Problem3.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "j4Wbb4H7UDcy"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "from skimage import data, io, filters\n",
        "from matplotlib import pyplot as plt\n",
        "from PIL import Image\n",
        "from skimage.transform import resize\n",
        "import random\n",
        "%matplotlib inline"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "N = 10\n",
        "\n",
        "city_x = np.random.rand((10))\n",
        "city_y = np.random.rand((10))\n",
        "\n",
        "print('The co-ordinates of the 10 cities are:')\n",
        "for city in zip(city_x, city_y):\n",
        "    print(city)"
      ],
      "metadata": {
        "id": "YNmxLOqKULtr",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "684185c0-a8fe-4896-a9fa-a9ead8180fb1"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The co-ordinates of the 10 cities are:\n",
            "(0.5868049708707317, 0.33515993594687343)\n",
            "(0.6745983401738592, 0.8840485368972216)\n",
            "(0.3606474001577742, 0.4080916433281344)\n",
            "(0.830386367920734, 0.7051376497908406)\n",
            "(0.3804281639100282, 0.6433892932305992)\n",
            "(0.7652034651580247, 0.1651428696231021)\n",
            "(0.09992588891925225, 0.36074224411250566)\n",
            "(0.5181643463738399, 0.9859834847023625)\n",
            "(0.3993690050315435, 0.2234231384992239)\n",
            "(0.5225384447449909, 0.26795927216412907)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "JiHAKDIUUQi5"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(city_x, city_y, 'o')\n",
        "plt.title('Map of cities')"
      ],
      "metadata": {
        "id": "9j0aWpm_VVGs",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 298
        },
        "outputId": "36af44a7-cd81-470d-80fe-51df207e3fa0"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Map of cities')"
            ]
          },
          "metadata": {},
          "execution_count": 3
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAEICAYAAABPgw/pAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAATvElEQVR4nO3df5Dcd33f8ecLWSZHYqxOJKbRL8vJCIESMxW9uHTSSUggkey0tgqZjJ1xEzMGFxrTdqAarIFQ10mGELXJtI1bMIlroIMdl/Fo1ImpSojdTChOLSpj1XbFyMaudQqx7CBCyQGyePePXbmr851uT9rb3fvc8zGjmd3v93O7L+2dXvre5/vdz6aqkCQtfS8bdQBJ0mBY6JLUCAtdkhphoUtSIyx0SWqEhS5JjbDQpRmS/FqS55J8dYFf95kkv3SW/R9J8ivnn1CaXbwOXaOU5ClgLbC2qp7r2X4Q+BvApVX11BDzbAQOA5dU1bPn8TjXA2+vqr8zqGzSfDxC1zj4CnDt6TtJLgNeMaIsG4Hnz6fMpVGx0DUOPgn8Ys/9XwI+0Tsgyc8mOZjkL5M8k+SWnn2bklSSG5McS/JnSf7ZXE+W5OIkn0hyPMnTST6Q5GVJ3gx8Flib5P8muXOOr786ycPdLE8k2dHd/kCStyd5LfAR4G93H+dEd/+dSX6t53H+bvdxTiT570le17PvfUmmknwjyeEkb+r71dSyZaFrHDwIvDLJa5OsAK4B/uOMMd+kU/qrgJ8F3pVk54wxPwlsBn4GeF+3oGfzb4GLgR8EfqL7uG+rqj8ErgCOVdX3VdX1M78wyeV0/rPZ1c3y48BTvWOq6nHgncAXuo+zapbH2QbcAfxD4PuBjwL7krw8yRbgJuBHq+oiYPvM55BmY6FrXJw+Sv9p4HFgqndnVT1QVYeq6rtV9QhwF50y7vUvquqbVXUI+A/0TOOc1vMfxu6q+kZ3fv5fAf+gz5w3AHdU1We7Waaq6n/3/9d80Y3AR6vqT6vqVFV9HPg28AbgFPByYGuSlVX1VFU9cQ7PoWXGQte4+CTwC8D1zJhuAUjyt5Lc350m+TqdI+DVM4Y903P7aTonW2daDazs7u8du67PnBuAQZTrJcB7u9MtJ7rTMhvonBw+AvxT4Bbg2SR3J5nt7yKdwULXWKiqp+mcHL0SuHeWIZ8C9gEbqupiOnPUmTFmQ8/tjcCxWR7nOeAknULtHTs1y9jZPAP8UB/j5rt87Bng16tqVc+fV1TVXQBV9anuFTKXdB/rw33m0zJmoWuc3AD8VFV9c5Z9FwF/UVXf6s5j/8IsY34lySuS/DDwNuD3Zw6oqlPAPcCvJ7koySXAe3jpnP1cfg94W5I3dU+krkvymlnG/TmwPsmFczzOx4B3dn/zSJLv7Z74vSjJliQ/leTlwLeAaeC7febTMmaha2xU1RNVdWCO3f8IuDXJN4AP0inlmf4bcAT4HPAvq+q/zvFY76ZzkvVJ4E/oHP3f0WfG/0HnP4vfBr7efc5LZhn6R8CjwFeTPDdzZ/fv+Q7gd4CvdXNf3939cuA36Pw28VXgVcDufvJpefONRVrykmyiM12zsqpeGG0aaXQ8QpekRljoktQIp1wkqREeoUtSIy4Y1ROvXr26Nm3aNKqnl6Ql6Ytf/OJzVbVmtn0jK/RNmzZx4MBcV6hJkmaT5Om59jnlIkmNsNAlqRHzFnqSO5I8m+R/zbE/Sf5NkiNJHkny+sHHlCTNp58j9DuBHWfZfwWdNag301kS9N+ffyxJ0kLNW+hV9cfAX5xlyNXAJ6rjQWBVkh8YVEBJUn8GcZXLOs5ch/pod9ufzRyY5EY6R/Fs3LhxAE8tLQ17D06xZ/9hjp2YZu2qCXZt38LObf0uwS71Z6gnRavq9qqarKrJNWtmvYxSas7eg1PsvvcQUyemKWDqxDS77z3E3oP9LsEu9WcQhT7FmR8ssJ7+PyxAat6e/YeZPnnqjG3TJ0+xZ//hESVSqwZR6PuAX+xe7fIG4OtV9ZLpFmm5OnZiekHbpXM17xx6kruANwKrkxwF/jmdz2Skqj4C3EfnY8OOAH9FZ/F/SV1rV00wNUt5r101MYI0atm8hV5VL/nk9Bn7C/jlgSWSGrNr+xZ233vojGmXiZUr2LV9ywhTqUUjW8tFWi5OX83iVS5abBa6NAQ7t62zwLXoXMtFkhphoUtSIyx0SWqEhS5JjbDQJakRFrokNcJCl6RGWOiS1AgLXZIaYaFLUiMsdElqhIUuSY2w0CWpERa6JDXCQpekRljoktQIC12SGuEnFkkair0Hp/wYvkVmoUtadHsPTp3xQdlTJ6bZfe8hAEt9gJxykbTo9uw//GKZnzZ98hR79h8eUaI2WeiSFt2xE9ML2q5zY6FLWnRrV00saLvOjYUuadHt2r6FiZUrztg2sXIFu7ZvGVGiNnlSVNKiO33i06tcFpeFLmkodm5bZ4EvMqdcJKkRFrokNcJCl6RGWOiS1AgLXZIaYaFLUiMsdElqhIUuSY2w0CWpERa6JDXCQpekRljoktSIvgo9yY4kh5McSXLzLPs3Jrk/ycEkjyS5cvBRJUlnM2+hJ1kB3AZcAWwFrk2ydcawDwD3VNU24Brg3w06qCTp7Po5Qr8cOFJVT1bVd4C7gatnjCngld3bFwPHBhdRktSPfgp9HfBMz/2j3W29bgGuS3IUuA9492wPlOTGJAeSHDh+/Pg5xJUkzWVQJ0WvBe6sqvXAlcAnk7zksavq9qqarKrJNWvWDOipJUnQX6FPARt67q/vbut1A3APQFV9AfgeYPUgAkqS+tNPoT8EbE5yaZIL6Zz03DdjzP8B3gSQ5LV0Ct05FUkaonkLvapeAG4C9gOP07ma5dEktya5qjvsvcA7knwJuAu4vqpqsUJLkl6qrw+Jrqr76Jzs7N32wZ7bjwE/NthokqSF8J2iktQIC12SGmGhS1IjLHRJaoSFLkmNsNAlqREWuiQ1wkKXpEZY6JLUCAtdkhphoUtSIyx0SWqEhS5JjbDQJakRfS2fK0k6f3sPTrFn/2GOnZhm7aoJdm3fws5tMz+i+dxZ6JI0BHsPTrH73kNMnzwFwNSJaXbfewhgYKXulIskDcGe/YdfLPPTpk+eYs/+wwN7Dgtdkobg2InpBW0/Fxa6JA3B2lUTC9p+Lix0SRqCXdu3MLFyxRnbJlauYNf2LQN7Dk+KStIQnD7x6VUuktSAndvWDbTAZ3LKRZIaYaFLUiMsdElqhIUuSY2w0CWpERa6JDXCQpekRngdukZqsZcTlZYTC10jM4zlRKXlxCkXjcwwlhOVlhMLXSMzjOVEpeXEQtfIDGM5UWk5sdA1MsNYTlRaTjwpqpEZxnKi0nJioWukFns5UWk5ccpFkhphoUtSI/oq9CQ7khxOciTJzXOM+fkkjyV5NMmnBhtTkjSfeefQk6wAbgN+GjgKPJRkX1U91jNmM7Ab+LGq+lqSVy1WYEnS7Po5Qr8cOFJVT1bVd4C7gatnjHkHcFtVfQ2gqp4dbExJ0nz6KfR1wDM99492t/V6NfDqJJ9P8mCSHbM9UJIbkxxIcuD48ePnlliSNKtBnRS9ANgMvBG4FvhYklUzB1XV7VU1WVWTa9asGdBTS5Kgv0KfAjb03F/f3dbrKLCvqk5W1VeAL9MpeEnSkPRT6A8Bm5NcmuRC4Bpg34wxe+kcnZNkNZ0pmCcHmFOSNI95C72qXgBuAvYDjwP3VNWjSW5NclV32H7g+SSPAfcDu6rq+cUKLUl6qVTVSJ54cnKyDhw4MJLnlqSlKskXq2pytn2+U1SSGmGhS1IjLHRJaoSFLkmNsNAlqREWuiQ1wkKXpEZY6JLUCAtdkhphoUtSIyx0SWqEhS5JjbDQJakRFrokNcJCl6RGWOiS1AgLXZIaYaFLUiMsdElqhIUuSY2w0CWpERa6JDXCQpekRljoktQIC12SGmGhS1IjLHRJaoSFLkmNsNAlqREWuiQ1wkKXpEZY6JLUCAtdkhphoUtSIyx0SWqEhS5JjbDQJakRF4w6gNq29+AUe/Yf5tiJadaummDX9i3s3LZu1LGkJlnoWjR7D06x+95DTJ88BcDUiWl233sIwFKXFkFfUy5JdiQ5nORIkpvPMu6tSSrJ5OAiaqnas//wi2V+2vTJU+zZf3hEiaS2zVvoSVYAtwFXAFuBa5NsnWXcRcA/Af500CG1NB07Mb2g7ZLOTz9H6JcDR6rqyar6DnA3cPUs434V+DDwrQHm0xK2dtXEgrZLOj/9FPo64Jme+0e7216U5PXAhqr6g7M9UJIbkxxIcuD48eMLDqulZdf2LUysXHHGtomVK9i1fcuIEkltO+/LFpO8DPgt4L3zja2q26tqsqom16xZc75PrTG3c9s6PvSWy1i3aoIA61ZN8KG3XOYJUWmR9HOVyxSwoef++u620y4CfgR4IAnAXwf2Jbmqqg4MKqiWpp3b1lng0pD0c4T+ELA5yaVJLgSuAfad3llVX6+q1VW1qao2AQ8ClrkkDdm8hV5VLwA3AfuBx4F7qurRJLcmuWqxA0qS+tPXG4uq6j7gvhnbPjjH2DeefyxJ0kK5loskNWJJvfXfdUEkaW5LptBdF0SSzm7JTLm4Logknd2SKXTXBZGks1syhe66IJJ0dkum0F0XRJLObsmcFD194tOrXKT5eUXY8rRkCh1cF0Tqh1eELV9LZspFUn+8Imz5stClxnhF2PJloUuN8Yqw5ctClxrjFWHL15I6KSppfl4RtnxZ6FKDvCJseXLKRZIaYaFLUiMsdElqhIUuSY2w0CWpERa6JDXCQpekRljoktQI31gkDYlrlGuxWejSELhGuYbBKRdpCFyjXMNgoUtD4BrlGgYLXRoC1yjXMFjo0hC4RrmGwZOi0hC4RrmGwUKXhsQ1yrXYnHKRpEZY6JLUCAtdkhrhHLrGmm+Xl/pnoWts+XZ5aWGcctHY8u3y0sJY6Bpbvl1eWhgLXWPLt8tLC9NXoSfZkeRwkiNJbp5l/3uSPJbkkSSfS3LJ4KNqufHt8tLCzFvoSVYAtwFXAFuBa5NsnTHsIDBZVa8DPg385qCDavnZuW0dH3rLZaxbNUGAdasm+NBbLvOEqDSHfq5yuRw4UlVPAiS5G7gaeOz0gKq6v2f8g8B1gwyp5cu3y0v962fKZR3wTM/9o91tc7kB+Mz5hJIkLdxAr0NPch0wCfzEHPtvBG4E2Lhx4yCfWpKWvX6O0KeADT3313e3nSHJm4H3A1dV1bdne6Cqur2qJqtqcs2aNeeSV5I0h34K/SFgc5JLk1wIXAPs6x2QZBvwUTpl/uzgY0qS5jNvoVfVC8BNwH7gceCeqno0ya1JruoO2wN8H/CfkjycZN8cDydJWiR9zaFX1X3AfTO2fbDn9psHnEuStEAuziVp2WptNU8LXdKy1OJqnq7lImlZanE1Twtd0rLU4mqeFrqkZanF1TwtdEnLUoureXpSVNKydPrEp1e5SFIDWlvN0ykXSWqEhS5JjbDQJakRFrokNcJCl6RGpKpG88TJceDpc/zy1cBzA4yzWMw5OEshI5hzkJZCRhh+zkuqatZPCBpZoZ+PJAeqanLUOeZjzsFZChnBnIO0FDLCeOV0ykWSGmGhS1Ijlmqh3z7qAH0y5+AshYxgzkFaChlhjHIuyTl0SdJLLdUjdEnSDBa6JDVirAs9yY4kh5McSXLzLPt/PMn/TPJCkp8bRcZujvlyvifJY0keSfK5JJeMYcZ3JjmU5OEkf5Jk67Az9pOzZ9xbk1SSkVwu1sfreX2S493X8+Ekbx+3jN0xP9/92Xw0yaeGnbGbYb7X8rd7XscvJzkxpjk3Jrk/ycHuv/Urhx6yqsbyD7ACeAL4QeBC4EvA1hljNgGvAz4B/NwY5/xJ4BXd2+8Cfn8MM76y5/ZVwH8Zx9eyO+4i4I+BB4HJccwJXA/8zih+JheQcTNwEPhr3fuvGsecM8a/G7hjHHPSOTn6ru7trcBTw845zkfolwNHqurJqvoOcDdwde+Aqnqqqh4BvjuKgF395Ly/qv6qe/dBYP0YZvzLnrvfC4zibPm8Obt+Ffgw8K1hhuvRb85R6ifjO4DbquprAFX17JAzwsJfy2uBu4aS7Ez95Czgld3bFwPHhpgPGO8pl3XAMz33j3a3jZuF5rwB+MyiJnqpvjIm+eUkTwC/CfzjIWXrNW/OJK8HNlTVHwwz2Az9fs/f2v3V+9NJNgwn2ov6yfhq4NVJPp/kwSQ7hpbu/+v73093qvJS4I+GkGumfnLeAlyX5ChwH53fJoZqnAu9OUmuAyaBPaPOMpuquq2qfgh4H/CBUeeZKcnLgN8C3jvqLH34z8Cmqnod8Fng4yPOM5sL6Ey7vJHOke/HkqwaaaKzuwb4dFWdGnWQOVwL3FlV64ErgU92f2aHZpwLfQroPapZ3902bvrKmeTNwPuBq6rq20PKdtpCX8u7gZ2Lmmh28+W8CPgR4IEkTwFvAPaN4MTovK9nVT3f833+XeBvDinbaf18z48C+6rqZFV9BfgynYIfpoX8bF7DaKZboL+cNwD3AFTVF4DvobNw1/AMe9J+ASchLgCepPMr1umTED88x9g7Gd1J0XlzAtvonFDZPMYZN/fc/nvAgXHMOWP8A4zmpGg/r+cP9Nz++8CDY5hxB/Dx7u3VdKYUvn/ccnbHvQZ4iu6bIcf0e/4Z4Pru7dfSmUMfat6hvzALfBGvpHPU8ATw/u62W+kc5QL8KJ2jjG8CzwOPjmnOPwT+HHi4+2ffGGb818Cj3Xz3n61IR5lzxtiRFHqfr+eHuq/nl7qv52vGMGPoTGE9BhwCrhnH17J7/xbgN0aRbwGv51bg893v+cPAzww7o2/9l6RGjPMcuiRpASx0SWqEhS5JjbDQJakRFrokNcJCl6RGWOiS1Ij/B3yu4Pqdxm74AAAAAElFTkSuQmCC\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "d = np.zeros((N,N))\n",
        "for i in range(N):\n",
        "    for j in range(N):\n",
        "        d[i, j] = np.sqrt((city_x[i] - city_x[j])**2 + (city_y[i] - city_y[j])**2)\n",
        "\n",
        "print(d);"
      ],
      "metadata": {
        "id": "QCVpGtE6VXeg",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7d603ab9-323c-453d-e778-a42ecc911264"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.         0.55586543 0.23762635 0.44296208 0.37094032 0.24643828\n",
            "  0.48755071 0.65443321 0.21821401 0.09298449]\n",
            " [0.55586543 0.         0.57017555 0.23723199 0.38006968 0.72459275\n",
            "  0.77723735 0.18671456 0.7156655  0.63457718]\n",
            " [0.23762635 0.57017555 0.         0.55577966 0.23612764 0.47190011\n",
            "  0.26498617 0.5989746  0.18868444 0.2141163 ]\n",
            " [0.44296208 0.23723199 0.55577966 0.         0.45417535 0.54391467\n",
            "  0.80757706 0.41994878 0.64639372 0.53469176]\n",
            " [0.37094032 0.38006968 0.23612764 0.45417535 0.         0.6138173\n",
            "  0.39820959 0.36924522 0.42039306 0.40142625]\n",
            " [0.24643828 0.72459275 0.47190011 0.54391467 0.6138173  0.\n",
            "  0.69343592 0.85720922 0.37044762 0.26354796]\n",
            " [0.48755071 0.77723735 0.26498617 0.80757706 0.39820959 0.69343592\n",
            "  0.         0.75223003 0.32942786 0.43267777]\n",
            " [0.65443321 0.18671456 0.5989746  0.41994878 0.36924522 0.85720922\n",
            "  0.75223003 0.         0.77175813 0.71803754]\n",
            " [0.21821401 0.7156655  0.18868444 0.64639372 0.42039306 0.37044762\n",
            "  0.32942786 0.77175813 0.         0.13097396]\n",
            " [0.09298449 0.63457718 0.2141163  0.53469176 0.40142625 0.26354796\n",
            "  0.43267777 0.71803754 0.13097396 0.        ]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "A = 500 \n",
        "B = 500 \n",
        "C = 1000 \n",
