Nonograms project .ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1><center>Nonograms project</center></h1>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3><center>Julia Taborek</center></h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Introduction to the problem"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nonograms, also known as Hanjie, Paint by Numbers, Picross, Griddlers, and Pic-a-Pix, and by various other names, are picture logic puzzles in which cells in a grid must be colored or left blank according to numbers at the side of the grid to reveal a hidden pixel art-like picture. In this puzzle type, the numbers are a form of discrete tomography that measures how many unbroken lines of filled-in squares there are in any given row or column. For example, a clue of \"4 8 3\" would mean there are sets of four, eight, and three filled squares, in that order, with at least one blank square between successive sets.\n",
    "\n",
    "Nonograms were named after Non Ishida, one of the two inventors of the puzzle.\n",
    "\n",
    "In my project I will show ways to solve nonograms using genetic algorithms."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# importing libraries\n",
    "import numpy as np\n",
    "import pygad\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import math\n",
    "import pandas as pd\n",
    "from random import randint\n",
    "import time"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.1 First method"
   ]
  },
  {
   "attachments": {
    "image.png": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Gene is the coordinate of the column where the next row requirement starts. The length of the chromosome is equal to the number of requirements in the rows.\n",
    "\n",
    "The value of the first gene tells in which column the sequence for the first condition begins. Columns are numbered from 0.\n",
    "\n",
    "Example \n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "solution: [1., 3., 2., 1., 0., 0.]\n",
    "\n",
    "First gene tells that first requirement for row (1) starts in 1 column.\n",
    "\n",
    "Third gene tells that third requirement for row (3) starts in 2 column.\n",
    "\n",
    "Fourth gene tells that fourth requirement for row (2) starts in 1 column."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Small inputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitness value of the best solution = 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x165b0f01a90>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x864 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# coding inputs\n",
    "# req_col - list of lists with requirements for each column\n",
    "# for example: in first column (column number 0) 2 cells must be colored\n",
    "req_col = [[2], [1,3], [4], [2], [1]]\n",
    "# req_rows - same as req_col\n",
    "req_rows = [[1,1], [3], [2], [3], [3]]\n",
    "\n",
    "row  = [item for sublist in req_rows for item in sublist]\n",
    "\n",
    "# genes are number of column in with start current sequence\n",
    "gene_space = [0,1,2,3,4] \n",
    "\n",
    "\n",
    "def nonogram(solution):\n",
    "    \"\"\"\n",
    "    a function that converts the solution into a matrix representing a filled nonogram and punish for incorrectly filled rows\n",
    "    \n",
    "    Inputs:\n",
    "    - solution - given by genetic algorithm solution\n",
    "    \n",
    "    Returns:\n",
    "    - completed nonogram as matrix\n",
    "    - penalty \n",
    "    \"\"\"\n",
    "    # nono is nonogram represented as metrix\n",
    "    # firstly it is only filled with zeros\n",
    "    # size of nono is number of column x number of columns, because our nonogram is square\n",
