template/introducing_pig.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Artificial Intelligence UE\n",
    "## pig_lite\n",
    "\n",
    "In this class we are going to work with a small framework called `pig_lite`. `pig` stands for Problem Instance Generation and `pig_lite` is a simplified version of the framework that we have used in previous years. The main purpose of this framework is to generate problems that can be used to test your algorithms.\n",
    "\n",
    "The purpose of this notebook is to show you how to work with `pig_lite`, and more specifically, with instances of the class `Problem`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import random\n",
    "\n",
    "from pig_lite.problem.base import Problem\n",
    "from pig_lite.instance_generation.problem_factory import ProblemFactory"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Creating problems\n",
    "\n",
    "For generating problems we first need an object of the class `ProblemFactory`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "factory = ProblemFactory()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Create a random problem\n",
    "\n",
    "The function `generate_problem` takes three parameters:\n",
    "- problem_type: for now we are going to use `maze` (but you can also try `terrain` and `rooms`)\n",
    "- problem_size: the size of the problems, for a maze this means the width and height\n",
    "- random generator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA94AAAIYCAYAAACbqzQ2AAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjEwLjUsIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvWftoOwAAAAlwSFlzAAAPYQAAD2EBqD+naQAARsBJREFUeJzt3XucF3W9P/D3lwV2QXaXIBcWogXMG4K3vCR6VA5qIpJdzWuo1a+UzlHLjpYWqEdJKo+dRExPKeYFTcMsTypqYqUo3iqlNBXBFMVEWUUB2e/8/lh3j+ty2WXnyw47z+fjMY/aYfYz79kvOLx5feYzhSRJkgAAAABKoltnFwAAAABdmcYbAAAASkjjDQAAACWk8QYAAIAS0ngDAABACWm8AQAAoIQ03gAAAFBCGm8AAAAoIY03AAAAlJDGm1wrFApt2u6555645557olAoxI033ljyuh599NHYb7/9orq6OgqFQlx00UXN57/nnnvaPV57vve4446LoUOHtvscAJuzrN4PNqUXX3wxpkyZEo899ljqY59wwglx8MEHt9i3tntdZ1qwYEFMmTIlnnvuuU6t4/2ee+65KBQKceWVV3Z2KZl1ySWXrPXns7af3ZVXXhmFQmGjPuef/vSnMXjw4FixYsXGF0tude/sAqAz3X///S2+Pvfcc+N3v/td3H333S32jxgxIh555JFNVtcJJ5wQK1asiFmzZsUHPvCBGDp0aPTu3Tvuv//+GDFixCarAyAvsno/2JRefPHFOPvss2Po0KGx8847pzbuo48+GjNnzowHHnigxf613es604IFC+Lss8+O/fffv9Nrea/a2tq4//77Y6uttursUjLrkksuiQ9+8INx3HHHtdif9s9u4sSJccEFF8S0adPi7LPPTmVM8kPjTa597GMfa/H1lltuGd26dWu1f1N7/PHH48tf/nKMGzeuxf7Orgugq8rq/aAr+N73vhd77LFH7Lbbbi32r+tet7HeeeedKBQK0b171/rrbXl5ud+HGyntn1337t3jK1/5Spx77rlx+umnR+/evVMbm67PVHNop3feeSfOPPPMGDRoUFRVVcUBBxwQTz75ZKvj7rzzzhg7dmxUVVVF7969Y++994677rprvWM3TX9as2ZNzJgxo3lqY8S6p4s/9NBD8YlPfCL69esXFRUVscsuu8QNN9zQpmu58sorY9ttt43y8vLYfvvt46qrrmrbDwGAkt4Pmrz++uvxjW98I4YPHx7l5eVRU1MThxxySPztb39rPmbZsmVx0kknxeDBg6Nnz54xfPjwOPPMM2PVqlUtxvrFL34Re+65Z1RXV0fv3r1j+PDhccIJJ0RE4z1m9913j4iI448/vvn+M2XKlIiIePbZZ+OII46IQYMGRXl5eQwYMCDGjh27wWnpL7/8csyePTuOPfbY5n3ru9dFNDbkhx12WHzgAx+IioqK2HnnnWPmzJktxm26J/785z+Pb3zjGzF48OAoLy+Pp59+ep21zJgxI3baaafo06dPVFZWxnbbbRff/va3m2v63Oc+FxERY8aMaa7pvVOU2/I5TpkyJQqFQjz66KPx6U9/OqqqqqK6ujqOOeaYeOWVV1ocO3To0Dj00ENj9uzZseOOO0ZFRUUMHz48/vu//7vFcWubLt10nieeeCKOPPLIqK6ujgEDBsQJJ5wQy5cvb/H9r7/+enzxi1+Mfv36RZ8+fWL8+PHx7LPPtvh812fx4sVxzDHHRE1NTfPfF374wx9GsVhsVeMPfvCDuPDCC2PYsGHRp0+f2GuvvWLevHkbPMcrr7wSJ510UowYMSL69OkTNTU18a//+q/x+9//foPfO3To0HjiiSdi7ty5zZ9b04yF9kzTb+uf06OPPjrq6+tj1qxZGxwT3kvjDe307W9/OxYtWhT/8z//E5dddln8/e9/jwkTJkRDQ0PzMVdffXUcdNBBUVVVFTNnzowbbrgh+vXrFx//+MfX+5et8ePHN093/OxnPxv3339/q+mP7/W73/0u9t5773j99dfj0ksvjV/96lex8847x+c///kN3mSuvPLKOP7442P77bePm266Kc4666w499xzW02rBGDtSnk/iIh44403Yp999omf/OQncfzxx8evf/3ruPTSS2ObbbaJJUuWRETEypUrY8yYMXHVVVfF17/+9bj11lvjmGOOiWnTpsWnP/3p5rHuv//++PznPx/Dhw+PWbNmxa233hrf/e53Y82aNRERseuuu8YVV1wRERFnnXVW8/3nS1/6UkREHHLIIfHwww/HtGnTYs6cOTFjxozYZZdd4vXXX1/vNdxxxx3xzjvvxJgxY5r3re9e9+STT8bo0aPjiSeeiP/+7/+OX/7ylzFixIg47rjjYtq0aa3G/9a3vhWLFy+OSy+9NH79619HTU3NWuuYNWtWnHTSSbHffvvF7Nmz4+abb45TTz21+Vnd8ePHx/nnnx8REdOnT2+uafz48RHR/s/xU5/6VHzkIx+JG2+8MaZMmRI333xzfPzjH4933nmnxXGPPfZYnHLKKXHqqafG7NmzY/To0XHyySfHD37wg/X+XJt85jOfiW222SZuuummOOOMM+Laa6+NU089tfnXi8ViTJgwIa699to4/fTTY/bs2bHnnnu2et5+XV555ZUYPXp03HHHHXHuuefGLbfcEgcccECcdtpp8bWvfa3V8dOnT485c+bERRddFNdcc02sWLEiDjnkkFb/GPB+y5Yti4iIyZMnx6233hpXXHFFDB8+PPbff/8Nrk8ze/bsGD58eOyyyy7Nn9vs2bPbdH1N2vP5Dhw4MLbbbru49dZb23UOiARoNnHixGSLLbZY66/97ne/SyIiOeSQQ1rsv+GGG5KISO6///4kSZJkxYoVSb9+/ZIJEya0OK6hoSHZaaedkj322GODdUREMmnSpLWe/3e/+13zvu222y7ZZZddknfeeafFsYceemhSW1ubNDQ0rPV7GxoakkGDBiW77rprUiwWm7/vueeeS3r06JHU1dVtsEaAriwL94NzzjkniYhkzpw56zzm0ksvTSIiueGGG1rsv+CCC5KISO64444kSZLkBz/4QRIRyeuvv77OsebPn59ERHLFFVe02P/Pf/4ziYjkoosuWm+9a3PiiScmvXr1anGvabK2e90RRxyRlJeXJ4sXL26xf9y4cUnv3r2b62/6DPbdd9821fG1r30t6du373qP+cUvftHqPpsk7fscJ0+enEREcuqpp7Y49pprrkkiIrn66qub99XV1SWFQiF57LHHWhx74IEHJlVVVcmKFSuSJEmShQsXtvpcms4zbdq0Ft970kknJRUVFc0/71tvvTWJiGTGjBktjps6