        "D = 500 \n",
        "alpha = 0.0001 "
      ],
      "metadata": {
        "id": "U2djFqFaVZJM"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "def hopfield():\n",
        "    u0 = 0.02 \n",
        "    toend = 0\n",
        "    udao = np.zeros((N, N)) \n",
        "    ctr = 0\n",
        "    while toend == 0:\n",
        "        ctr += 1\n",
        "        v = np.random.rand(N,N)\n",
        "        u = np.ones([N, N])*(-u0*np.log(N-1)/2)\n",
        "        u += u*0.91\n",
        "        for _ in range(1000):\n",
        "            for vx in range(N):\n",
        "                for vi in range(N):\n",
        "                    j1, j2, j3, j4 = 0, 0, 0, 0\n",
        "                    for j in range(N):\n",
        "                        if j != vi:\n",
        "                            j1 += v[vx, j]\n",
        "                    j1 *= -A\n",
        "\n",
        "                    for y in range(N):\n",
        "                        if y != vx:\n",
        "                            j2 += v[y, vi]\n",
        "                    j2 *= -B\n",
        "                   \n",
        "                    j3 = np.sum(v)\n",
        "                    j3 = -C*(j3-N)\n",
        "\n",
        "                    for y in range(N):\n",
        "                        if y != vx:\n",
        "                            if vi == 0:\n",
        "                                j4 += d[vx, y]*(v[y, vi+1]+v[y, N-1])\n",
        "                            elif vi == N-1:\n",
        "                                j4 += d[vx, y]*(v[y, vi-1]+v[y, 0])\n",
        "                            else:\n",
        "                                j4 += d[vx, y]*(v[y, vi+1]+v[y, vi-1])\n",
        "                    j4 *= -D\n",
        "                    udao[vx, vi] = -u[vx, vi]+j1+j2+j3+j4\n",
        "                 \n",
        "\n",
        "            u = u + alpha*udao\n",
        "\n",
        "            v = (1+np.tanh(u/u0)) / 2\n",
        "\n",
        "            for vx in range(N):\n",
        "                for vi in range(N):\n",
        "                    if(v[vx, vi] < 0.7):\n",
        "                        v[vx, vi] = 0\n",
        "                    if(v[vx, vi] >= 0.7):\n",
        "                        v[vx, vi]=1\n",
        "\n",
        "      \n",
        "        t1, t2, t3 = 0, 0, 0\n",
        "\n",
        "     \n",
        "        t1=0\n",
        "        for vx in range(N):\n",
        "            for vi in range(N):\n",
        "                t1+=v[vx, vi]\n",
        "\n",
        "        \n",
        "        t2=0\n",
        "        for x in range(N):\n",
        "            for i in range(N-1):\n",
        "                for j in range(i+1, N):\n",
        "                    t2+=np.multiply(v[x, i], v[x, j])\n",
        "\n",
        "      \n",
        "        t3=0\n",
        "        for i in range(N):\n",
        "            for x in range(N-1):\n",
        "                for y in range(x+1, N):\n",
        "                    t3+=np.multiply(v[x, i], v[y, i])\n",
        "\n",
        "        # stop the loop after getting the valid solution\n",
        "        if t1 == N and t2 == 0 and t3 == 0:\n",
        "            toend = 1\n",
        "        else:\n",
        "            toend = 0\n",
        "    # returns the resulting matrix v and the number of iterations ctr that were required to obtain a valid solution.\n",
        "    return(v, ctr)"
      ],
      "metadata": {
        "id": "05OvUp-9VbYQ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "def total_distance(v):\n",
