MazeAlgo_main.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# MazeAlgo_main"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {},
      "outputs": [],
      "source": [
        "import MazeGen as mg\n",
        "import ipywidgets as widgets"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uyjoExPRR1s2"
      },
      "source": [
        "## General maze "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 368
        },
        "id": "j41DrcoBf1gY",
        "outputId": "f4010ba6-d171-4779-80d1-7ec1c6f73be7"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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kSX0YOMCr6v1VdURVLQZeAVxTVa8e2cgkSTPyc+CS1FEjuRphVa0B1oxiX5Kk2fEIXJI6ygCXpI4ywCWpowxwSeooA1ySOsoAl6SOMsAlqaMMcEnqKANckjrKAJekjho4wJPsm+Rfknw3yY1Jzh3lwCRJMxvmWigPAadW1YNJ9gK+meTvqurbIxqbJGkGAwd49XqxPdg83Kv5Grw/mySpL8P2xFwArAOeCnyiqv5kpu3tiWnd+VjbObfLOfdvLD0xq+rRqloCHAGcmOS4ydvYE1OSxmOoI/AddpR8APhFVX1kum2WLl1aa9eu7XvfXe5lZ935X9s5t8s59y/JaI/AkzwxyYHN/ccBzwG+P+j+JEn9GeZTKIcBFzXr4HsAl1TVVaMZliRpZ4b5FMr3gGeMcCySpD54JqYkdZQBLkkdZYBLUkcZ4JLUUQa4JHWUAS5JHWWAS1JHGeCS1FEGuCR1lAEuSR1lgEtSRw1zNcIjk3wjyU1NT8x3jHJgkqSZDXM1wkeA91TV9Un2B9YlubqqNo5obJKkGYyyocMVwMer6urptrGlmnXnY23n3C7n3L/pWqoNcwT+K0kW07u07HVTvLYCWAGwzz77jKKcJIkRHIEneTxwLbCyqi6baVtbqll3PtZ2zu1yzv0beUu1Zqd7AV8EVu8svCVJozXMp1ACXADcVFUfHd2QJEmzMcwR+MnAa4BTk6xvvl44onFJknZimJ6Y3wQywrFIkvrgmZiS1FEGuCR1lAEuSR1lgEtSRxngktRRBrgkdZQBLkkdZYBLUkcZ4JLUUQa4JHWUAS5JHTXs5WQvTLI5yYZRDUiSNDvDHoF/Bnj+CMYhSerTKDryLAauqqrjdratPTGtOx9rO+d2Oef+jbUn5kzsiSlJ4zH2AK+qVcAq6PXEHKQnXJd72Vl3/td2zu1yzv3rNUB7LD+FIkkdZYBLUkcN+zHCi4FvAcckuTPJ60czLEnSzgy1Bl5VrxzVQCRJ/XEJRZI6ygCXpI4ywCWpowxwSeooA1ySOsoAl6SOMsAlqaMMcEnqKANckjrKAJekjjLAJamjhr2Y1fOT3JzkB0nOHtWgJEk7N3CAJ1kAfAJ4AXAs8Mokx45qYJKkmQ3cEzPJs4E/q6rnNY/fD1BV5033HntiWnc+1nbO7XLO/ZuuJ+YwSyiHA3dMeHxn89wOkqxIsjbJ2m3btg1RTpI00TDXA5+qSdtjDuftiWnd+V7bObfLOfdvHD0x7wSOnPD4COCuIfYnSerDMAH+r8DTkjwlyd7AK4Avj2ZYkqSdGXgJpaoeSfJW4O+BBcCFVXXjyEYmSZrRsD0xvwJ8ZURjkST1wTMxJamjDHBJ6igDXJI6ygCXpI4a+FT6gYoldwO3Dfj2Q4B7RjicLtTe3erOZW3nvHvU7uqcj6qqJ05+stUAH0aStVNdC2BXrr271Z3L2s5596i9q83ZJRRJ6igDXJI6qksBvmo3rL271Z3L2s5596i9S825M2vgkqQddekIXJI0gQEuSR3ViQCfq+bJSS5MsjnJhrZqNnWPTPKNJDcluTHJO1qqu2+Sf0ny3abuuW3UnVB/QZLvJLmq5bq3Jrkhyfoka1use2CSS5N8v/leP7ulusc0c93+