dWoSEcnkyZPX+zM544wzkohIHnjggRb7TzzxxKRQKCRPPvlkixpHjRqVrFmzpvm4Bx98MImI5Lrrrlvved5vzZo1yTvvvJOMHTs2+dSnPrXB43fYYYdkv/32a7V/bT+7K664IomIZOHChUmSbNyf06OPPjoZMGBAu64JJN7QTp/4xCdafL3jjjtGRMSiRYsiIuK+++6LZcuWxcSJE2PNmjXNW7FYjIMPPjjmz5+fymqYTz/9dPztb3+Lo48+OiKixbkOOeSQWLJkyVqnPEY0JgovvvhiHHXUUS2m99XV1cXo0aM7XBtAHpT6fvDb3/42ttlmmzjggAPWeczdd98dW2yxRXz2s59tsb9pkammtK5pGvnhhx8eN9xwQ7zwwgttvs5+/frFVlttFd///vfjwgsvjEcffbTFNOP1efHFF2PLLbdsca9Zn7vvvjvGjh0bQ4YMabH/uOOOi7feeqvVLLDPfOYzbRp3jz32iNdffz2OPPLI+NWvfhX//Oc/2/R9ERv3OTbdm5scfvjh0b179/jd737XYv8OO+wQO+20U4t9Rx11VNTX17dpEb+1/R5cuXJlLF26NCIi5s6d23z+9zryyCM3OHZE4+cxYsSI2GOPPVrsP+644yJJklaz5MaPHx9lZWUt6on4vz8T63PppZfGrrvuGhUVFdG9e/fo0aNH3HXXXfHXv/61TbVurI35fGtqamLp0qXNM0agLTTe0E79+/dv8XV5eXlERLz99tsR0fg8W0Tj9LkePXq02C644IJIkqR5SlVHNJ3ntNNOa3Wek046KSJinX+xePXVVyOicbrU+61tHwCtlfp+8Morr8SHPvSh9dbw6quvxsCBA1s1tjU1NdG9e/fm/97vu+++cfPNN8eaNWviC1/4QnzoQx+KkSNHxnXXXbfB6ywUCnHXXXfFxz/+8Zg2bVrsuuuuseWWW8a///u/xxtvvLHe73377bejoqJig+d47/XU1ta22j9o0KDmX3+vtR27Nscee2z87Gc/i0WLFsVnPvOZqKmpiT333DPmzJmzwe/dmM/x/ffS7t27R//+/VvVv7778PuPXZsN/R589dVXo3v37tGvX78Wxw0YMGCDYzd9f3s+jw3Vsy4XXnhhnHjiibHnnnvGTTfdFPPmzYv58+fHwQcfvMHv7aiN+XwrKioiSZJYuXJlSWuja+layz5CBnzwgx+MiIgf//jH61xJs603vLac51vf+laL5/jea9ttt13r/qYb40svvdTq19a2D4D26+j9YMstt4x//OMf6z1H//7944EHHogkSVo0301pXFMNERGHHXZYHHbYYbFq1aqYN29eTJ06NY466qgYOnRo7LXXXus9T11dXfz0pz+NiIinnnoqbrjhhpgyZUqsXr06Lr300nV+3wc/+MF2vX6tf//+zc+vv9eLL77YPN57tTVJj2hcNO7444+PFStWxL333huTJ0+OQw89NJ566qmoq6tb5/dtzOf40ksvxeDBg5u/XrNmTbz66qutGtP13Yfff+zG6N+/f6xZsyaWLVvWovlu672+vZ/Hxrr66qtj//33jxkzZrTYv6F/2EnDxny+y5Yti/Ly8ujTp0/J66PrkHhDyvbee+/o27dvLFiwIHbbbbe1bj179uzwebbddtvYeuut409/+tM6z1NZWbnO762trY3rrrsukiRp3r9o0aK47777OlwbAB2/H4wbNy6eeuqp9S56OXbs2HjzzTfj5ptvbrG/6S0VY8eObfU95eXlsd9++8UFF1wQEY3v2W7aH7HhdHKbbbaJs846K0aNGrXBpnq77baLV199dYOLa733eu6+++7mxu6919O7d+9UXg21xRZbxLhx4+LMM8+M1atXxxNPPBER677+jfkcr7nmmhZf33DDDbFmzZrYf//9W+x/4okn4k9/+lOLfddee21UVlbGrrvu2uFr3W+//SIi4vrrr2+xv60rco8dOzYWLFjQ6nO+6qqrolAotFg0ryMKhULzz7/Jn//85/UuMPte5eXlG52Mb8zn++yzz8aIESM26nzkl8QbUtanT5/48Y9/HBMnToxly5bFZz/72aipqYlXXnkl/vSnP8Urr7zS6l90N9ZPfvKTGDduXHz84x+P4447LgYPHhzLli2Lv/71r/HII4/EL37xi7V+X7du3eLcc8+NL33pS/GpT30qvvzlL8frr78eU6ZMMdUcICUdvR+ccsopcf3118dhhx0WZ5xxRuyxxx7x9ttvx9y5c+PQQw+NMWPGxBe+8IWYPn16TJw4MZ577rkYNWpU/OEPf4jzzz8/DjnkkObnw7/73e/GP/7xjxg7dmx86EMfitdffz1+9KMfRY8ePZqbs6222ip69eoV11xzTWy//fbRp0+fGDRoUPzzn/+Mr33ta/G5z30utt566+jZs2fcfffd8ec//znOOOOM9f4M9t9//0iSJB544IE46KCDNvgzmzx5cvzmN7+JMWPGxHe/+93o169fXHPNNXHrrbfGtGnTorq6uh2fwP/58pe/HL169Yq99947amtr46WXXoqpU6dGdXV18/PvI0eOjIiIyy67LCorK6OioiKGDRsW/fv3b/fn+Mtf/jK6d+8eBx54YDzxxBPxne98J3baaadWz1oPGjQoPvGJT8SUKVOitrY2rr766pgzZ05ccMEFqbwj+uCDD4699947vvGNb0R9fX189KMfjfvvv7/5H2a6dVt/BnfqqafGVVddFePHj49zzjkn6urq4tZbb41LLrkkTjzxxNhmm206XGNExKGHHhrnnntuTJ48Ofbbb7948skn45xzzolhw4a16TnqUaNGxaxZs+L666+P4cOHR0VFRYwaNapN527vn9NisRgPPvhgfPGLX9zo6yWnOm1ZN8igtqxi+4tf/KLF/rWtmJkkSTJ37txk/PjxSb9+/ZIePXokgwcPTsaPH9/q+9cm2riqeZIkyZ/+9Kfk8MMPT2pqapIePXokAwcOTP71X/81ufTSSzf4vf/zP/+TbL311knPnj2TbbbZJvnZz36WTJw40armQO5l5X7w2muvJSeffHLy4Q9/OOnRo0dSU1OTjB8/Pvnb3/7WfMyrr76afPWrX01qa2uT7t27J3V1dcm3vvWtZOXKlc3H/OY3v0nGjRuXDB48OOnZs2dSU1OTHHLIIcnvf//7Fue77rrrku222y7p0aNH86rXL7/8cnLccccl2223XbLFFlskffr0SXbcccfkv/7rv1qsYL02DQ0NydChQ5OTTjqp1a+t7V6XJEnyl7/8JZkwYUJSXV2d9OzZM9lpp51a/UzX9Rmsy8yZM5MxY8YkAwYMSHr27JkMGjQoOfzww5M///nPLY676KKLkmHDhiVlZWWtPsu2fI5Nq40//PDDyYQJE5I+ffoklZWVyZFHHpm8/PLLLc5VV1eXjB8/PrnxxhuTHXbYIenZs2cydOjQ5MILL2xx3PpWNX/llVdaHPv+FbuTJEmWLVuWHH/88Unfvn2T3r17JwceeGAyb968JCKSH/3oRxv82S1atCg56qijkv79+yc9evRItt122+T73/9+85tT3lvj97///VbfH21YPX3VqlXJaaedlgwePDipqKhIdt111+Tmm29u899JnnvuueSggw5KKisrk4ho/p62rGrepK1/Tu+6667mzxjao5Ak75lnCgAAKfrhD38Y5513XrzwwgvRq1evzi6npKZMmRJnn312vPLKKxt8/nno0KExcuTI+M1vfrOJqvs/1157bRx99NHxxz/+0dtM2unYY4+NZ599Nv74xz92dilsZkw1BwCgZCZNmhQXX3xxTJ8+PU477bTOLid3rrvuunjhhRdi1KhR0a1bt5g3b158//vfj3333VfT3U7PPPNMXH/99etddwHWReMNAEDJVFRUxM9//vPmRdzYtCorK2PWrFnxn//5n7FixYqora2N4447Lv7zP/+zs0vb7CxevDguvvji2GeffTq7FDZDppoDAABACXmdGABsAvfee29MmDAhBg0aFIVCodXrnwCATW9D9+ckSWLKlCkxaNCg6NWrV+y///7NryFsD403AGwCK1asiJ122ikuvvjizi4FAHjXhu7P06ZNiwsvvDAuvvjimD9/fgwcODAOPPDAeOONN9p1HlPNAWATKxQKMXv27PjkJz/Z2aUAAO96//05SZIYNGhQnHLKKXH66adHRMSqVatiwIABccEFF8RXvvKVNo/d7sXVisVivPjii1FZWRmFQqG93w4Am1SSJM2v9unWLb2JXkmStLoPlpeXR3l5eWrnaA/3ZwA2J6W6PzeNncY9euHChfHSSy/FQQcd1GKc/fbbL+67777SNN7Tp0+P6dOnx+rVq+OZZ55pV8EA0NX06dMn3nzzzRb7Jk+eHFOmTNmkdbg/A7C5GlhTFi8tbUh93LTu0S+99FJERAwYMKDF/gEDBsSiRYvaNVabG+9JkybFpEmTYvny5dG3b994/vnno6qqql0nA/Kpurq6s0soieXLl3d2CbTBCy+8ECNGjEh93DfffLPVvbAz0u7335/32P9b0b17xSavo5TeGNI1335a+fyazi6BNur13GudXUJJNDy9sLNLIMdWxlsxb+mcWPTw0KiqTC/xrn+jGHUffS7Ve/T70/O1Jeob0u47WdMJqqqqNN5Arvlv4Oahvr6++f+nNQW7aXmULN0Lm66te/eK6N6jazXeZT27ZuPdvYfGe3PRvaxzHiEptUKhR2eXQI51Txp///WpLESfyvQekSpGev3qwIEDI6Ix+a6trW3ev3Tp0lYp+IZY1RyAXCgUCqluAEDHNSTF1Le0DBs2LAYOHBhz5sxp3rd69eqYO3dujB49ul1jdc1/QgaAjHnzzTfj6aefbv564cKF8dhjj0W/fv3iwx/+cCdWBgD5taH78ymnnBLnn39+bL311rH11lvH+eefH717946jjjqqXefReAOQC2kn1e19G+dDDz0UY8aMaf7661//ekRETJw4Ma688srU6gKAzUkxkihGem+4bu9YG7o//8d//Ee8/fbbcdJJJ8Vrr70We+65Z9xxxx1RWVnZrvNovAFgE9h///3b3awDAKW1oftzoVCIKVOmdPitJRpvAHLBs9kAkD3FKEZ6T2VHyqOlR+MNQC5ovAEgexqSJBpSnBGW5lhpsqo5AAAAlJDEG4BckHgDQPZ09uJqm4rEGwAAAEpI4g1ALki8ASB7ipFEQw4Sb403ALmg8QaA7DHVHAAAAOgwiTcAuSDxBoDs8ToxAAAAoMMk3gDkgsQbALKn+O6W5nhZpPEGIBc03gCQPQ0pr2qe5lhpMtUcAAAASkjiDUAuSLwBIHsaksYtzfGySOINAAAAJZTZxLuhmMSDC5fF0jdWRk1lRewxrF+UdZNUALBxJN4AkD0WV+tEtz2+JM7+9YJYsnxl877a6oqYPGFEHDyythMrA2BzpfEGgOwpRiEaIr37czHFsdKUuanmtz2+JE68+pEWTXdExEvLV8aJVz8Stz2+pJMqAwAAgPbLVOPdUEzi7F8vWOsC8E37zv71gmgoZvSJeQAyqynxTmsDADqumKS/ZVGmGu8HFy5rlXS/VxIRS5avjAcXLtt0RQEAAEAHZOoZ76VvrLvp3pjjAKCJpBoAsqch5We80xwrTZlqvGsqK1I9DgCaaLwBIHvy0nhnaqr5HsP6RW11xTp/VIVoXN18j2H9NmVZAAAAsNEy1XiXdSvE5AkjIiJaNd9NX0+eMML7vAFoN4urAUD2FJNC6lsWZarxjog4eGRtzDhm1xhY3XI6+cDqiphxzK7e4w0AAMBmJVPPeDc5eGRtHDhiYDy4cFksfWNl1FQ2Ti+XdAPQEWkl1UmS0XeVAMBmJi/PeGey8Y5onHa+11b9O7sMAAAA6JDMNt4AkKY0n832jDcApKMhukVDik9AN6Q2Uro03gDkgsYbALInSXlBtMTiagAAAJA/Em8AckHiDQDZk5fF1STeAAAAUEISbwByQeINANnTkHSLhiTFxdUy+sZPjTcAuaDxBoDsKUYhiilOxC5GNjtvU80BAACghCTeAOSCxBsAssfiagAAAECHabwByIWmxDutDQDouKbF1dLc2uONN96IU045Jerq6qJXr14xevTomD9/furXaao5ALlgqjkAZE/j4mrp3VfbO9aXvvSlePzxx+PnP/95DBo0KK6++uo44IADYsGCBTF48ODU6pJ4AwAAkDtvv/123HTTTTFt2rTYd9994yMf+UhMmTIlhg0bFjNmzEj1XBJvAHJB4g0A2VOMbtFQgteJ1dfXt9hfXl4e5eXlLfatWbMmGhoaoqKiosX+Xr16xR/+8IfUaoqQeAMAANDFDBkyJKqrq5u3qVOntjqmsrIy9tprrzj33HPjxRdfjIaGhrj66qvjgQceiCVLlqRaj8QbgFyQeANA9mzMgmjrH68x8X7++eejqqqqef/70+4mP//5z+OEE06IwYMHR1lZWey6665x1FFHxSOPPJJaTREabwByQuMNANlTjG5RLMFU86qqqhaN97pstdVWMXfu3FixYkXU19dHbW1tfP7zn49hw4alVlOEqeYAAADk3BZbbBG1tbXx2muvxe233x6HHXZYquNLvAHIBYk3AGRPQ1KIhiS9+2p7x7r99tsjSZLYdttt4+mnn45vfvObse2228bxxx+fWk0RGm8A6FLeGNI9ynp2rdv7w1PSfaVLVmx3+UmdXUJJ1N7/TmeXkLq3h/fr7BJKoldnF0C7NDz1TGeX0CUtX748vvWtb8U//vGP6NevX3zmM5+J8847L3r06JHqedp8Z54+fXpMnz49GhoaUi0AADaFrpp4uz8DsDlrSPl1Yg3vPuPdVocffngcfvjhqZ1/Xdp8hZMmTYoFCxbE/PnzS1kPAJREU+Od1pYV7s8AbM6KSbfUtyzKZlUAAADQRXSth8AAYB266lRzANicdfZU801F4g0AAAAlJPEGIBck3gCQPcVo/yvANjReFmm8AcgFjTcAZE8xukUxxYnYaY6VpmxWBQAAAF2ExBuA3JBUA0C2NCTdoiHFV4ClOVaaslkVAAAAdBESbwBywTPeAJA9xShEMdJcXC2b92iNNwC5oPEGgOwx1RwAAADoMIk3ALkg8QaA7GmIbtGQYh6c5lhpymZVAAAA0EVIvAHIBYk3AGRPMSlEMUlxcbUUx0qTxhuAXNB4A0D2FFOeal7M6KTubFYFAAAAXYTEG4BckHgDQPYUk25RTPEVYGmOlaZsVgUAAABdhMQbgFyQeANA9jREIRoivftqmmOlSeINAAAAJSTxBiAXJN4AkD15ecZb4w1ALmi8ASB7GiLd6eENqY2Urmz+cwAAAAB0ERJvAHJB4g0A2ZOXqebZrAoAAAC6CIk3ALkg8QaA7GlIukVDiil1mmOlSeMNQC5ovAEge5IoRDHFxdUS7/EGAACA/JF4A5ALEm8AyJ68TDXPZlUAAADQRUi8AcgFiTcAZE8xKUQxSe++muZYadJ4A5ALGm8AyJ6G6BYNKU7ETnOsNGWzKgAAAOgiJN4A5ILEGwCyJy9TzSXeAAAAUEIabwByoSnxTmsDADquGN1S39pqzZo1cdZZZ8WwYcOiV69eMXz48DjnnHOiWCymfp2mmgOQGxpmAMiWhqQQDSlOD2/PWBdccEFceumlMXPmzNhhhx3ioYceiuOPPz6qq6vj5JNPTq2mCI03AAAAOXT//ffHYYcdFuPHj4+IiKFDh8Z1110XDz30UOrnMtUcgFww1RwAsqdpcbU0t7baZ5994q677oqnnnoqIiL+9Kc/xR/+8Ic45JBDUr9OiTcAAABdSn19fYuvy8vLo7y8vMW+008/PZYvXx7bbbddlJWVRUNDQ5x33nlx5JFHpl6PxBuAXJB4A0D2JEm3KKa4JUljiztkyJCorq5u3qZOndrq3Ndff31cffXVce2118YjjzwSM2fOjB/84Acxc+bM1K9T4g1ALniPNwBkT0MUoiFSXFzt3bGef/75qKqqat7//rQ7IuKb3/xmnHHGGXHEEUdERMSoUaNi0aJFMXXq1Jg4cWJqNUVovAEAAOhiqqqqWjTea/PWW29Ft24tJ4GXlZV5nRgAbCyJNwBkTzGJdi2I1pbx2mrChAlx3nnnxYc//OHYYYcd4tFHH40LL7wwTjjhhNTqaaLxBgAAIHd+/OMfx3e+85046aSTYunSpTFo0KD4yle+Et/97ndTP5fGG4BckHgDQPY0LYqW5nhtVVlZGRdddFFcdNFFqZ1/XTTeAOSCxhsAsqcYhSimuLhammOlyevEAAAAoIQk3gDkgsQbALKnISlEQ4qLq6U5Vpok3gAAAFBCEm8AckHiDQDZ05mLq21KbW68p0+fHtOnT4+GhoaIiKiuri5ZUdAWSdKOl/RtJvxlHkqnqzbe778/d0XbXX5SZ5dAO9R/uOvlOlWL13R2CSXx9vB+nV1CSfR6dllnl1ASZdts1dklpKrsnfqIZ99dXC3N93hv7ourTZo0KRYsWBDz588vZT0AQDu4PwNA9nW9f5IEgLXoqok3AGzOkpRfJ5Zs7ok3AAAA0H4SbwByQeINANlTTFJ+xtvrxAAAACB/JN4A5ILEGwCyx+vEAKAL0XgDQPaYag4AAAB0mMQbgFyQeANA9hRTfp1YmmOlSeINAAAAJSTxBiAXJN4AkD15ecZb4w1ALmi8ASB78tJ4m2oOAAAAJSTxBiAXJN4AkD0SbwAAAKDDJN4A5IakGgCyJS+Jt8YbgFww1RwAsieJdN+9naQ2UrpMNQcAAIASkngDkAsSbwDInrxMNZd4AwAAQAlJvAHIBYk3AGRPXhJvjTcAuaDxBoDsyUvjbao5AAAAlJDEG4BckHgDQPZIvAEAAIAOk3gDkAsSbwDIniQpRJJiSp3mWGnSeAOQCxpvAMieYhSiGClONU9xrDSZag4AAAAlJPEGIBck3gCQPRZXAwAAADpM4g1ALki8ASB78rK4msQbgFxoarzT2gCAjmuaap7m1lZDhw5d6z1+0qRJqV+nxBsAAIDcmT9/fjQ0NDR//fjjj8eBBx4Yn/vc51I/l8YbgFww1RwAsqczp5pvueWWLb7+3ve+F1tttVXst99+qdXTROMNAABAl1JfX9/i6/Ly8igvL1/n8atXr46rr746vv71r5fkH9g94w1ALnjGGwCyJ0n5+e6mxHvIkCFRXV3dvE2dOnW9ddx8883x+uuvx3HHHVeS65R4A5ALppoDQPYkEZEk6Y4XEfH8889HVVVV8/71pd0RET/96U9j3LhxMWjQoPSKeQ+NNwAAAF1KVVVVi8Z7fRYtWhR33nln/PKXvyxZPRpvAHJB4g0A2VOMQhQivftqcSPGuuKKK6KmpibGjx+fWh3v5xlvAAAAcqlYLMYVV1wREydOjO7dS5dLS7wByAWJNwBkT2e+Tiwi4s4774zFixfHCSeckFoNa6PxBiAXNN4AkD3FpBCFFBvvYjvHOuiggyJJc3W3dTDVHAAAAEpI4g1ALki8ASB7kiTl14mVPrzeKBJvAAAAKCGJNwC5IPEGgOzp7MXVNhWJNwAAAJSQxBuA3JBUA0C25CXx1ngDkAummgNA9nT268Q2FVPNAQAAoIQk3gDkgsQbALLH68QAAACADpN4A5ALEm8AyJ7GxDvNxdVSGypVbW68p0+fHtOnT4+GhoaIiFi+fHlUVVWVrDDS4y+Im48kq/+lgC6gqzbe778/Vz6/Jrr3WNPJVaWta+YEKwZn5/dRmrrmdXXN34NdV7/OLqAkej27rLNLKIm8rGre5qnmkyZNigULFsT8+fNLWQ8A0A7uzwCQff75DoBc6KqJNwBszpJ3tzTHyyKLqwEAAEAJSbwByAWJNwBkT16e8dZ4A5ALGm8AyKCczDU31RwAAABKSOINQC5IvAEgg1Keah4ZnWou8QYAAIASkngDkAsSbwDIniRp3NIcL4s03gDkgsYbALInL6uam2oOAAAAJSTxBiAXJN4AkEFJId0F0STeAAAAkD8SbwByQeINANljcTUA6EI03gCQQcm7W5rjZZCp5gAAAFBCEm8AckHiDQDZ43ViAAAAQIdJvAHIBYk3AGRURp/LTpPGG4Bc0HgDQPaYag4AAAB0mMQbgFyQeANABnmdGAAAANBREm8AckNSDQBZU3h3S3O87NF4A5ALppoDQAaZag4AAABd1wsvvBDHHHNM9O/fP3r37h0777xzPPzww6mfR+INQC5IvAEggzox8X7ttddi7733jjFjxsRvf/vbqKmpiWeeeSb69u2bYkGNNN4AAADkzgUXXBBDhgyJK664onnf0KFDS3IuU80ByIWmxDutDQBIQVJIf4uI+vr6FtuqVatanfqWW26J3XbbLT73uc9FTU1N7LLLLnH55ZeX5DI13gDkgsYbALInSdLfIiKGDBkS1dXVzdvUqVNbnfvZZ5+NGTNmxNZbbx233357fPWrX41///d/j6uuuir16zTVHAAAgC7l+eefj6qqquavy8vLWx1TLBZjt912i/PPPz8iInbZZZd44oknYsaMGfGFL3wh1Xo03gDkgsXVACCDSrS4WlVVVYvGe21qa2tjxIgRLfZtv/32cdNNN6VYUCNTzQEAAMidvffeO5588skW+5566qmoq6tL/VwSbwByQeINABn0ngXRUhuvjU499dQYPXp0nH/++XH44YfHgw8+GJdddllcdtll6dXzLok3AAAAubP77rvH7Nmz47rrrouRI0fGueeeGxdddFEcffTRqZ9L4g1ALki8ASB7CknjluZ47XHooYfGoYceml4B66DxBiAXNN4AkEElWlwta0w1BwAAgBKSeAOQCxJvAMigTlxcbVOSeAMAAEAJSbwByAWJNwBkUE6e8dZ4A5ALGm8AyKCcNN6mmgMAAEAJSbwByAWJNwBkkMQbAAAA6CiJNwC5IPEGgAzKyevENN4A5ILGGwCyp5A0bmmOl0WmmgMAAEAJSbwByAWJNwBkkMXVAAAAgI6SeAOQCxJvAKCzaLwByAWNNwBkTyFSXlwtvaFSpfHOgSTJ6IMO5EZXbVL82QJobdXg1Z1dQupWDe7sCkqj/IWenV1CiXTVFqdfZxeQqpVvd4t4trOr2HTa/Iz39OnTY8SIEbH77ruXsh4AKJmm1LujW5a4PwOwWWt6j3eaWwa1ufGeNGlSLFiwIObPn1/KegCAdnB/BoDs66rzMACgBc94A0AG5eR1YhpvAHJB4w0AGZSTxtt7vAEAAKCEJN4A5ILEGwCyp5Ck/DoxiTcAAADkj8QbgFyQeANABuXkGW+NNwC5oPEGgAzKSeNtqjkAAACUkMQbgFyQeANA9lhcDQAAAOgwiTcAuSDxBoAMSgqNW5rjZZDGG4Bc0HgDQAZZXA0AAADoKIk3ALkg8QaA7LG4GgAAANBhEm8AckHiDQAZlJNnvDXeAOSCxhsAMijlqeZZbbxNNQcAAIAS0ngDkAtNiXdaGwCQgqQEWxtNmTKl1f194MCB6VzX+5hqDgAAQC7tsMMOceeddzZ/XVZWVpLzaLwByAXPeANABnXy4mrdu3cvWcr9XqaaAwAA0KXU19e32FatWrXW4/7+97/HoEGDYtiwYXHEEUfEs88+W5J6NN4A5IJnvAEgewpJ+ltExJAhQ6K6urp5mzp1aqtz77nnnnHVVVfF7bffHpdffnm89NJLMXr06Hj11VdTv05TzQHIBVPNASA/nn/++aiqqmr+ury8vNUx48aNa/7/o0aNir322iu22mqrmDlzZnz9619PtR6NNwAAAF1KVVVVi8a7LbbYYosYNWpU/P3vf0+9HlPNAcgFU80BIIM68XVi77dq1ar461//GrW1tRs/yDpovAEAAMid0047LebOnRsLFy6MBx54ID772c9GfX19TJw4MfVzmWoOQC54xhsAsue9C6KlNV5b/eMf/4gjjzwy/vnPf8aWW24ZH/vYx2LevHlRV1eXXkHv0ngDkBsaZgDIoDTf490Os2bN2mTnMtUcAAAASkjiDUAumGoOABnUwQXR1jpeBkm8AQAAoIQk3gDkgsQbALKnMxdX25Q03gDkgsYbADLIVHMAAACgoyTeAOSCxBsAsicvU80l3gAAAFBCEm8AckHiDQAZlJNnvDXeAOSCxhsAMignjbep5gAAAFBCEm8AckHiDQDZY3E1AAAAoMMk3gDkgsQbADIoJ894a7wByAWNNwBkUE4ab1PNAQAAoIQk3gDkgsQbALLH4moAAABAh0m8AcgFiTcAZFBOnvHWeAOQCxpvAMgeU80BAACADpN4A5ALEm8AyCBTzekquupfEJMko3+qAKANVg1e3dkllMRhuzzW2SWkbt7LQzu7hJJ4Ofp2dgklscULPTq7BGilzVPNp0+fHiNGjIjdd9+9lPUAQEk0Jd5pbVnh/gzAZi0pwZZBbW68J02aFAsWLIj58+eXsh4AKImu2ni7PwOwOSuUYMsii6sBAABACXnGG4BcsLgaAGRQThZXk3gDAABACUm8AcgFiTcAZE8hadzSHC+LNN4A5IaGGQAyxlRzAAAAoKMk3gDkgqnmAJBRGU2p0yTxBgAAgBKSeAOQCxJvAMievCyuJvEGAACAEpJ4A5ALEm8AyKCcrGqu8QYgFzTeAJA9ppoDAABATkydOjUKhUKccsopqY8t8QYgFyTeAJBBGZlqPn/+/Ljssstixx13TLGY/yPxBgAAILfefPPNOProo+Pyyy+PD3zgAyU5h8YbgFxoSrzT2gCAjmt6xjvNLSKivr6+xbZq1ap11jBp0qQYP358HHDAASW7TlPNAcgFU80BIINKNNV8yJAhLXZPnjw5pkyZ0urwWbNmxSOPPBLz589PsYjWNN4AAAB0Kc8//3xUVVU1f11eXr7WY04++eS44447oqKioqT1aLwByAWJNwBkUIkS76qqqhaN99o8/PDDsXTp0vjoRz/avK+hoSHuvffeuPjii2PVqlVRVlaWSlkabwAAAHJn7Nix8Ze//KXFvuOPPz622267OP3001NruiM03gDkhMQbALLnvQuipTVeW1VWVsbIkSNb7Ntiiy2if//+rfZ3lMYbgFzQeANABmXkPd6lpvEGAACAiLjnnntKMq7GG4BckHgDQPYUkiQKSXoxdZpjpalbZxcAAAAAXZnEG4BckHgDQAZ5xhsAug6NNwBkT2euar4pmWoOAAAAJSTxBiAXJN4AkEE5mWou8QYAAIASkngDkAsSbwDInrw8463xBiAXNN4AkEGmmgMAAAAdJfEGIBck3gCQPXmZai7xBgAAgBKSeAOQCxJvAMignDzjrfEGIDc0zACQPVmdHp4mU80BAACghCTeAOSCqeYAkEFJ0rilOV4GSbwBAACghCTeAOSCxBsAsicvrxPTeAOQCxpvAMignKxqbqo5AAAAlJDEG4BckHgDQPYUio1bmuNlkcQbAAAASkjiDUAuSLwBIIM84w0AAAB0lMQbgFyQeANA9nidGAB0IRpvAMigJGnc0hwvg0w1BwAAgBKSeAOQCxJvAMgeU80BACiZ8hd6dnYJJTFv0NDOLgEgc9o81Xz69OkxYsSI2H333UtZDwCURFPindaWFe7PAGzWkhJsGdTmxnvSpEmxYMGCmD9/finrAYCS6KqNt/szAJuzpqnmaW5ZZHE1AAAAKCHPeAOQCxZXA4AM8joxAAAAoKMk3gDkgsQbALLH68QAoAvReANABqW9EnlGG29TzQEAAMidGTNmxI477hhVVVVRVVUVe+21V/z2t78tybkk3gDkgsQbALKnM6eaf+hDH4rvfe978ZGPfCQiImbOnBmHHXZYPProo7HDDjukV1RovAEAAMihCRMmtPj6vPPOixkzZsS8efM03gCwMSTeAJBBxaRxS3O8iKivr2+xu7y8PMrLy9f5bQ0NDfGLX/wiVqxYEXvttVd69bzLM94A5EJT453WBgCkICnBFhFDhgyJ6urq5m3q1KlrPf1f/vKX6NOnT5SXl8dXv/rVmD17dowYMSL1y5R4AwAA0KU8//zzUVVV1fz1utLubbfdNh577LF4/fXX46abboqJEyfG3LlzU2++Nd4A5IKp5gCQPYVIeXG1d/+3aaXyDenZs2fz4mq77bZbzJ8/P370ox/FT37yk/SKClPNAQAAICIikiSJVatWpT6uxBuA3JBUA0DGJEnjluZ4bfTtb387xo0bF0OGDIk33ngjZs2aFffcc0/cdttt6dXzLo03ALlgqjkAZE9nvsf75ZdfjmOPPTaWLFkS1dXVseOOO8Ztt90WBx54YHoFvUvjDQAAQO789Kc/3WTn0ngDkAsSbwDIoPe8Aiy18TLI4moAAABQQhJvAHJB4g0A2VNIkiikuLhammOlSeMNQC5ovAEgg4rvbmmOl0GmmgMAAEAJSbwByAWJNwBkT16mmku8AQAAoIQk3gDkgsQbADIoJ68T03gDkAsabwDIoCRp3NIcL4NMNQcAAIASkngDkAsSbwDInkLSuKU5XhZJvAEAAKCEJN4A5ILEGwAyKCfPeGu8AcgFjTcAZE+h2LilOV4WmWoOAAAAJSTxBiAXJN4AkEE5mWou8QYAAIASkngDkAsSbwDIoOTdLc3xMkjiDQAAACUk8QYgFyTeAJA9hSSJQorPZac5Vpo03gDkgsYbADLI4moAAABAR0m8AcgFiTcAZFASEcWUx8sgiTcAAACUkMQbgFyQeANA9lhcDQC6EI03AGRQEikvrpbeUGky1RwAAABKSOINQG5IqgEgY7xODAAAAOgoiTcAueAZbwDIoGJEpHlbTfPVZCnSeAOQCxpvAMievKxqbqo5AAAAlJDEG4BckHgDQAZZXA0AAADoKIk3ALkg8QaADMpJ4t3mxnv69Okxffr0aGhoKGU9AFASXbXxfv/9uddzr0X3svJOript/Tq7gJJYMbhHZ5dAG738Yt/OLqEkyl/o2dkllEg2Gy/WISeNd5unmk+aNCkWLFgQ8+fPL2U9AEA7uD8DQPZ5xhuAXGhKvNPaAIAUFEuwtdHUqVNj9913j8rKyqipqYlPfvKT8eSTT6ZzXe+j8QYAACB35s6dG5MmTYp58+bFnDlzYs2aNXHQQQfFihUrUj+XxdUAyIWu+ow3AGzOCkkShRSfy27PWLfddluLr6+44oqoqamJhx9+OPbdd9/UaorQeAOQExpvAMigEi2uVl9f32J3eXl5lJevf/HR5cuXR0REv37pL+ppqjkAAABdypAhQ6K6urp5mzp16nqPT5Ikvv71r8c+++wTI0eOTL0eiTcAuSDxBoAMKiYRhRQT72LjWM8//3xUVVU1795Q2v21r30t/vznP8cf/vCH9Gp5D403AAAAXUpVVVWLxnt9/u3f/i1uueWWuPfee+NDH/pQSerReAOQCxJvAMigEj3j3bZDk/i3f/u3mD17dtxzzz0xbNiw9Op4H403ALmg8QaALEq58Y62jzVp0qS49tpr41e/+lVUVlbGSy+9FBER1dXV0atXrxRrsrgaAAAAOTRjxoxYvnx57L///lFbW9u8XX/99amfS+INQC5IvAEggzp5qvmmIvEGAACAEpJ4A5ALEm8AyKBiEu15Lrtt42WPxhuAXNB4A0AGJcXGLc3xMshUcwAAACghiTcAuSDxBoAM6sTF1TYliTcAAACUkMQbgFyQeANABllcDQC6Do03AGSQqeYAAABAR0m8Adi0ig0Ri+6LePPliD4DIupGR3Qr2ySnllQDQMYkkXLind5QadJ4A7DpLLgl4rbTI+pf/L99VYMiDr4gYsQnOq8uAIASMtUcgE1jwS0RN3yhZdMdEVG/pHH/gltKevqmZ7zT2gCAFDQ9453mlkEabwBKr9jQmHSvdf7Xu/tuO6PxOACALsZUcwBKb9F9rZPuFpKI+hcajxv2LyUpwarmAJBBxWJEFFMeL3s03gCU3psvp3vcRtB4A0AGeZ0YAKSkz4B0jwMA2IxIvAEovbrRjauX1y+JtT/nXWj89brRJStB4g0AGSTxBoCUdCtrfGVYRES8v2l99+uDv7fJ3ucNALApabwB2DRGfCLi8Ksiqmpb7q8a1Li/xO/x9joxAMigYpL+lkGmmgOw6Yz4RMR24xtXL3/z5cZnuutGb5Kk21RzAMieJClGkqS3EnmaY6VJ4w3AptWtrGSvDAMAyCKNNwC5IPEGgAxKUp4ebnE1AAAAyB+JNwC5IPEGgAxKklj7q0Y7Ml72aLwByAWNNwBkULEYUUhxQbSMLq5mqjkAAACUkMQbgFyQeANABuVkqrnEGwAAAEpI4g1ALki8ASB7kmIxkhSf8U4y+oy3xhuAXNB4A0AGmWoOAAAAdJTEG4BckHgDQAYVk4iCxBsAAADoAIk3ALkg8QaADEqSiEhxQbSMJt4abwByQeMNANmTFJNIUpxqnmS08TbVHAAAAEpI4g1ALki8ASCDkmKkO9U8m+/xlngDwCZyySWXxLBhw6KioiI++tGPxu9///vOLgkAcu3ee++NCRMmxKBBg6JQKMTNN99ckvNovAHIhabEO62tva6//vo45ZRT4swzz4xHH300/uVf/iXGjRsXixcvLsHVAsDmISkmqW/tsWLFithpp53i4osvLtEVNjLVHIBc6Oyp5hdeeGF88YtfjC996UsREXHRRRfF7bffHjNmzIipU6emUhcAbHY6ear5uHHjYty4cemdfx3a3Xg3rRJXX1+fejHQHn4P0tn8Htw8vPHGGxGR7ufVNNb7xywvL4/y8vJWx69evToefvjhOOOMM1rsP+igg+K+++5Lpaam+/Oa4qpUxsuSNe+s7OwSSqJhZUNnl1ASDSu63u/B4ttd9fdgNp+F7aiG1dlc1bqj1ryzprNLSFXDmsb/VqyJdyJS/MjWxDsR0fZ79KbS5sZ7+vTpMX369Fi9enVERAwZMqRkRUFbVFdXd3YJ5Jzfg5uXtO9bffr0aTXm5MmTY8qUKa2O/ec//xkNDQ0xYMCAFvsHDBgQL730UofqeP/9ee6zMzo0XiY93dkFlMidnV0AQOf7Q/xv6mO25x69qbS58Z40aVJMmjQpisVibLPNNvHwww93uVVdd99995g/f35nl5GqrnhNEa5rc9MVr6srXlNE17yuJElil112iUceeSS6dUtvaZMkSVrdBzf0L+nvP35tY7SX+/PmqSteU4Tr2tx0xevqitcU0TWvq1T356ax23uPLrV2TzXv1q1b9OzZs0smPWVlZVFVVdXZZaSqK15ThOva3HTF6+qK1xTRda+roqIi+vbt22nn/+AHPxhlZWWt0u2lS5e2SsE3lvvz5qUrXlOE69rcdMXr6orXFNF1r6uz78+b0kb908KkSZPSriMTuuJ1dcVrinBdm5uueF1d8ZoiXFep9OzZMz760Y/GnDlzWuyfM2dOjB49OrXzdPZ1lkpXvK6ueE0Rrmtz0xWvqyteU4Tr6goKSdNqLABAyVx//fVx7LHHxqWXXhp77bVXXHbZZXH55ZfHE088EXV1dZ1dHgDk0ptvvhlPP924mMguu+wSF154YYwZMyb69esXH/7wh1M7j8YbADaRSy65JKZNmxZLliyJkSNHxn/913/Fvvvu29llAUBu3XPPPTFmzJhW+ydOnBhXXnllaufReAMAAEAJpbt8HAAAANCCxhsAAABKSOMNAAAAJaTxBgAAgBLSeAMAAEAJabwBAACghDTeAAAAUEIabwAAACghjTcAAACUkMYbAAAASkjjDQAAACWk8QYAAIAS6t7ZBcCmVCwWY/Xq1Z1dxmapR48eUVZW1tllAADAZkfjTW6sXr06Fi5cGMVisbNL2Wz17ds3Bg4cGIVCobNLAQCAzYbGm1xIkiSWLFkSZWVlMWTIkOjWzVMW7ZEkSbz11luxdOnSiIiora3t5IoAAGDzofEmF9asWRNvvfVWDBo0KHr37t3Z5WyWevXqFRERS5cujZqaGtPOAQCgjcR+5EJDQ0NERPTs2bOTK9m8Nf2jxTvvvNPJlQAAwOZD402ueDa5Y/z8AACg/TTeAAAAUEIabwAAACghjTdspo477rj45Cc/mdp4+++/f5xyyimpjQcAADSyqjm0Q0MxiQcXLoulb6yMmsqK2GNYvyjrtnk/9/zOO+9Ejx49OrsMAADosiTe0Ea3Pb4k9rng7jjy8nlx8qzH4sjL58U+F9wdtz2+pKTnvfHGG2PUqFHRq1ev6N+/fxxwwAHxzW9+M2bOnBm/+tWvolAoRKFQiHvuuSciIk4//fTYZpttonfv3jF8+PD4zne+02IV8ilTpsTOO+8cP/vZz2L48OFRXl4eEydOjLlz58aPfvSj5vGee+65kl4XAADkhcQb2uC2x5fEiVc/Esn79r+0fGWcePUjMeOYXePgkbWpn3fJkiVx5JFHxrRp0+JTn/pUvPHGG/H73/8+vvCFL8TixYujvr4+rrjiioiI6NevX0REVFZWxpVXXhmDBg2Kv/zlL/HlL385Kisr4z/+4z+ax3366afjhhtuiJtuuinKysqirq4u/v73v8fIkSPjnHPOiYiILbfcMvXrAQCAPNJ4wwY0FJM4+9cLWjXdERFJRBQi4uxfL4gDRwxMfdr5kiVLYs2aNfHpT3866urqIiJi1KhRERHRq1evWLVqVQwcOLDF95x11lnN/3/o0KHxjW98I66//voWjffq1avj5z//eYvmumfPntG7d+9W4wEAAB1jqjlswIMLl8WS5SvX+etJRCxZvjIeXLgs9XPvtNNOMXbs2Bg1alR87nOfi8svvzxee+219X7PjTfeGPvss08MHDgw+vTpE9/5zndi8eLFLY6pq6uTaAMAwCai8YYNWPrGupvujTmuPcrKymLOnDnx29/+NkaMGBE//vGPY9ttt42FCxeu9fh58+bFEUccEePGjYvf/OY38eijj8aZZ54Zq1evbnHcFltskXqtAADA2plqDhtQU1mR6nHtVSgUYu+994699947vvvd70ZdXV3Mnj07evbsGQ0NDS2O/eMf/xh1dXVx5plnNu9btGhRm86ztvEAAICO03jDBuwxrF/UVlfES8tXrvU570JEDKxufLVY2h544IG466674qCDDoqampp44IEH4pVXXontt98+Vq5cGbfffns8+eST0b9//6iuro6PfOQjsXjx4pg1a1bsvvvuceutt8bs2bPbdK6hQ4fGAw88EM8991z06dMn+vXrF926mRQDAAAd5W/VsAFl3QoxecKIiGhsst+r6evJE0aU5H3eVVVVce+998YhhxwS22yzTZx11lnxwx/+MMaNGxdf/vKXY9ttt43ddtstttxyy/jjH/8Yhx12WJx66qnxta99LXbeeee477774jvf+U6bznXaaadFWVlZjBgxIrbccstWz4UDAAAbp5AkydpCPOhSVq5cGQsXLoxhw4ZFRcXGTQm/7fElcfavF7RYaK22uiImTxhRkleJZVEaP0cAAMgbU82hjQ4eWRsHjhgYDy5cFkvfWBk1lY3Ty0uRdAMAAF2HxhvaoaxbIfbaqn9nlwEAAGxGPOMNAAAAJaTxBgAAgBLSeAMAAEAJabwBAACghDTeAAAAUEIabwAAACghjTcAAACUkMYbcmjKlCmx8847d3YZAACQCxpvAAAAKKHunV0AbFaKDRGL7ot48+WIPgMi6kZHdCvr7KoAAIAMk3hDWy24JeKikREzD4246YuN/3vRyMb9JZQkSUybNi2GDx8evXr1ip122iluvPHGiIi45557olAoxF133RW77bZb9O7dO0aPHh1PPvlkizG+973vxYABA6KysjK++MUvxsqVK0taMwAA8H803tAWC26JuOELEfUvttxfv6Rxfwmb77POOiuuuOKKmDFjRjzxxBNx6qmnxjHHHBNz585tPubMM8+MH/7wh/HQQw9F9+7d44QTTmj+tRtuuCEmT54c5513Xjz00ENRW1sbl1xyScnqBQAAWiokSZJ0dhFQaitXroyFCxfGsGHDoqKion3fXGxoTLbf33Q3K0RUDYo45S+pTztfsWJFfPCDH4y777479tprr+b9X/rSl+Ktt96K//f//l+MGTMm7rzzzhg7dmxERPzv//5vjB8/Pt5+++2oqKiI0aNHx0477RQzZsxo/v6PfexjsXLlynjsscfaVU+Hfo4AAJBTEm/YkEX3rafpjohIIupfaDwuZQsWLIiVK1fGgQceGH369GnerrrqqnjmmWeaj9txxx2b/39tbW1ERCxdujQiIv7617+2aNojotXXAABA6VhcDTbkzZfTPa4disViRETceuutMXjw4Ba/Vl5e3tx89+jRo3l/oVBo8b0AAEDnknjDhvQZkO5x7TBixIgoLy+PxYsXx0c+8pEW25AhQ9o0xvbbbx/z5s1rse/9XwMAAKUj8YYNqRvd+Ax3/ZKIWNuSCO8+4103OvVTV1ZWxmmnnRannnpqFIvF2GeffaK+vj7uu+++6NOnT9TV1W1wjJNPPjkmTpwYu+22W+yzzz5xzTXXxBNPPBHDhw9PvV4AAKA1jTdsSLeyiIMvaFy9PArRsvlunNYdB3+vZO/zPvfcc6OmpiamTp0azz77bPTt2zd23XXX+Pa3v92m6eSf//zn45lnnonTTz89Vq5cGZ/5zGfixBNPjNtvv70k9QIAAC1Z1ZxcSGU17gW3RNx2esuF1qoGNzbdIz6RTqEZZ1VzAABoP4k3tNWIT0RsN75x9fI3X258prtudMmSbgAAoGvQeEN7dCuLGPYvnV0FAACwGbGqOQAAAJSQxhsAAABKSONNrlhLsGP8/AAAoP003uRCWVnjAmirV6/u5Eo2b2+99VZERPTo0aOTKwEAgM2HxdXIhe7du0fv3r3jlVdeiR49ekS3bv7NqT2SJIm33norli5dGn379m3+hwwAAGDDvMeb3Fi9enUsXLgwisViZ5ey2erbt28MHDgwCoVCZ5cCAACbDY03uVIsFk0330g9evSQdAMAwEbQeAMAAEAJedAVAAAASkjjDQAAACWk8QYAAIAS0ngDAABACWm8AQAAoIQ03gAAAFBCGm8AAAAoof8PcPgw4FUMv3IAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 1000x700 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rng = np.random.RandomState(seed=123)\n",
    "\n",
    "problem = factory.generate_problem('rooms', 8, rng)\n",
    "problem.visualize()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Read a previously stored problem from a JSON file\n",
    "\n",
    "The function `create_problem_from_json` takes the file path of a stored problem instance as a parameter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1000x700 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "problem = factory.create_problem_from_json('boards/tiny0.json')\n",
    "problem.visualize()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Create a problem manually\n",
    "\n",
    "We can also manually create problem by passing a dictionary that contains the keys `board`, `costs`, `start_state`, and `end_state`. Here you might notice that transposed versions of the board and costs are visualized."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1000x700 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = {\n",
    "    'board': [\n",
    "        [0, 1, 0],\n",
    "        [0, 1, 0],\n",
    "        [0, 0, 0]\n",
    "    ],\n",
    "    'costs': [\n",
    "        [9, 9, 9],\n",
    "        [9, 0, 9],\n",
    "        [9, 0, 9]\n",
    "    ],\n",
    "    'start_state': [0, 0],\n",
    "    'end_state': [2, 2]\n",
    "}\n",
    "\n",
    "problem = factory.create_problem_from_dict(data)\n",
    "problem.visualize()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interacting with problems\n",
    "\n",
    "Let's create a small problem named `maze`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1000x700 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "maze = factory.generate_problem('maze', 8, rng)\n",
    "maze.visualize()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Practical Hints:**\n",
    "- Use 'maze.get_start_node()' to get the node with the start state.\n",
    "- Use 'maze.is_end(node)' to check whether 'node' is the node with the end state.\n",
    "- Use 'maze.successors(node)' to get a list of nodes containing successor states. Successors will be returned in the order that they can be reached using the following actions: R(ight), U(p), D(own), L(eft) (omitting actions that will cause the agent to bump into the wall). \n",
    "\n",
    "In the following these methods are shown for a problem named `maze`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Node(id:139885768164176, parent:139886059131184, state:(0, 0), action:None, cost:0, depth:0)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# - use 'problem.get_start_node()' to get the node with the start state\n",
    "maze.get_start_node()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# - use 'problem.is_end(node)' to check whether 'node' is the node with the end state\n",
    "maze.is_end(maze.get_start_node())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Node(id:139885138912480, parent:139885138912720, state:(1, 0), action:R, cost:1, depth:1)]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# - use 'problem.successors(node)' to get a list of nodes containing successor states\n",
