuf/GG0mSo4cPszg46DR/PB7n8PCw07ZX0TVnlU3lTNrJ2krORNZNcvzW29Wsa5VrZ48fJy+9dH77k0+SO3ee//MAsEO85goAxZQrABRTrgBQTLkCQDHlCgDFlCsAFFOuAFBMuQJAMeUKAMWUKwAUU64AUEy5AkAx5QoAxZQrABRTrgBQTLkCQDHlCgDFlCsAFFOuAFBMuQJAMeUKAMWUKwAUG66z8WQyyenp6ZW3G5yd5f7F7aOjoywODjrNH4/HOTw87LTtVcxmsywWi97nPMtgMMj+/v5GZrWStZWciayb5Pitt6tZ95bL5bLLwMlkkldffbXLprmd5PHF7TtJnnTay7mTk5NeC3Y2m+X4+DjT6bS3Gb/LaDTK3bt3ez+YW8naSs5E1k1z/Nba5aydz1y7nLH2oe91LBaLTKfTDIfDDIdrneh3Mp/PM51ON/LIrZWsreRMZN0kx2+9Xc66+dXuqOFwuLGnQb5oPp9vdF4rWVvJmci6KY7ffuxiVhc0AUAx5QoAxZQrABRTrgBQTLkCQDHlCgDFlCsAFFOuAFBMuQJAMeUKAMWUKwAUU64AUEy5AkAx5QoAxbbykXNPcv4h6Ze3AeAm2drnuSpVAG4qTwsDQDHlCgDFlCsAFFOuAFBMuQJAMeUKAMWUKwAUU64AUEy5AkAx5QoAxZQrABRTrgBQbGtv3L9r5vN5M3NbydpKzm3N3NbcVrK2knNbM9ed27lcx+Nx56GV+l7HYDDIaDTKdDrd2h08Go0yGPT/JEMrWVvJmci6aY7fWrucdW+5XC67Dp1MJjk9Pe26+drG43EODw97nzObzbJYLHqf8yyDwSD7+/sbmdVK1lZyJrJukuO33q5mXatcAYAvc0ETABRTrgBQTLkCQDHlCgDFlCsAFFOuAFBMuQJAMeUKAMWUKwAUU64AUEy5AkAx5QoAxZQrABRTrgBQTLkCQDHlCgDFlCsAFFOuAFBMuQJAMeUKAMWUKwAUU64AUGy4zsaz2SyLxaJqLVc2GAyyv7/f+5xWcibtZG0lZyLrJjl+6+1q1s7lOpvNcnx8nOl02nUXaxuNRrl7926vd3IrOZN2sraSM5F10xy/tXY5a+dyXSwWmU6nGQ6HGQ7XOgHuZD6fZzqd9v6IppWcSTtZW8mZyLpJjt96u5x17dUOh8ONPT3wRfP5fGOzWsmZtJO1lZyJrJvi+O3HLmZ1QRMAFFOuAFBMuQJAMeUKAMWUKwAUU64AUEy5AkAx5QoAxZQrABRTrgBQTLkCQDHlCgDFlCsAFFOuAFBMuQJAMeUKAMWUKwAUU64AUEy5AkAx5QoAxZQrABRTrgBQTLkCQDHlCgDFlCsAFFOuAFBMuQJAMeUKAMWG6+5gPp9XrOPaz20l57ZmbmNuKzm3NXNbc1vJ2krObc1cd27nch0MBhmNRplOp1sLPhqNMhj0e/LdSs6knayt5Exk3TTHb61dzrq3XC6XXYfOZrMsFouum69tMBhkf3+/9zmt5EzaydpKzkTWTXL81tvVrGuVKwDwZS5oAoBiyhUAiilXACimXAGgmHIFgGLKFQCKKVcAKKZcAaCYcgWAYsoVAIopVwAoplwBoJhyBYBiyhUAiilXACimXAGgmHIFgGLKFQCKKVcAKKZcAaCYcgWAYsoVAIoN19l4NptlsVhUreXKBoNB9vf3e5/TSs6knayt5Exk3STHb71dzdq5XGezWY6PjzOdTrvuYm2j0Sh3797t9U5uJWfSTtZWciaybprjt9YuZ+1crovFItPpNMPhMMPhWifAnczn80yn094f0bSSM2knays5E1k3yfFbb5ezrr3a4XC4sacHvmg+n29sVis5k3aytpIzkXVTHL/92MWsLmgCgGLKFQCKKVcAKKZcAaCYcgWAYsoVAIopVwAoplwBoJhyBYBiyhUAiilXACimXAGgmHIFgGLKFQCKKVcAKKZcAaCYcgWAYsoVAIopVwAoplwBoJhyBYBiyhUAiilXACimXAGgmHIFgGLKFQCKKVcAKKZcAaDYcN0dzOfzinVc+7mt5NzWzG3MbSXntmZua24rWVvJua2Z687tXK6DwSCj0SjT6XRrwUejUQaDfk++W8mZtJO1lZyJrJvm+