tSXJO1uq/a7mv60NSS5Osm8bdZva72jq3jjO+U6VG0l+LcnVSW5pbg8aSbGqmtdf9C5V+0PgaGBv4LvAsS3VPgU4AdjQ8pwPA05o7u8P/L825kyvy9Ljm/t7AdcBz2px3u8GPgdc1fK/963AIW3WbOpeBLyhub83cOAcjGEB8FN6J4qMu9bhwI+BxzWPLwHObGmexwEbgIX0rsL6D8DTxlTrMbkBfBg4u7l/NvChUdTqwhH4icAPqupHVfUw8HngjDYKV9U/Ave2UWtS3U1VdX1z/wHgJqboNzqGulVVDzYP92q+Wvkrd5IjgN8FPtVGvbmW5AB6/6NfAFBVD1fVfXMwlNOAH1bVoGdI92tP4HFJ9qQXpm118Xo68O2q2lpVjwDXAr83jkLT5MYZ9H5g09y+ZBS1uhDgs2qevKtKshh4Br2j4TbqLUiyHtgMXF1VrdQFzgfeB/xHS/UmKuBrSdYlWdFSzaOBu4FPN8tGn0qyX0u1J3oFcHEbharqJ8BHgNuBTcD9VfW1NmrTO/o+JcnBSRYCL2THlpDj9qSq2gS9AzTg0FHstAsBPqvmybuiJI8Hvgi8s6q2tFGzqh6tqiX0epyemOS4cddM8iJgc1WtG3etaZxcVScALwDOSnJKCzX3pPdr9l9X1TOAX9D71bo1TSvEFwN/21K9g+gdiT4FeDKwX5JXt1G7qm4CPgRcDXyV3lLsI23UHqcuBPhu2Tw5yV70wnt1VV3Wdv3m1/k1wPNbKHcy8OIkt9JbIjs1yWdbqAtAVd3V3G4GLqe3bDdudwJ3TvgN51J6gd6mFwDXV9XPWqr3HODHVXV3VW0DLgN+u6XaVNUFVXVCVZ1Cb4njlrZqAz9LchhAc7t5FDvtQoDvds2Tk4Te2uhNVfXRFus+McmBzf3H0fsf7vvjrltV76+qI6pqMb3v7zVV1cqRWZL9kuy//T7wXHq/bo9VVf0UuCPJMc1TpwEbx113klfS0vJJ43bgWUkWNv+Nn0bv7zutSHJoc7sIeCntzv3LwGub+68FrhjFTofqidmGmsPmyUkuBpYBhyS5E/hAVV3QQumTgdcANzTr0QD/s3o9SMfpMOCiJAvo/XC/pKpa/UjfHHgScHkvT9gT+FxVfbWl2m8DVjcHJj8CXtdSXZp14NOBN7VVs6quS3IpcD295Yvv0O6p7V9McjCwDTirqn4+jiJT5QbwQeCSJK+n94PsD0dSq/lYiySpY7qwhCJJmoIBLkkdZYBLUkcZ4JLUUQa4JHWUAS5JHWWAS1JH/X8QK7ppU5LhnwAAAABJRU5ErkJggg==",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Algorithm converged.\n",
            "Number of turns: 5\n",
            "Path length: 10\n",
            "Number of iterations: 1\n",
            "Execution time: 0.21 seconds\n"
          ]
        }
      ],
      "source": [
        "numTurns = 5\n",
        "pathLength=10\n",
        "mg.genMaze(numTurns=numTurns, pathLength=pathLength)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## More complicated maze with more iterations"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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y5qTyUn0+m5mZdaTuTMwJwFLgpcD5EfGxkfb3TMy889pcW+q8NtfWRJ41a91+xwEwbcWlle7fyEzMiHgmImYBewMHSdp/8D6eiWlm1oxaR+CbBUlnAU9ExLnD7TN79uzo6+vrOLvN8wTbXFvqvDbXljqvzbU1kWfNOu4/fgpUfxuhpLRH4JJ2lzS1vL498Ebgl1XzzMysM3XehTINuLhcB98GuCwirk1TlpmZjabOu1BuBV6TsBYzM+uAz8Q0M8uUG7iZWabcwM3MMuVPIzTbSn1jyRquXnZ30sxjZ+3FO16XZhhBm6X+2a1Yt4H9pu2ULK+fj8DNtlJXL7ubFes2JMtbsW5