    "maze.successors(maze.get_start_node())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Provided data structures\n",
    "\n",
    "<p><strong>Usage of provided datatypes:</strong></p>\n",
    "\n",
    "*Queue:*\n",
    "- to put an item in the the Queue, use `fringe.put(<item>)`\n",
    "- to get an item out of the Queue, use `fringe.get()`\n",
    "- to check whether there are any elements in the Queue, use `fringe.has_elements()`\n",
    "\n",
    "*Stack:*\n",
    "- to put an item in the the Stack, use `fringe.put(<item>)`\n",
    "- to get an item out of the Stack, use `fringe.get()`\n",
    "- to check whether there are any elements in the Stack, use `fringe.has_elements()`\n",
    "\n",
    "*PriorityQueue:*\n",
    "- to put an item into the PriorityQueue, use `fringe.put(<priority>, <item>)`\n",
    "- to get an item out of the PriorityQueue, use `fringe.get()`\n",
    "- to check whether there are any elements in the PriorityQueue, use `fringe.has_elements()`\n",
    "\n",
    "Let's have a look at a queue:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from pig_lite.datastructures.queue import Queue\n",
    "\n",
    "queue = Queue()\n",
    "\n",
    "# does the newly created queue have elements?\n",
    "queue.has_elements()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's store the start node of the previously created maze in the queue\n",
    "queue.put(maze.get_start_node())\n",
    "\n",
    "# does the queue have elements now?\n",
    "queue.has_elements()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Node(id:139881658566416, parent:139886059131184, state:(0, 0), action:None, cost:0, depth:0)\n"
     ]
    }
   ],
   "source": [
    "# let's retrieve an item from the queue\n",
    "item = queue.get()\n",
    "\n",
    "# (and print it for the fun of it)\n",
    "print(item)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# does the queue have elements now?\n",
    "queue.has_elements()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Implementing a search algorithm\n",
    "\n",
    "Here we demonstrate how a search algorithm will look like based on a very dumb search, namely *Random Search*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "class RS(object):\n",
    "    def solve(self, problem: Problem):\n",
    "        current = problem.get_start_node()\n",
    "\n",
    "        while not problem.is_end(current):       # as long as the current node is not the end\n",
    "            nodes = problem.successors(current)  # get the successor nodes for the current node\n",
    "            current = random.choice(nodes)       # choose a random successor node\n",
    "        return current\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the following we instantiate the search algorithm `RS` and call the function `solve()`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "rs_search = RS()\n",
    "rs_solution = rs_search.solve(maze)\n",
    "\n",
    "# Since this random search is not very smart and might revisit previous states,\n",
    "# you might receive a warning \"overflow encountered in scalar add node.cost + cost\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We provide you with a method to print information about the found solution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "state (6, 6) was reached following the sequence ['R', 'R', 'R', 'R', 'R', 'R', 'D', 'D', 'D', 'D', 'U', 'U', 'U', 'D', 'U', 'D', 'U', 'U', 'D', 'U', 'D', 'U', 'L', 'R', 'L', 'L', 'R', 'L', 'R', 'R', 'L', 'L', 'L', 'R', 'R', 'R', 'L', 'R', 'L', 'L', 'R', 'L', 'L', 'R', 'L', 'L', 'L', 'R', 'D', 'U', 'L', 'L', 'R', 'R', 'D', 'D', 'D', 'U', 'U', 'U', 'D', 'D', 'U', 'U', 'D', 'U', 'L', 'R', 'L', 'R', 'L', 'R', 'D', 'U', 'D', 'D', 'L', 'D', 'L', 'D', 'D', 'U', 'U', 'U', 'D', 'D', 'U', 'D', 'D', 'U', 'U', 'R', 'L', 'R', 'U', 'D', 'U', 'D', 'L', 'U', 'D', 'R', 'L', 'D', 'U', 'U', 'R', 'D', 'U', 'R', 'L', 'R', 'L', 'R', 'U', 'D', 'D', 'U', 'L', 'L', 'R', 'R', 'L', 'D', 'L', 'U', 'R', 'R', 'U', 'D', 'L', 'R', 'L', 'R', 'L', 'R', 'U', 'D', 'U', 'U', 'L', 'R', 'D', 'U', 'D', 'D', 'U', 'U', 'D', 'U', 'L', 'L', 'R', 'L', 'R', 'L', 'R', 'R', 'D', 'D', 'U', 'U', 'R', 'L', 'L', 'R', 'L', 'L', 'R', 'R', 'D', 'D', 'L', 'D', 'L', 'U', 'R', 'D', 'L', 'U', 'D', 'U', 'R', 'L', 'R', 'D', 'L', 'D', 'U', 'D', 'D', 'D', 'U', 'D', 'U', 'U', 'D', 'U', 'D', 'D', 'U', 'D', 'U', 'U', 'U', 'U', 'D', 'D', 'D', 'U', 'U', 'D', 'D', 'U', 'D', 'D', 'U', 'D', 'U', 'U', 'D', 'U', 'D', 'U', 'D', 'U', 'D', 'U', 'D', 'U', 'D', 'D', 'U', 'U', 'D', 'U', 'U', 'U', 'D', 'R', 'R', 'D', 'U', 'D', 'U', 'D', 'D', 'R', 'U', 'D', 'U', 'R', 'U', 'U', 'D', 'D', 'L', 'D', 'U', 'L', 'D', 'U', 'D', 'R', 'D', 'R', 'L', 'L', 'R', 'U', 'L', 'U', 'R', 'R', 'L', 'L', 'R', 'L', 'D', 'D', 'U', 'D', 'U', 'R', 'U', 'L', 'U', 'D', 'U', 'L', 'R', 'D', 'R', 'R', 'L', 'D', 'D', 'R', 'R', 'L', 'L', 'L', 'U', 'R', 'D', 'U', 'D', 'L', 