K21y1n3lsvlsuvQ2WyWxWLRdfO1DQaD7O/v9z6nlZxJO1lbyZnIukmO33q7mnWtcgUAvswFTQBQTLkCQDHlCgDFlCsAFFOuAFBMuQJAMeUKAMWUKwAUU64AUEy5AkAx5QoAxZQrABRTrgBQTLkCQDHlCgDFlCsAFFOuAFBMuQJAMeUKAMWUKwAUU64AUEy5AkCx4Tobz2azLBaLqrVc2WAwyP7+fu9zWsmZtJO1lZyJrJvk+K23q1k7l+tsNsvx8XGm02nXXaxtNBrl7t27vd7JreRM2snaSs5E1k1z/Nba5aydy3WxWGQ6nWY4HGY4XOsEuJP5fJ7pdNr7I5pWcibtZG0lZyLrJjl+6+1y1rVXOxwON/b0wBfN5/ONzWolZ9JO1lZyJrJuiuO3H7uY1QVNAFBMuQJAMeUKAMWUKwAUU64AUEy5AkAx5QoAxZQrABRTrgBQTLkCQDHlCgDFlCsAFFOuAFBMuQJAMeUKAMWUKwAUU64AUEy5AkAx5QoAxZQrABRTrgBQTLkCQDHlCgDFlCsAFFOuAFBMuQJAMeUKAMWUKwAUG667g/l8XrGOaz+3lZzbmrmNua3k3NbMbc1tJWsrObc1c925nct1MBhkNBplOp1uLfhoNMpg0O/Jdys5k3aytpIzkXXTHL+1djnr3nK5XHYdOpvNslgsum6+tsFgkP39/d7ntJIzaSdrKzkTWTfJ8VtvV7OuVa4AwJe5oAkAiilXACimXAGgmHIFgGLKFQCKKVcAKKZcAaCYcgWAYsoVAIopVwAoplwBoNj/A0t/XbUvukdyAAAAAElFTkSuQmCC\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "cntu = True\n",
        "counter =0\n",
        "while (cntu and counter< 7):\n",
        "\n",
        "  A= [v.Not() for i,v in U.items() if solver.value(v)==1]\n",
        "  B= [v for i,v in U.items() if solver.value(v)==0]\n",
        "\n",
        "  expressions = A+ B\n",
        "  model.AddAtLeastOne(expressions)\n",
        "  status = solver.Solve(model,solution_printer)\n",
        "  #print(status, solver.StatusName(status), solver.ObjectiveValue())\n",
        "  if status != cp_model.OPTIMAL:\n",
        "    cntu = False\n",
        "  else:\n",
        "    counter+=1\n",
        "    print(counter)\n",
        "    #pass\n",
        "    plt.figure(figsize=(5,5))\n",
        "    for i , v in U.items():\n",
        "      #print(i, dic)\n",
        "      if solver.value(v):\n",
        "        plt.scatter(info[i][0],info[i][1],s=500, marker = 's', c= 'k')\n",
        "      else:\n",
        "        plt.scatter(info[i][0],info[i][1],s=500, marker = 's', c= 'grey', alpha = 0.3)\n",
        "    plt.tight_layout()\n",
        "    plt.axis('off')\n",
        "    plt.show()\n",
        "\n",
        "    #\"\"\"\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "0hUYCxmOO0I8",