D8j8IbZX6Z7fftJ04dtZeyfL6+QjcbCu237Sdkn0Gdf/JKM8XKX92TfERuJlZptzAzcwy5QZuZpYpN3Azs0y5gZuZZarOpxHuI+lHklaWMzFPS1mYmZmNrM7bCJ8GPhIRN0uaAiyVdENErEhUm5mZjSDlQIergfMi4obh9vFItbzz2lxb6rw21zbWvLpjvJrOa7O2PdfhRqolOZFHUjfFR8suGeJ7C4AFANtuu22KhzMzMxIcgUvaEVgMLIyIK0fa1yPV8s5rc22p89pc21jz6o7xajqvzdr2XJOPVCtDJwFXAL2jNW8zM0urzrtQBFwArIyIz6UryczMxqLOEfihwLuAwyQtKy9HJarLzMxGUWcm5o2AEtZiZmYd8JmYZmaZcgM3a4ne23rp/kI325y9Dd1f6Kb3tt4tXZK1nAc6mLVA7229LPj2AjZu2gjA6kdXs+DbCwCY/6r5W7I0azE3cLMWOPMHZ7Jx00Z2eepkJseMYuOTcOZl67nmJ8+dhNN/puBIU3KW/OahUffpROo8SDdjM5cZlql5CcWsBdY8umbI7b9/5slxrmT8pJyxmcsMy9R8BG7WAvvuvC+rH13Nw5O/stn26TtP59L3n/Gc/efO/TgAl/7b3w6b2fYzMVPP2MxhhmVqPgI3a4GF8xbSNalrs21dk7pYOG/hFqrIcuAGbtYC8181n5639DB95+kIMX3n6fS8pccvYNqIvIRi1hLzXzXfDds64iNwM7NMuYGbmWWq7sfJXihpvaTlqQoyM7OxqXsEfhFwRII6zMysQykm8nQD10bE/qPt65mYeee1ubbUeW2ubax5bZ+JmTKvbTMsU2t0JuZIPBPTzKwZ43oE7pmYeee1ubbUeW2ubax5uZyJmSKvbTMsU2tkJqaZmW05buBmZpmq+zbCS4CfAjMlrZX03jRlmZnZaGq9iBkRJ6QqxMzMOuMlFDOzTLmBm5llyg3czCxT/jhZs63YinUbkk2+aWJOZKr6cplhmZobuNlWKvVMx9RzIlNm5TLDMjU3cLOt1Dtet2+Sie9NaXt9OfAauJlZptzAzcwy5QZuZpYpN3Azs0y5gZuZZaruh1kdIWmVpF9JOiNVUWZmNrrKDVzSBOB84EhgP+AESfulKszMzEZWeSKPpEOAT0fEm8vbHweIiH8e7j6eiZl3XptrS53X5tqayLN2G24mZp0llL2A3w64vbbcthlJCyT1SerbtGlTjYczM7OB6pyJqSG2PedwPiJ6gB4oZmJWmQnY5vmEba4tdV6ba0ud1+bamsizdpOGarf1jsDXAvsMuL03cE+NPDMz60CdBv5z4GWSXixpMnA8cE2asszMbDSVl1Ai4mlJpwL/DUwALoyI25NVZmZmI6o7E/O7wHcT1WJmZh3wmZhmZplyAzczy5QbuJlZptzAzcwyVflU+koPJt0PrK54992ABxKWkzKvzbWlzmtzbanz2lxbE3nWXtMjYvfBG8e1gdchqW+ozwJoQ16ba0ud1+baUue1ubYm8iw/XkIxM8uUG7iZWaZyauA9Lc5rc22p89pcW+q8NtfWRJ5lJps1cDMz21xOR+BmZjaAG7iZWaayaOAphydLulDSeknLE9S1j6QfSVop6XZJp9XM207SzyTdUuadnaDGCZJ+IenaBFl3SbpN0jJJfQnypkq6XNIvy5/hIRVzZpY19V82SDq9Zm0fKn8HyyVdImm7GlmnlTm3V6lrqH+zkl4g6QZJd5Rfd6lan2UsIlp9ofio2l8DM4DJwC3AfjXy5gAHAMsT1DYNOKC8PgX4v5q1CdixvD4JWAIcXLPGDwPfAK5N8HzvAnZL+Lu9GHhfeX0yMDXRv5d7KU58qJqxF/AbYPvy9mXAuytm7Q8sB7ooPv3z+8DLOsx4zr9Z4LPAGeX1M4BzUv1efMnnksMR+EHAryLizoh4CvgmcGzVsIj4MfBQisIiYl1E3FxefwxYyRBzQTvIi4h4vLw5qbxUfpVZ0t7AnwNfrZrRFEk7UTSmCwAi4qmIeCRB9Dzg1xFR9YzffhOB7SVNpGi+VadNvQK4KSI2RsTTwGLgLzsJGObf7LEUfwApv/5FxfosYzk08DENT97SJHUDr6E4aq6TM0HSMmA9cENE1Mn7AvBR4Nk6NQ0QwPWSlkpaUDNrBnA/8LVyieerknaoXyLHA5fUCYiIu4FzgTXAOuDRiLi+YtxyYI6kXSV1AUex+SjCqvaMiHVlveuAPRJkWmZyaOBjGp68JUnaEbgCOD0iNtTJiohnImIWxYzRgyTtX7Gmo4H1EbG0Tj2DHBoRBwBHAqdImlMjayLFssC/R8RrgCcolgIqK0f7HQN8q2bOLhRHuC8GXgTsIOmdVbIiYiVwDnADcB3FEuDTdeoz65dDA2/18GRJkyiad29EXJkqt1xOWAQcUTHiUOAYSXdRLDsdJunrNWu6p/y6HriKYnmrqrXA2gH/h3E5RUOv40jg5oi4r2bOG4HfRMT9EbEJuBJ4fdWwiLggIg6IiDkUSyF31KwP4D5J0wDKr+sTZFpmcmjgrR2eLEkUa7grI+JzCfJ2lzS1vL49RSP5ZZWsiPh4ROwdEd0UP7MfRkSlo8iynh0kTem/DhxOsTxQSUTcC/xW0sxy0zxgRdW80gnUXD4prQEOltRV/o7nUby+UYmkPcqv+wJvTVTjNcCJ5fUTgasTZFpmas3EHA+ReHiypEuAucBuktYCZ0XEBRXjDgXeBdxWrlsD/H0Us0KrmAZcLGkCxR/XyyKi9tv/EtkTuKroZ0wEvhER19XM/ADQW/5hvhM4qWpQub78JuD9NWsiIpZIuhy4mWK54xfUO239Ckm7ApuAUyLi4U7uPNS/WeAzwGWS3kvxB+ftNeqzTPlUejOzTOWwhGJmZkNwAzczy5QbuJlZptzAzcwy5QZuZpYpN3Azs0y5gZuZZer/AaKcFpLxMrShAAAAAElFTkSuQmCC",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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/CK6NiFvKScvMzAbTcAGPiF8B7yoxFzMzq4N7oZiZJcqX0psl6uqla7hp+RMNvbb7XO7uM0rqsXL9JqaOH9tQXCuXZ+Bmibpp+ROsXL+p8rhTx4/l+GkTKo9rr+UZuFnCpo4f29D52DNnngfANd/+RNkpWYU8AzczS5QLuJlZolzAzcwSVeRKzL0l/VTSqrwf+FllJmZmZgMr8ibmFuAzEXGfpDHAMkmLImJlSbmZmdkASulGCCDpJuDiiFjU3z7uB+64QzF2qmMu0pc71TGnGLeM2P31Ay/lNEJJ7WSX1ffZDxyYAzB69OgywpmZGSXMwCXtDCwB5kfEDQPt637gjjsUY6c65iJ9uVMdc4pxy4jdlH7g+WdhXg90DFa8zcysXEXOQhFwKbAqIr5eXkpmZlaLIjPwQ4EPA++TtDz/OqakvMzMbBBF+oHfDajEXMzMrA6+EtPMLFHuRmhWkPtyW6t4Bm5WkPtyW6t4Bm5WAvfltlbwDNzMLFEu4GZmiSp6JeZlkjZIWlFWQmZmVpuiM/ArgKNKyMPMzOpUqIBHxF3AMyXlYmZmdSijG2E7cEtE7DfYvu4H7rhDMXbRuCn25fbPuVpDuh/4QNwP3MysOSqdgbsfuOMOxdhF46bYl9s/52oNyX7gZmbWOkVPI1wI/ByYImmtpI+Wk5aZmQ2m0Bp4RJxUViJmZlYfL6GYmSXKzazMSrBy/aaGWsIWaScLcPy0CZx80KSGXmvpcwE3K6hVLV27W9i6gA9fLuBmBZ180KSGi2iRdrKNztpt2+E1cDOzRLmAm5klygXczCxRRS/kOUrSakm/lnRuWUmZmdngGi7gkkYAlwBHA1OBkyRNLSsxMzMbWMPNrCQdAnwpIo7MH58HEBH/3N9r3E7WcYdi7FTHnGIb21bGTnnM/bWTLbKEMgF4vMfjtfm2rUiaI6lTUmdXV1eBcGZm1lOR88DVx7bXTOcjYgGwALJ2so20U0y5DaTjDv3YqY751Ta2DZxDnuqYU4xbRmypr3JbbAa+Fti7x+OJwLoCxzMzszoUKeC/APaV9EZJo4ATgZvLScvMzAbT8BJKRGyRNBf4ETACuCwiHiwtMzMzG1DRT6W/LSLeEhFvioj5ZSVlloyODmhvh+22y247OlqdkQ0jbmZl1qiODpgzBzZvzh4/9lj2GGD27NblZcOGC7hZo+bN+//i3W3zZtb+3Tn8+QPjajvGwZ8FoP3cW8vNzYYF90Ixa9SaNX1u3mvT0xUnYsOVZ+BmjZo0KVs26WW7fSbx6FffX9MhyjgP3IYvz8DNGjV/PrS1bb2trS3bblYBF3CzRs2eDQsWsPH1e/IKgn32gQUL/AamVcZLKGZFzJ7N3BcmA3DNxw9pcTI23HgGbmaWKBdwM7NEuYCbmSXKBdzMLFEu4GZmiXIBNzNLlAu4mVmiXMDNzBLlAm5mligXcDOzRPlSerMSrFy/qaHugOunngA01llw6W+fafi1ReICHD9tAicfNKmh11p5XMDNCjp+2oRWp1Cples3AbiADwEu4GYFnXzQpIaL2cyZ5wFwzbc/Ufdru2fPjTTRKiOutZ7XwM3MEuUCbmaWKBdwM7NEuYCbmSXKBdzMLFEu4GZmiXIBNzNLlAu4mVmiXMDNzBLlAm5mligXcDOzRLmAm5klygXczCxR7kZolrBW9CFfuX4TU8ePrft1Vj4XcLNEtaoP+dTxY4ddD/ShygXcLFGt6kNuQ4fXwM3MEuUCbmaWKBdwM7NEuYCbmSXKBdzMLFEu4GZmiXIBNzNLlAu4mVmiFBHVBZM2Ao81+PLdgKdLTCeF2MMtbitje8zDI3aqY94nInbvvbHSAl6EpM6ImD6cYg+3uK2M7TEPj9jb2pi9hGJmligXcDOzRKVUwBcMw9jDLW4rY3vMwyP2NjXmZNbAzcxsaynNwM3MrAcXcDOzRCVRwCUdJWm1pF9LOrfCuJdJ2iBpRVUx87h7S/qppFWSHpR0VkVxd5B0r6T787hfriJuj/gjJP1S0i0Vx31U0gOSlkvqrDDuOEnXSXoo/1kfUlHcKflYu782STq7otjn5P+2VkhaKGmHKuLmsc/K4z7YzPH2VTckvV7SIkkP57e7lBIsIob0FzAC+A0wGRgF3A9MrSj2DGB/YEXFYx4P7J/fHwP8bxVjBgTsnN/fHlgKHFzhuD8NXA3cUvH3+1Fgtypj5nGvBD6W3x8FjGtBDiOAJ8kuFGl2rAnAb4Ed88fXAqdVNM79gBVAG9knkf0Y2LdJsV5TN4CvAefm988FLigjVgoz8AOBX0fEIxHxEvA94PgqAkfEXcAzVcTqFXd9RNyX338eWEX2j7/ZcSMiXsgfbp9/VfIut6SJwPuB71YRr9UkjSX7j34pQES8FBHPtiCVWcBvIqLRK6TrNRLYUdJIsmK6rqK4bwPuiYjNEbEFWAL8VTMC9VM3jif7hU1++5dlxEqhgE8AHu/xeC0VFLOhQlI78C6y2XAV8UZIWg5sABZFRCVxgYuAzwGvVBSvpwDukLRM0pyKYk4GNgKX58tG35W0U0WxezoRWFhFoIh4ArgQWAOsB56LiDuqiE02+54haVdJbcAxwN4VxQbYMyLWQzZBA/Yo46ApFHD1sW1YnPsoaWfgeuDsiNhURcyIeDkipgETgQMl7dfsmJKOBTZExLJmx+rHoRGxP3A0cKakGRXEHEn2Z/a/RcS7gD+Q/WldGUmjgOOA71cUbxeymegbgb2AnSSdUkXsiFgFXAAsAm4nW4rdUkXsZkqhgK9l69+UE6nuz66WkbQ9WfHuiIgbqo6f/zm/GDiqgnCHAsdJepRsiex9kq6qIC4AEbEuv90A3Ei2bNdsa4G1Pf7CuY6soFfpaOC+iHiqoniHAb+NiI0R0QXcALynothExKURsX9EzCBb4ni4qtjAU5LGA+S3G8o4aAoF/BfAvpLemM8YTgRubnFOTSVJZGujqyLi6xXG3V3SuPz+jmT/4R5qdtyIOC8iJkZEO9nP9ycRUcnMTNJOksZ03weOIPtzu6ki4kngcUlT8k2zgJXNjtvLSVS0fJJbAxwsqS3/Nz6L7P2dSkjaI7+dBHyAasd+M3Bqfv9U4KYyDjqyjIM0U0RskTQX+BHZO+aXRcSDVcSWtBCYCewmaS1wfkRcWkHoQ4EPAw/k69EA/xARtzU57njgSkkjyH65XxsRlZ7S1wJ7Ajdm9YSRwNURcXtFsT8JdOQTk0eA0yuKS74OfDjw8apiRsRSSdcB95EtX/ySai9tv17SrkAXcGZE/L4ZQfqqG8BXgWslfZTsF9mHSomVn9ZiZmaJSWEJxczM+uACbmaWKBdwM7NEuYCbmSXKBdzMLFEu4GZmiXIBNzNL1P8BbHAet2IquHIAAAAASUVORK5CYII=",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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XiLhX0s7AEuDUiLhuvP1dUq3+OHXG8ph6P06dsfpxTN1SRUk1IuLe/OswcBlwYJH2zMysdR0ncEnbSpo+ch84HFhVVsfMzGxiRT6FsgtwmaSRdr4ZEVeX0iszM2uq4wQeEXcCLy2xL2Zm1gafiWlmligncDOzRDmBm5klygnczCxRTuBmZolyAjczS5QTuJlZopzAzcwS5QRuZpaowglc0