    "    nono = np.zeros((len(gene_space), len(gene_space)))\n",
    "    # transformt solution to list\n",
    "    sol = list(solution.copy())\n",
    "    # r_c - list with cell length values to color without division into rows\n",
    "    r_c = [item for sublist in req_rows for item in sublist]\n",
    "    # set initial penalty to 0\n",
    "    penalty = 0 \n",
    "    for j in range(len(req_rows)):\n",
    "        # n_row - counts how many colored sequences are in the rows\n",
    "        # initial value for each row is equal to 1\n",
    "        n_row = 1 \n",
    "        # k_row - list with values of solution for current row\n",
    "        # shows in which columns sequences of colored cells begin\n",
    "        k_row = [] \n",
    "        # stays on the current row until the number of colored sequences is less or equal than required\n",
    "        while n_row <= len(req_rows[j]):\n",
    "            # k - current position \n",
    "            k = sol[0]\n",
    "            # checks if in a given row another sequence doesn't already start with k\n",
    "            if k in k_row: \n",
    "                penalty += 10\n",
    "            # adding k to list of values for current row\n",
    "            k_row.append(k)\n",
    "            # r - length of the current sequence (number of cells to fill in)\n",
    "            r = r_c[0]\n",
    "            # checks if the next sequence is in a later column\n",
    "            if n_row > 1 and k <= k_row[-2]: \n",
    "                penalty += 10\n",
    "            # penalty if there is no break between sequences\n",
    "            if k >= 1 and nono[j, int(k)-1] == 1:\n",
    "                penalty += 10\n",
    "            # penalty if there is no break between sequences\n",
    "            if k < len(req_rows)-1 and nono[j, int(k)+1] == 1: \n",
    "                penalty += 10\n",
    "            # changing nono values to 1 depending on k and r value\n",
    "            for i in range(int(k), int(k)+r):\n",
    "                if i < len(req_rows):\n",
    "                    nono[j, i] = 1\n",
    "                # penalty for going off the board\n",
    "                else:\n",
    "                    penalty += 1\n",
    "            # deleting first element of solution and firs requirement\n",
    "            # to always be able to refer to 0 elements of the list\n",
    "            del sol[0]\n",
    "            del r_c[0]\n",
    "            # changing n_row value, adding 1, because 1 add one sequence\n",
    "            n_row += 1\n",
    "    return nono, penalty\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "def columns(matrix):\n",
    "    \"\"\"\n",
    "    a function that counts the number of 1 (collored cells) in each column\n",
    "    \n",
    "    Inputs:\n",
    "    - matrix - completed nonogram\n",
    "    \n",
    "    Returns:\n",
    "    - l - list of lists of the length of the sequence of colored cells in each column\n",
    "    \"\"\"\n",
    "    # l - an empty list to which I will add the results for each column\n",
    "    l = []\n",
    "    for j in range(len(matrix)):\n",
    "        # column - list with values for current column\n",
    "        column = matrix[:, j]\n",
    "        # l_col - a list containing the length of the consecutive painted cell sequences for the current column\n",
    "        l_col = []        \n",
    "        # seq - counts the length of occurrences of 1 in a row in each row\n",
    "        seq = 0\n",
    "        for i in range(len(column)):\n",
    "             # if current element is equal to 1, adds one to the length of the sequence\n",