        "    city_x_final = np.zeros((N+1))\n",
        "    city_y_final = np.zeros((N+1))\n",
        "\n",
        "    for j in range(N):\n",
        "        for i in range(N):\n",
        "            if v[i,j] == 1:\n",
        "                city_x_final[j] = city_x[i]\n",
        "                city_y_final[j] = city_y[i]\n",
        "\n",
        "    city_x_final[N] = city_x_final[0]\n",
        "    city_y_final[N] = city_y_final[0]\n",
        "\n",
        "    # calculate the total distance\n",
        "    td = 0\n",
        "    for i in range(N-1):\n",
        "        td += np.sqrt((city_x_final[i] - city_x_final[i+1])**2\n",
        "                    + (city_y_final[i] - city_y_final[i+1])**2)\n",
        "    td += np.sqrt((city_x_final[N-1] - city_x_final[0])**2\n",
        "                + (city_y_final[N-1] - city_y_final[0])**2)\n",
        "    \n",
        "    return(td, city_x_final, city_y_final)"
      ],
      "metadata": {
        "id": "7C2tQY8rVdtB"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#It initializes a v matrix with zeros\n",
        "v = np.zeros([N,N])\n",
        "\n",
        "ct = 0\n",
        "\n",
        "min_dist = 20\n",
        "best_path = None\n",
        "\n",
        "# runs the hopfield() function 20 times and \n",
        "# at each iteration, checks if the resulting path has a lower total distance than the current minimum distance. \n",
        "# If the total distance is less than the previous minimum distance, \n",
        "# it updates the minimum distance and stores the binary matrix as the best path\n",
        "\n",
        "for i in range(20):\n",
        "    v, steps = hopfield()\n",
        "    print(v)\n",
        "    td, _, _ = total_distance(v)\n",
        "    print(f\"Epoch {i}: Ran for {steps} steps, total distance {td}\")\n",
        "    if td < min_dist:\n",
        "        min_dist = td\n",
        "        best_path = v\n",
        "print(min_dist)\n",
        "print(best_path)\n",
        "# At the end of the loop, it prints the final minimum distance and the best path found.\n"
      ],
      "metadata": {
        "id": "EAbrdudeVfZM",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "5efbebf9-6275-4dc5-c35e-42752b9c1674"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]\n",
            " [0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 1. 0.]\n",
            " [0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]\n",
            " [0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]]\n",
            "Epoch 0: Ran for 13 steps, total distance 3.3233486623836566\n",
            "[[0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]\n",
            " [0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 1. 0.]\n",
            " [0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]\n",
            " [0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]\n",
            " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]\n",
            " [0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]]\n",
            "Epoch 1: Ran for 3 steps, total distance 3.2490695643593552\n",
            "[[0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 1. 0.]\n",
            " [0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]\n",
            " [0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]\n",
            " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]\n",
            " [0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]]\n",
            "Epoch 2: Ran for 27 steps, total distance 2.983270667570208\n",