hRJN0m6sowOmZlZa8qYgZ8GrCmhHTMza0OhBC5pd+D1wFfL6Y6ZmbWqaEGHi4GzgOnAX0fE0RPt75Jq9cepM5bH1Ptx6ozVj2PqltJLqkk6GhiOiBVN9nNJNTOzCnQ8A5d0FvAOYBOwNTADuDQijh/vGJdUqz9OnbE8pt6PU2esfhxTt5ReUi0iPhwRu0fEIHAs8MOJkreZmZXLnwM3M0tUkZJqz4iIpcDSMtoyM7PWeAZuZpYoJ3Azs0Q5gZuZJcoJ3MwsUU7gZmaJcgI3M0uUE7iZWaKcwM3MEuUEbmaWKCdwM7NEFbmc7NaSfirpZkm3SfpkmR0zM7OJFbkWypPAayLicUlTgeslfS8ibiipb2ZmNoFCFXmeaUQaAK4H3hsRy8bbzxV56o9TZyyPqffj1BmrH8fULaVX5IFnKtKvBIaBJWMlb1fkMTOrRlkz8JnAZcCpEbFqvP1ckaf+OHXG8ph6P06dsfpxTN1SekWeRhHxCNn1wI8soz0zM2uuyKdQdspn3kjaBngt8POS+mVmZk0U+RTKbOB8SVPI/hFcFBFXltMtMzNrpuMEHhG3AC8rsS9mZtYGn4lpZpYoJ3Azs0Q5gZuZJcoJ3MwsUU7gZmaJcgI3M0uUE7iZWaKcwM3MEuUEbmaWKCdwM7NEFbmY1R6SfiRpTV5S7bQyO2ZmZhMrcjGrTcAHI+JGSdOBFZKWRMTqkvpmZmYTKKWgA4Cky4EvR8SS8fZxSbX649QZy2Pq/Th1xurHMXXLeCXViszAnyFpkOzKhGOWVAMWAkybNq2McGZmRgkzcEnbAdcCiyLi0on2dUm1+uPUGctj6v04dcbqxzF1SyUl1SRNBS4BhpolbzMzK1eRT6EIOBdYExGfK69LZmbWiiIz8IOBdwCvkbQyv72upH6ZmVkTRUqqXQ+oxL6YmVkbfCammVminMDNzBLlBG5mligncDOzRDmBm5klygnczCxRTuBmZolyAjczS5QTuJlZopzAzcwSVfRqhF+TNCxpVVkdMjOz1hSdgZ8HHFlCP8zMrE1lFHQYBK6MiH2a7euSavXHqTOWx9T7ceqM1Y9j6pZKS6pNxCXVzMyqUXkCj4jFwGLISqp1UvKoH0szeUxpxOq3OHXG6scxdUtWP+fZ/CkUM7NEOYGbmSWq6McILwB+AsyVtE7Su8rplpmZNVNoDTwijiurI2Zm1h4voZiZJcoJ3MwsUU7gZmaJcgI3M0uUE7iZWaKcwM3MEuUEbmaWKCdwM7NEOYGbmSXKCdzMLFFFr4VypKTbJf1C0hlldcrMzJrrOIFLmgKcAxwF7A0cJ2nvsjpmZmYT67ikmqRXAp+IiCPyxx8GiIizxjvGJdXqj1NnLI+p9+PUGasfx9Qt45VUK7KEshvw64bH6/Jtm5G0UNJyScs3btxYIJyZmTUqcjnZsWr8PGs675Jq3Y1TZyyPqffj1BmrH8fULVWUVFsH7NHweHfg3gLtmZlZG4ok8J8BL5T0PElbAccCV5TTLTMza6bjJZSI2CTpFOC/gCnA1yLittJ6ZmZmEypaUu0q4KqS+mJmZm3wmZhmZolyAjczS5QTuJlZopzAzcwS1fGp9B0Fkx4A1nZ4+I7AgyV2pxdieUxpxOq3OHXG6scxdcOciNhp9MZaE3gRkpaPdS2AlGN5TGnE6rc4dcbqxzH1Ei+hmJklygnczCxRKSXwxX0Yy2NKI1a/xakzVj+OqWckswZuZmabS2kGbmZmDZzAzcwSlUQCr6t4sqSvSRqWtKqqGHmcPST9SNIaSbdJOq2iOFtL+qmkm/M4n6wiTkO8KZJuknRlxXHuknSrpJWSllcca6akiyX9PP95vbKCGHPzsYzcNkg6vew4eawP5L8LqyRdIGnrKuLksU7L49xW9njG+luV9BxJSyTdkX/docyYPSkievpGdqnaXwJ7AVsBNwN7VxRrPrA/sKriMc0G9s/vTwf+t4oxkVVN2i6/PxVYBhxU4bj+CvgmcGXF37+7gB2rjNEQ63zg3fn9rYCZFcebAtxHduJG2W3vBvwK2CZ/fBFwYkXj2AdYBQyQXfX0+8ALS2z/WX+rwGeAM/L7ZwBn1/E70s1bCjPwA4FfRMSdEfEH4D+BY6oIFBHXAQ9V0faoOOsj4sb8/mPAGsaoJ1pCnIiIx/OHU/NbJe9aS9odeD3w1Sra7wZJM8gSxbkAEfGHiHik4rCHAr+MiE7PWG5mS2AbSVuSJdeqqmi9GLghIp6IiE3AtcCfldX4OH+rx5D9