    "            if column[i] == 1:\n",
    "                seq += 1\n",
    "            else:\n",
    "                # if element of the list is equal to 0:\n",
    "                if seq!=0:\n",
    "                    # if seq is different from 0, adding length of this sequence to list for current column\n",
    "                    l_col.append(seq)\n",
    "                    # changing seq value to 0\n",
    "                    seq = 0\n",
    "        # if seq is different from 0, adding length of last sequence to list for current column\n",
    "        if seq != 0:\n",
    "            l_col.append(seq)\n",
    "        # adding values for the current row to the main list\n",
    "        l.append(l_col)\n",
    "    return l\n",
    "\n",
    "\n",
    "def fitness_func(solution, solution_idx):\n",
    "    \"\"\"\n",
    "    Fitness function - checks the quality of the solution\n",
    "    \n",
    "    Inputs:\n",
    "    solution, solution_idx\n",
    "    \n",
    "    Description:\n",
    "    penalty function for invalid values of shaded cells in each column\n",
    "    \n",
    "    Max value: 0\n",
    "    \"\"\"\n",
    "    nono = nonogram(solution)[0]\n",
    "    penalty = nonogram(solution)[1]\n",
    "    for i in range(len(nono)):\n",
    "        if columns(nono)[i] != req_col[i]:\n",
    "            penalty += 10\n",
    "    return -penalty\n",
    "\n",
    "fitness_function = fitness_func\n",
    "\n",
    "# population size\n",
    "sol_per_pop = 200\n",
    "\n",
    "\n",
    "# how many parents we choose (about 50% of the population)\n",
    "num_parents_mating = 100\n",
    "# number of generations\n",
    "num_generations = 100\n",
    "# how many parents to keep\n",
    "keep_parents = 5\n",
    "\n",
    "\n",
    "# number of genes is equal to number of sequence to color and put in nonogram\n",
    "num_genes=len(row)\n",
    "\n",
    "# parent selection\n",
    "#sss = steady\n",
    "parent_selection_type = \"sss\"\n",
    "\n",
    "# crossover\n",
    "crossover_type = \"two_points\"\n",
    "\n",
    "# mutation set to minimum value\n",
    "# 1/num_genes\n",
    "mutation_type = \"random\"\n",
    "\n",
    "\n",
    "\n",
    "# initiation of the algorithm with higher parameters stored in attributes\n",
    "ga_instance = pygad.GA(gene_space=gene_space,\n",
    "                       num_generations=num_generations,\n",
    "                       num_parents_mating=num_parents_mating,\n",
    "                       fitness_func=fitness_function,\n",
    "                       sol_per_pop=sol_per_pop,\n",
    "                       num_genes=len(row),\n",
    "                       parent_selection_type=parent_selection_type,\n",
    "                       keep_parents=keep_parents,\n",
    "                       crossover_type=crossover_type,\n",
    "                       mutation_type=mutation_type,\n",
    "                       mutation_num_genes=1,\n",
    "                      stop_criteria=['reach_0'])\n",
    "\n",
    "#running the algorithm\n",
    "ga_instance.run()\n",
    "\n",
    "#summary: best solution\n",
    "solution, solution_fitness, solution_idx = ga_instance.best_solution()\n",
    "print(\"Fitness value of the best solution = {solution_fitness}\".format(solution_fitness=solution_fitness))\n",
    "ga_instance.plot_fitness()\n",
    "\n",
    "# visualisation\n",
    "def visualisation(solution):\n",
    "    plt.figure(figsize=(14, 12))\n",
    "    # the black color corresponds to the painted ones, white - blank \n",
    "    # row and column captions match the requirements of the nonogram\n",