            "[[0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]\n",
            " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]\n",
            " [0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]\n",
            " [0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 1. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]]\n",
            "Epoch 3: Ran for 4 steps, total distance 3.1761215421570794\n",
            "[[0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 1. 0.]\n",
            " [0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]\n",
            " [0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]\n",
            " [0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]\n",
            " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]]\n",
            "Epoch 4: Ran for 3 steps, total distance 2.868295603745608\n",
            "[[1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]\n",
            " [0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]\n",
            " [0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 1. 0.]]\n",
            "Epoch 5: Ran for 2 steps, total distance 2.728994260510732\n",
            "[[0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]\n",
            " [0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]\n",
            " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]\n",
            " [0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]\n",
            " [0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 1. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]]\n",
            "Epoch 6: Ran for 3 steps, total distance 3.0442057327970597\n",
            "[[0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]\n",
            " [0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]\n",
            " [0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 1. 0.]\n",
            " [0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]\n",
            " [0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]]\n",
            "Epoch 7: Ran for 7 steps, total distance 3.355054759942739\n",
            "[[0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]\n",
            " [0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]\n",
            " [0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]\n",
            " [0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 1. 0.]\n",
            " [0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]\n",
            " [0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]]\n",
            "Epoch 8: Ran for 5 steps, total distance 2.6380448548001327\n",
            "[[0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 1. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]\n",
            " [0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]\n",
            " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]\n",
            " [0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]]\n",
            "Epoch 9: Ran for 2 steps, total distance 3.0009976483418748\n",
            "[[0. 0. 0. 0. 0. 0. 0. 0. 1. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]\n",
            " [0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]\n",
            " [0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]\n",
            " [0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]\n",
            " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]]\n",
            "Epoch 10: Ran for 12 steps, total distance 3.1955643913882614\n",
            "[[0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]\n",