'U', 'D', 'R', 'U', 'U', 'R', 'U', 'U', 'D', 'D', 'U', 'U', 'D', 'D', 'U', 'U', 'D', 'D', 'L', 'D', 'U', 'D', 'D', 'U', 'L', 'U', 'U', 'U', 'U', 'U', 'D', 'D', 'L', 'L', 'D', 'D', 'D', 'U', 'U', 'D', 'U', 'U', 'D', 'R', 'U', 'R', 'D', 'U', 'D', 'L', 'L', 'D', 'D', 'U', 'D', 'D', 'U', 'U', 'U', 'U', 'R', 'D', 'U', 'L', 'R', 'L', 'D', 'R', 'L', 'U', 'R', 'D', 'R', 'D', 'U', 'D', 'D', 'R', 'U', 'L', 'R', 'R', 'U', 'U', 'D', 'U', 'D', 'D', 'L', 'R', 'L', 'D', 'D', 'R', 'L', 'U', 'D', 'L', 'U', 'R', 'U', 'R', 'L', 'L', 'U', 'D', 'R', 'L', 'D', 'U', 'U', 'D', 'D', 'R', 'U', 'R', 'U', 'D', 'L', 'D', 'U', 'D', 'L', 'U', 'R', 'L', 'U', 'U', 'U', 'U', 'L', 'L', 'R', 'R', 'D', 'D', 'U', 'U', 'L', 'L', 'R', 'L', 'R', 'L', 'R', 'R', 'D', 'U', 'D', 'U', 'D', 'U', 'D', 'D', 'U', 'U', 'D', 'D', 'L', 'D', 'U', 'D', 'R', 'L', 'U', 'L', 'D', 'R', 'U', 'L', 'D', 'U', 'R', 'D', 'R', 'L', 'L', 'R', 'R', 'U', 'L', 'R', 'D', 'U', 'L', 'R', 'U', 'U', 'D', 'U', 'R', 'L', 'D', 'U', 'R', 'R', 'L', 'R', 'L', 'L', 'D', 'D', 'U', 'U', 'R', 'R', 'R', 'L', 'R', 'L', 'L', 'L', 'D', 'U', 'L', 'L', 'R', 'L', 'R', 'R', 'D', 'D', 'U', 'D', 'U', 'U', 'D', 'U', 'R', 'R', 'R', 'R', 'D', 'D', 'D', 'U', 'D', 'U', 'U', 'U', 'L', 'R', 'D', 'D', 'U', 'D', 'D', 'D', 'U', 'U', 'U', 'U', 'D', 'D', 'D', 'D', 'U', 'D', 'U', 'U', 'D', 'U', 'D', 'U', 'U', 'U', 'L', 'L', 'L', 'L', 'L', 'R', 'D', 'D', 'L', 'D', 'L', 'R', 'R', 'L', 'U', 'D', 'L', 'R', 'R', 'U', 'L', 'L', 'R', 'L', 'R', 'R', 'U', 'U', 'D', 'U', 'D', 'D', 'U', 'D', 'D', 'L', 'R', 'U', 'L', 'L', 'D', 'U', 'R', 'R', 'D', 'L', 'R', 'L', 'U', 'R', 'L', 'D', 'L', 'R', 'U', 'D', 'U', 'D', 'L', 'D', 'D', 'U', 'D', 'U', 'U', 'R', 'U', 'L', 'R', 'L', 'R', 'D', 'U', 'L', 'D', 'R', 'L', 'D', 'D', 'D', 'U', 'U', 'U', 'R', 'L', 'D', 'D', 'D', 'U', 'U', 'U', 'R', 'L', 'R', 'U', 'R', 'L', 'D', 'U', 'L', 'R', 'L', 'D', 'U', 'R', 'D', 'U', 'R', 'U', 'D', 'L', 'R', 'L', 'L', 'R', 'D', 'R', 'L', 'R', 'L', 'L', 'R', 'L', 'U', 'D', 'U', 'R', 'D', 'U', 'L', 'D', 'D', 'D', 'D', 'U', 'U', 'D', 'U', 'U', 'D', 'D', 'D', 'U', 'U', 'D', 'U', 'U', 'R', 'L', 'U', 'R', 'R', 'L', 'D', 'U', 'R', 'U', 'U', 'R', 'L', 'D', 'D', 'D', 'D', 'U', 'L', 'U', 'L', 'D', 'U', 'R', 'L', 'R', 'D', 'L', 'R', 'L', 'R', 'L', 'U', 'R', 'R', 'L', 'L', 'D', 'U', 'D', 'U', 'R', 'D', 'U', 'L', 'R', 'D', 'U', 'R', 'D', 'D', 'U', 'D', 'R', 'R', 'U', 'D', 'L', 'R', 'U', 'D', 'U', 'U', 'D', 'U', 'D', 'U', 'D', 'U', 'D', 'D', 'L', 'R', 'L', 'D', 'L', 'R', 'L', 'D', 'R', 'R', 'L', 'L', 'R', 'R', 'R', 'R'] (cost: 108, depth: 808)\n"
     ]
    }
   ],
   "source": [
    "rs_solution.pretty_print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualizing the solution\n",
    "\n",
    "Now you can also visualize the found path on top of the maze:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/quirinecker/Downloads/tmp/notebook0/pig_lite/problem/simple_2d.py:306: RuntimeWarning: overflow encountered in scalar add\n",
      "  node.cost + cost,\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1000x700 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "maze.visualize(sequences=[('rs', rs_solution.get_action_sequence())])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This also works for several sequences, e.g.: \n",
    "```\n",
    "maze.visualize(sequences=[('rs', rs_solution.get_action_sequence()), ('bfs', bfs_solution.get_action_sequence())])\n",
    "```\n",
    "or even a manually created one:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/quirinecker/Downloads/tmp/notebook0/pig_lite/problem/simple_2d.py:306: RuntimeWarning: overflow encountered in scalar add\n",
      "  node.cost + cost,\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1000x700 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "maze.visualize(sequences=[('rs', rs_solution.get_action_sequence()),\n",
    "                          ('test', ['R', 'R', 'D', 'D', 'D', 'L', 'U', 'R', 'D', 'D', 'R', 'D', 'D', 'R', 'R', 'R'])])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tests Cases\n",
    "\n",
    "After the cell where you have to implement e.g., a search algorithm, there will be cells with some tests like the following. These tests let you test the behaviour and correctness of your algorithms (although they might not check for all possible edge cases!). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# this is a testing cell, do not edit or delete\n",
    "\n",
    "assert(rs_solution is not None)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now you should know everything about the framework that you need to all future practical exercises.\n",
    "\n",
    "**Feel free to play around with the mazes and functions in this notebook!**"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "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": "3.13.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}