wyX/+qay4vWqFBJ4S8WTUyVpEHgZ2ey4ivanSFoJDANLIqKSOMAXgL8Bnq6o/UYBXCNphaSFFcbZC3gA+Hq+NPRVSdtWGA+yylYXVNFwRNwDfBa4G1gPPBoR11QRi2z2PV/SLEkDwOvYvARjFXaJiPWQTZKAnSuO13UpJPCWiienSNJ2wCXA6RGxoYoYEfFUROxHVrP0QEn7lB1D0tHAcESsKLvtcRwcEfsDRwHvkzS/ojhbkr1M/9eIeBnwW7KX5pXISxO+EfhWRe3vQDZLfR6wK7CtpOOriBURa4CzgSXA1WRLn5uqiDWZpZDA+7J4sqSpZMl7KCIurTpe/tJ/KXBkBc0fDLxR0l1kS1yvkfSNCuIAEBH35l+HgcvIltmqsA5Y1/Cq5WKyhF6Vo4AbI+L+itp/LfCriHggIjYClwKvqigWEXFuROwfEfPJljvuqCpW7n5JswHyr8MVx+u6FBJ43xVPliSyddU1EfG5CuPsJGlmfn8bsj/gn5cdJyI+HBG7R8Qg2c/nhxFRycxO0raSpo/cBw4ne7leuoi4D/i1pLn5pkOB1VXEyh1HRcsnubuBgyQN5L+Dh5K9/1IJSTvnX/cE3ky1Y4MsL5yQ3z8BuLzieF1XqCZmHaLG4smSLgAOAXaUtA44MyLOrSDUwcA7gFvz9WmAv4usxmiZZgPnS5pC9s/6ooio9CN+NdgFuCzLP2wJfDMirq4w3qnAUD55uBM4qYog+TrxYcDJVbQPEBHLJF0M3Ei2nHET1Z5+fomkWcBG4H0R8XBZDY/1twp8GrhI0rvI/lm9tax4vcqn0puZJSqFJRQzMxuDE7iZWaKcwM3MEuUEbmaWKCdwM7NEOYGbmSXKCdzMLFH/BzswJYXBxe3pAAAAAElFTkSuQmCC",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Algorithm converged.\n",
            "Number of turns: 15\n",
            "Path length: 16\n",
            "Number of iterations: 20\n",
            "Execution time: 3.32 seconds\n"
          ]
        }
      ],
      "source": [
        "numTurns=15\n",
        "pathLength=16\n",
        "mg.genMaze(numTurns=numTurns, pathLength=pathLength, maxIter=1000)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Maze that isn't square "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Algorithm converged.\n",
            "Number of turns: 5\n",
            "Path length: 10\n",
            "Number of iterations: 1\n",
            "Execution time: 0.31 seconds\n"
          ]
        }
      ],
      "source": [
        "numTurns=5\n",
        "pathLength = 10\n",
        "gridX=15\n",
        "mg.genMaze(numTurns=numTurns, pathLength=pathLength, xMax=gridX)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Widget input"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 592,
          "referenced_widgets": [
            "3ee45608fdb7451d8c72a830e7fedd90",
            "e8369a7979854cc3a041353506b42f75",
            "f9f1851327e2421ca23291af47fa4b28",
            "95e51c92bf0144c48542cf4848aa1f92",
            "a5e169e78a7440b2b12fda1c194db065",
            "e36e158c3dbd426299fd0a7088d17d60",