        "outputId": "ce9337c2-eb44-4042-fb53-1016be21c0d3"
      },
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "2\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "3\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "4\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "5\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "6\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAdcAAAHSCAYAAAC+SYFyAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAAA9hAAAPYQGoP6dpAAAQm0lEQVR4nO3aTW6j6haG0V0ImRbDcJT5jyYKw3ALhPBtnE6pfs5N4Rd8XN9afbzZ+oif2PK3+/1+LwAgpnv2DQDA30ZcASBMXAEgTFwBIExcASBMXAEgTFwBIExcASBMXAEgTFwBIExcASBMXAEgrH/k4mVZatu21L38sa7r6nK5HD5nmqa63W6Hz/mdcRzrer2eMquVM21lzyq7nsnzm/equ+6O67Is9fHxUfM8732Jhw3DUO/v74ce8jRN9fb2dtjrf9Xn5+fhgW3lTFvZs8quZ/P8Zr3yrrvjum1bzfNcfd9X3z/0AXiXdV1rnufD/6N55ifW751xH62caSt7Vtn1TJ7fvFfe9eG77fv+tK8HfrSu61Pm/u1aOdNW9qyy61k8v8d4xV39oAkAwsQVAMLEFQDCxBUAwsQVAMLEFQDCxBUAwsQVAMLEFQDCxBUAwsQVAMLEFQDCxBUAwsQVAMLEFQDCxBUAwsQVAMLEFQDCxBUAwsQVAMLEFQDCxBUAwsQVAMLEFQDCxBUAwsQVAMLEFQDCxBUAwvpHX2Bd18R9vMzcFrRypq3s+ayZz5rbyq6t7PmsmY/O3R3XrutqGIaa5/lpiw/DUF137IfvcRwPff2vOuM+WjnTVvassuvZPL9Zr7zrt/v9ft87dFmW2rZt7+UP67quLpfL4XOmaarb7Xb4nN8Zx7Gu1+sps1o501b2rLLrmTy/ea+660NxBQB+5gdNABAmrgAQJq4AECauABAmrgAQJq4AECauABAmrgAQJq4AECauABAmrgAQJq4AECauABAmrgAQJq4AECauABAmrgAQJq4AECauABAmrgAQJq4AECauABDWP3Lxsiy1bVvqXv5Y13V1uVwOnzNNU91ut8Pn/M44jnW9Xk+Z1cqurexZ1daurbwntbJn1evuujuuy7LUx8dHzfO89yUeNgxDvb+/H3rI0zTV29vbYa//VZ+fn4e/QbWyayt7VrW1ayvvSa3sWfXau+6O67ZtNc9z9X1fff/QB+Bd1nWteZ4P/4/mmf/xf++M+2hl11b2PGvGV5xxH628J7WyZ9Vr7/rw3fZ9f9rXAz9a1/Upc4H/rlbek1rZs+o1d/WDJgAIE1cACBNXAAgTVwAIE1cACBNXAAgTVwAIE1cACBNXAAgTVwAIE1cACBNXAAgTVwAIE1cACBNXAAgTVwAIE1cACBNXAAgTVwAIE1cACBNXAAgTVwAIE1cACBNXAAgTVwAIE1cACBNXAAgTVwAI6x99gXVdE/fxMnOB/7ZW3pNa2fNZMx+duzuuXdfVMAw1z/PTFh+Gobru2A/f4zge+vpfdcZ9tLJrK3ueNeMrzriPVt6TWtmz6rV3/Xa/3+97hy7LUtu27b38YV3X1eVyOXzONE11u90On/M74zjW9Xo9ZVYru7ayZ1Vbu7byntTKnlWvu+tDcQUAfuYHTQAQJq4AECauABAmrgAQJq4AECauABAmrgAQJq4AECauABAmrgAQJq4AECauABAmrgAQJq4AECauABAmrgAQJq4AECauABAmrgAQJq4AECauABAmrgAQ1j9y8TRNdbvdUvfyx8ZxrOv1evicVvasamfXVvasqlqWpbZtO2XWr3RdV5fL5ZRZrZxrS2f6qrvujus0TfX29