            " [0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]\n",
            " [0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 1. 0.]]\n",
            "Epoch 11: Ran for 28 steps, total distance 3.191860618099216\n",
            "[[0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]\n",
            " [0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]\n",
            " [0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]\n",
            " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]\n",
            " [0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 1. 0.]]\n",
            "Epoch 12: Ran for 1 steps, total distance 2.6380448548001327\n",
            "[[0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]\n",
            " [0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 1. 0.]\n",
            " [0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]\n",
            " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]\n",
            " [0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]\n",
            " [0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]]\n",
            "Epoch 13: Ran for 3 steps, total distance 2.889634138427449\n",
            "[[0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 1. 0.]\n",
            " [0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]\n",
            " [0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]\n",
            " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]\n",
            " [0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]]\n",
            "Epoch 14: Ran for 1 steps, total distance 3.0437900133038482\n",
            "[[0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 1. 0.]\n",
            " [0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]\n",
            " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]\n",
            " [0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]\n",
            " [0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]]\n",
            "Epoch 15: Ran for 4 steps, total distance 2.659383389481974\n",
            "[[0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]\n",
            " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 1. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]\n",
            " [0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]\n",
            " [0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]]\n",
            "Epoch 16: Ran for 1 steps, total distance 3.5715540919663757\n",
            "[[0. 0. 0. 0. 0. 0. 0. 0. 1. 0.]\n",
            " [0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]\n",
            " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]\n",
            " [0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]\n",
            " [0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]]\n",
            "Epoch 17: Ran for 2 steps, total distance 3.0692102090024926\n",
            "[[0. 0. 0. 0. 0. 0. 0. 0. 1. 0.]\n",
            " [0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]\n",
            " [0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]\n",
            " [0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]\n",
            " [0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]]\n",
            "Epoch 18: Ran for 3 steps, total distance 2.9551954286793247\n",
            "[[0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]\n",
            " [0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 1. 0.]\n",
            " [0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]\n",
            " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]\n",
            " [0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]]\n",
            "Epoch 19: Ran for 1 steps, total distance 2.728994260510732\n",
            "2.6380448548001327\n",
            "[[0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]\n",
            " [0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]\n",
            " [0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]\n",
            " [0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 1. 0.]\n",
            " [0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]\n",
            " [0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# takes in a Hopfield network state v and returns a string representation of the optimal route for the Traveling Salesman Problem (TSP) found by the network.\n",
        "# The function does this by iterating over each column of the state matrix and appending the index of the row with the highest activation to a string, \n",
        "# separated by arrows ->. Finally, the first index is appended to the end to create a cycle.\n",
        "#search for 1 column wise in  the best path matrix\n",
        "def get_route(v):\n",
        "    route = \"\"\n",
        "    for j in range(v.shape[1]):\n",
        "        route += str(np.argmax(v[:, j])) + ' -> '\n",
        "    return (route + str(np.argmax(v[:, 0])))\n",
        "#For each column, it finds the row with the highest value (which will be 1 in the case of the Hopfield network), using the np.argmax() function.\n",
        "#after the loop has finished, it appends the index of the first city to the route string to complete the tour.\n",
        "\n",
        "# For example, if v is a 5x5 matrix representing the optimal state of the Hopfield network for the TSP, \n",
        "# get_route(v) might return the string \"3 -> 1 -> 0 -> 4 -> 2 -> 3\", indicating that the optimal route starts at node 3, \n",
        "# then goes to node 1, node 0, and so on, before returning to node 3 to complete the cycle.    "
      ],
      "metadata": {
        "id": "O0FPDGzRVhiE"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(get_route(best_path))"
      ],
      "metadata": {
        "id": "twOUatsgVjTq",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "62ab3dda-34ef-4078-a410-541e9dacfe8c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "9 -> 8 -> 6 -> 2 -> 4 -> 7 -> 1 -> 3 -> 5 -> 0 -> 9\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "def get_route_indices(v):\n",
        "    indices = []\n",
        "    for j in range(v.shape[1]):\n",
        "        indices.append(np.argmax(v[:, j]))\n",
        "    indices.append(np.argmax(v[:, 0]))\n",
        "    return indices"
      ],
      "metadata": {
        "id": "ziN-BfoOVlJb"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "indices = get_route_indices(best_path)\n",
        "print(indices)"
      ],
      "metadata": {
        "id": "LF4mMVTaVmz9",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "83d45818-5fbb-46b2-d99c-c79afc7d31f6"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[9, 8, 6, 2, 4, 7, 1, 3, 5, 0, 9]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# indices = get_route_indices(best_path)\n",
        "for i in indices[1:]:\n",
        "    plt.plot([city_x[i], city_x[i-1]], [city_y[i], city_y[i-1]], '-')\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "ia8KcY9N0TTn",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "98f5ecd3-42a1-4600-d751-0ac0f405bd69"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}