            "cd03f815745b48899d16e94a6c64a478",
            "7d1ca4c29e074f63aa0a3c62b82b2552",
            "a513608c8f1e40c39d90a264cbcbf153",
            "49de817a156f40e3a98dff9dd94ee5a7",
            "d20c29378082408198ce732c5ac61ca9",
            "e3ad6271ebb14e54972ed28d4846c16d",
            "dee2e24460784bb09e9108c8e3cad0e3",
            "3ed2b6e9ee364266969d8c977885cc71",
            "1684c18e4ff44c468db6123c5e110522",
            "101f873720fc42a8979103212d8e98ec",
            "e27f3a3a81b142db931e5c4f1df20368",
            "84a842c71ad344e3be16230a8a4667cc",
            "3e81eed72797474c925c577dc5fe6748",
            "9e231383c19b4bdb9614b4619d79d4b2",
            "607589878827458bbfa57f5229b72cc5",
            "6dff07901df048f2aa51c60a08ffa9a1",
            "f2043401584344fa80711c1f2e903558",
            "fe691928de9347189224f1dcd3657fd5",
            "a61912b65e0f40a39cd2c6278a586869"
          ]
        },
        "id": "ngmHOvpWufkL",
        "outputId": "2c3e4143-c484-41d2-885c-78223fbca484"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "664a07da9fb642d78ec525874f26b20a",
              "version_major": 2,
              "version_minor": 0
            },
            "text/plain": [
              "interactive(children=(IntSlider(value=7, description='numTurns', max=15), IntSlider(value=10, description='pat…"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "_ = widgets.interact(mg.genMaze, numTurns = (0,15,1), pathLength=(1,20,1)) "
      ]
    }
  ],
  "metadata": {
    "colab": {
      "collapsed_sections": [],
      "name": "MazeAlgo.ipynb",
      "provenance": [],
      "toc_visible": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.8.10"
    },
    "widgets": {
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                  "text/plain": "<Figure size 432x288 with 1 Axes>"
                },
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                "text": [
                  "Algorithm converged.\n",
                  "Number of turns: 7\n",
                  "Path length: 10\n",
                  "Number of iterations: 59\n",
                  "Execution time: 0.40 seconds\n"
                ]
              }
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