rb38pjPz89DH+ZW9qxqZ9dW9qz6543p4+Oj5nk+dM6/GYah3t/fD38zbuVcWzrTV951d1yf+d/h946+j1b2PGvGVzjTnG3bap7n6vu++v6hL6p2Wde15nk+5ZNHK+fa0pm+8q7n3y1wur7vT/sa70fruj5l7t+upTN9xV39oAkAwsQVAMLEFQDCxBUAwsQVAMLEFQDCxBUAwsQVAMLEFQDCxBUAwsQVAMLEFQDCxBUAwsQVAMLEFQDCxBUAwsQVAMLEFQDCxBUAwsQVAMLEFQDCxBUAwsQVAMLEFQDCxBUAwsQVAMLEFQDCxBUAwvpn3wBwvHVdm5rbgpbO9BV33R3XcRx3D006+j5a2fOsGV/hTHO6rqthGGqe56e9QQ3DUF13/JdkrZxrS2f6yrt+u9/v971Dp2mq2+229/KHjeNY1+v18Dmt7FnVzq6t7FlVtSxLbdt2yqxf6bquLpfLKbNaOdeWzvRVd30orgDAz/ygCQDCxBUAwsQVAMLEFQDCxBUAwsQVAMLEFQDCxBUAwsQVAMLEFQDCxBUAwsQVAMLEFQDCxBUAwsQVAMLEFQDCxBUAwsQVAMLEFQDCxBUAwsQVAMLEFQDC+kcuXpaltm1L3csf67quLpfL4XNa2bOqapqmut1up8z6lXEc63q9Hj6nlT2r7Homz2/eq+66O67LstTHx0fN87z3JR42DEO9v78fGp5W9qz65yF+e3s7dMZXfH5+HvqH28qeVXZ9Bs9vzivvujuu27bVPM/V9331/UMfgHdZ17XmeT78E2Ure1bVU/87/N7R99HKnmfN+Aq7vs7rf5Uz/XcP16Lv+9O+svzRuq6nzWplTwAe5wdNABAmrgAQJq4AECauABAmrgAQJq4AECauABAmrgAQJq4AECauABAmrgAQJq4AECauABAmrgAQJq4AECauABAmrgAQJq4AECauABAmrgAQJq4AECauABAmrgAQJq4AECauABAmrgAQJq4AECauABDWP/oC67om7uM/P7eVPQF43O64dl1XwzDUPM9PC8AwDNV1x374bmXPqqpxHA+f8RVH30cre5414yvs+jqv/1XO9N99u9/v970Dl2Wpbdv2Xv6wruvqcrkcPqeVPauqpmmq2+12yqxfGcexrtfr4XNa2bPKrmfy/Oa96q4PxRUA+JkfNAFAmLgCQJi4AkCYuAJAmLgCQJi4AkCYuAJAmLgCQJi4AkCYuAJAmLgCQJi4AkCYuAJAmLgCQJi4AkCYuAJAmLgCQJi4AkCYuAJAmLgCQJi4AkCYuAJAWP/IxdM01e12S93LHxvHsa7X6+FzWtmzqp1dW9mzqmpZltq27ZRZv9J1XV0ul1NmtbKr5/c8e890d1ynaaq3t7e9l8d8fn4eesit7FnVzq6t7Fn1zxvTx8dHzfN86Jx/MwxDvb+/Hx6dVnb1/J5r75nujusz/2v63tH30cqeZ834Cmeas21bzfNcfd9X3z/0RdUu67rWPM+nfPJoZVfP73keOdPz7xY4Xd/3p301+6N1XU+d19KurXjFM/WDJgAIE1cACBNXAAgTVwAIE1cACBNXAAgTVwAIE1cACBNXAAgTVwAIE1cACBNXAAgTVwAIE1cACBNXAAgTVwAIE1cACBNXAAgTVwAIE1cACBNXAAgTVwAIE1cACBNXAAgTVwAIE1cACBNXAAgTVwAI6599A8Dx1nVtZm5Lu7biFc90d1zHcdw9NOno+2hlz7NmfIUzzem6roZhqHmen/YGNQxDdd3xX5K1sqvn91x7z/Tb/X6/7x06TVPdbre9lz9sHMe6Xq+Hz2llz6p2dm1lz6qqZVlq27ZTZv1K13V1uVxOmdXKrp7f8+w904fiCgD8zA+aACBMXAEgTFwBIExcASBMXAEgTFwBIExcASBMXAEgTFwBIExcASBMXAEgTFwBIExcASBMXAEgTFwBIExcASBMXAEgTFwBIExcASBMXAEgTFwBIExcASCsf+TiaZrqdrul7uWPjeNY1+v18DnLstS2bYfP+Z2u6+pyuZwyq5VdW3l2q9o506p2zrWVPate9/ndHddpmurt7W3v5TGfn5+HHvKyLPXx8VHzPB824/8ZhqHe398Pf4NqZddWnt2qds60qp1zbWXPqtd+fnfH9Zn/NX3v6PvYtq3mea6+76vvH/qgv8u6rjXP8yn/ubWyayvPblU7Z1rVzrm2smfVaz+/59/ti+r7/rSvtn60ruup81ratRXOlFf2is+vHzQBQJi4AkCYuAJAmLgCQJi4AkCYuAJAmLgCQJi4AkCYuAJAmLgCQJi4AkCYuAJAmLgCQJi4AkCYuAJAmLgCQJi4AkCYuAJAmLgCQJi4AkCYuAJAmLgCQJi4AkCYuAJAmLgCQJi4AkCYuAJAmLgCQFj/7Bt4Feu6NjO3pV1b4Ux5Za/4/O6O6ziOu4cmHX0fXdfVMAw1z/PTDngYhuq6479kaGXXVp7dqnbOtKqdc21lz6rXfn6/3e/3+96h0zTV7Xbbe/nDxnGs6/V6+JxlWWrbtsPn/E7XdXW5XE6Z1cqurTy7Ve2caVU759rKnlWv+/w+FFcA4Gd+0AQAYeIKAGHiCgBh4goAYeIKAGHiCgBh4goAYeIKAGHiCgBh4goAYeIKAGHiCgBh4goAYeIKAGHiCgBh4goAYeIKAGHiCgBh4goAYeIKAGHiCgBh4goAYf0jF0/TVLfbLXUvf2wcx7per4fPWZaltm07fM7vdF1Xl8vllFmtnGkre1Z5fs/kPSnvVXfdHddpmurt7W3v5TGfn5+HPszLstTHx0fN83zYjP9nGIZ6f38//GFu5Uxb2bPK8/sM3pNyXnnX3XF95n+H3zv6PrZtq3meq+/76vuHPujvsq5rzfN8yn9urZxpK3tWeX6fwXtSzivvev7dvqi+70/7GuRH67o+ZS5/D8/v36elM33FXf2gCQDCxBUAwsQVAMLEFQDCxBUAwsQVAMLEFQDCxBUAwsQVAMLEFQDCxBUAwsQVAMLEFQDCxBUAwsQVAMLEFQDCxBUAwsQVAMLEFQDCxBUAwsQVAMLEFQDCxBUAwsQVAMLEFQDCxBUAwsQVAMLEFQDC+mffwKtY17WpufxdPL9/n5bO9BV33R3XcRx3D006+j66rqthGGqe56cd8DAM1XXHf8nQypm2smeV5/cZvCflvPKu3+73+33v0Gma6na77b38YeM41vV6PXzOsiy1bdvhc36n67q6XC6nzGrlTFvZs8rzeybvSXmvuutDcQUAfuYHTQAQJq4AECauABAmrgAQJq4AECauABAmrgAQJq4AECauABAmrgAQJq4AECauABAmrgAQJq4AECauABAmrgAQJq4AECauABAmrgAQJq4AECauABAmrgAQ1j9y8TRNdbvdUvfyx8ZxrOv1evicVvasamfXZVlq27bD5/xO13V1uVxOmWXX85y1ayt7Vr3urrvjOk1Tvb297b085vPz89A341b2rGpn12VZ6uPjo+Z5PmzG/zMMQ72/vx/+BmXXc52xayt7Vr32rrvj+sxPN987+j5a2fOsGV9x9H1s21bzPFff99X3D315s8u6rjXP8yn/jdv1PGft2sqeVa+96/l3C/8Rfd+f9tXWj9Z1PXWeXc9x5q6t7Fn1mrv6QRMAhIkrAISJKwCEiSsAhIkrAISJKwCEiSsAhIkrAISJKwCEiSsAhIkrAISJKwCEiSsAhIkrAISJKwCEiSsAhIkrAISJKwCEiSsAhIkrAISJKwCEiSsAhIkrAISJKwCEiSsAhIkrAISJKwCEiSsAhPXPvgF4lnVdm5lr179vbit7Pmvmo3N3x3Ucx91Dk46+j1b2PGvGVxx9H13X1TAMNc/z0/5oh2Gorjv+iyO7nuuMXVvZs+q1d/12v9/ve4dO01S3223v5Q8bx7Gu1+vhc1rZs6qdXZdlqW3bDp/zO13X1eVyOWWWXc9z1q6t7Fn1urs+FFcA4Gd+0AQAYeIKAGHiCgBh4goAYeIKAGHiCgBh4goAYeIKAGHiCgBh4goAYeIKAGH/AynApNejZsz3AAAAAElFTkSuQmCC\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "7\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [],
      "metadata": {
        "id": "kgrhPumrnlXZ"
      }
    }
  ]
}