    "    ax = sns.heatmap(nonogram(solution)[0], cmap = ['white', 'black'], linewidths=0.1, linecolor = 'black',xticklabels=req_col, yticklabels=req_rows)\n",
    "    plt.yticks(rotation=0)\n",
    "    ax.xaxis.tick_top() # x axis on top\n",
    "    ax.xaxis.set_label_position('top')\n",
    "    return ax\n",
    "\n",
    "visualisation(solution)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Other examples for 5x5 nonograms:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2) Smile"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitness value of the best solution = 0\n"
     ]
    },
    {
     "data": {
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aRm9mVt4d/4IbHym0T9wXNhuYWzjtUhfnLCJit0rmk/Qn4NZODsfMrN0mT4X/vrbQ3n1LOHjH/OJpr7roWbREUvEN8AcAE/OKxcysEnPmwelj0vkKgHVXhdPqtEBgpeqiZ9GKCyRtAQTwOvCdfMMxM2teBIy6Ct7KTp0u0xvOPxaW7ZNvXO1V98kiIo7KOwYzs0pd/Q+475lC+7TDYL3V84uno9T9YSgzs67i6VfholsK7YO+BF/dKr94OpKThZlZB5gxC356eaFA4OABcOJ++cbUkZwszMzaadFiOPMKeDcrELjicjBqWNcoEFgpJwszs3b60x3wREmBwNXL3j7cdTlZmJm1wz+fg8vGFdrHfRW+uHF+8XQWJwszszZ6+104Z2yhve1GcOxX84unMzlZmJm1wfyPYcRlMGtuaq/WNx1+6moFAivVTT+WmVnn+vX1MKm4QOAw6NsFCwRWysnCzKxKtz0ONz1aaJ+0P2y6bn7x1IKThZlZFSZPhQv+VmjvvhUctEN+8dSKk4WZWYVmz4Xhl8KCrEDgwNXgtEO7doHASjlZmJlVIAJGXQ1T3k3t7lIgsFJOFmZmFbjqfri/qEDg6UNTz6JROFmYmbViwivw+6LHrh2yI+y2ZX7x5MHJwsysBe/NhDOKCgRuti78cN98Y8qDk4WZWTMWLsoKBM5M7b7LwbnHQK9uVCCwUk4WZmbNGH0HPDk5DUtw9lGwWjcrEFgpJwszszIenAhX/L3Q/taesM1G+cWTNycLM7MSU0oKBG63CQzbLb946oGThZlZkXkL4PQxMHteaq++Epx1JPRo8G/LBv/4ZmZL+p/r4eW303CvrEDgisvlGlJdcLIwM8vc+hjc8lihffIB6Vna5mRhZgbAS2/DL64rtPfYGg7YPr946o2ThZk1vFlz03mKpgKBg1aHUw9pjAKBlaqLZCHpEEnPSVosaUjJtOGSJkuaJGmPvGI0s+4pAs69Kj0iFVJhwPOOhWUapEBgperlPsSJwIHAH4tHShoMDAU2BdYExknaMCIW1T5EM+uOxt4HDzxbaJ8+FNZdNb946lVd9Cwi4oWImFRm0n7A1RExPyJeAyYD29Q2OjPrrp56BS6+rdA+dCfYdYv84qlndZEsWrAW8FZRe0o27lMkHS9pvKTx06dPr0lwZtZ1vfshnHFZUYHAgfCDr+caUl2r2WEoSeOA1ctMGhERNzW3WJlxUW7GiBgNjAYYMmRI2XnMzCAVCDzjCnhvVmr3XQ5GNWiBwErVbNNERFtulp8CrFPUXhuY2jERmVmjuvi29IwKgB6Cc46GVfvmG1O9q/fDUDcDQyX1kbQesAHweM4xmVkX9o9n00ntJt/eC76wYX7xdBV1kSwkHSBpCrAdcJukuwAi4jngGuB54E7g+74Sysza6q3p8LMrC+3tB8PRu+YXT1dSF0foIuIG4IZmpo0CRtU2IjPrbuYtgBFjYE5WIHCNleHMI1wgsFLeTGbWEH55HbycnfHs1TOd0HaBwMo5WZhZt3fzo3Bb0dnOHx0Im7hAYFWcLMysW5s0BX5VVCBwzyGw/3b5xdNVOVmYWbc1a246T7FgYWoPWsMFAtvKycLMuqXFi9OVT2+/l9rL9oHzh8HSvXMNq8tysjCzbmnsffDgxEJ7xFAY4AKBbdbuZCGpV0cEYmbWUZ6cvGSBwKFfhq+4QGC7VJUsJJ0o6aCi9l+AudmzJjbq8OjMzKo0/UM443JYnFWI23w9+L4LBLZbtT2LE4HpAJJ2Ag4FjgAmAL/q2NDMzKqzcFGqJDsjKxC40vLws6NhqZ75xtUdVHsH91rA69nw14FrI+IaSc8CD3ZkYGZm1fr9rfD0a2m4h1KicIHAjlFtz2Im0D8b3h34ezb8MbB0RwVlZlat+5+Bq+4vtI/fG7beILdwup1qexZ3A3+S9BSwPnBHNn5T4LWODMzMrFJvTU/P0W6yw2A46iv5xdMdVduz+D7wENAPODgiZmTjtwKuanYpM7NOMm8BDL+0UCBwzZXhzCNdILCjVdWziIiZwA/LjD+rwyIyM6tQBPzib/DKtNTuvRScNww+s2yuYXVL1V46O7j4EllJu0v6q6Thkny9gZnV1M2Pwu3/KrRPORA2Wqf5+a3tqu2o/QXYEkDS2sBNwMqkw1PndmxoZmbNm/QW/M/1hfbeX4B9v5hfPN1dtcliE+DJbPgQ4LGI2Bs4Cji8IwMzM2vOzI9g+JhCgcD114SfHOwCgZ2p2mTRE1iQDe8K3J4NvwKs1lFBmZk1Z/FiOGcsTMsur1lu6XSewgUCO1e1yWIi8F1JO5KSxZ3Z+LWAdzsyMDOzcq64Fx56vtD+6eGwTv/m57eOUW2yOBX4NnA/cFVEPJuN3xd4vLmFzMw6wviXYfTthfbhO8POm+cWTkOp9tLZByT1Bz4TEe8XTfoj8FGHRmZmVuSdD+DMogKBWwyC7+2Tb0yNpOrbViJiEdBT0raS+mTjXo+Idzo8OjMzsgKBl8P7s1N75RVcILDWqr3PYgVJ1wLvAA+TzlUg6WJJIzs+PDMzuOgWeKakQGC/FfONqdFU27P4b2BNUnmPuUXjbwUO6KigzMya3DsBrv5HoX3C12Cr9fOLp1FVmyz2BU6OiAlAFI1/ARjU1iAkHSLpOUmLJQ0pGj9Q0lxJE7LXxW19DzPret58B0ZdXWjvuBl8wwUCc1Ft1dmVgPfKjF8BWNSOOCYCB5JOlJd6JSL8QESzBjN3frrx7qP5qb3WKnDGEb7xLi/V9iz+RepdNGnqXXyHdA6jTSLihYiY1Nblzax7iYAL/gavFhUIHDUMVlgm17AaWrU9i9OBuyRtmi17Sja8DbBTRweXWS97fsZM4KcRUfaJfJKOB44HGDBgQCeFYma1cOMjcOf4Qvv/HQQbrZ1fPFZlzyIiHga2B3qTSnzsCkwFtouIJ1taVtI4SRPLvPZrYbFpwICI2BI4BbhS0meaiW10RAyJiCH9+/t2TrOu6oU34ddFBQK/to0LBNaDansWZHdtH9OG5XZrwzLzgfnZ8BOSXgE2BMa3uKCZdUkfzoHTx8DH2RnQDdaEHx+Ua0iWqTpZAEhaE1iVkp5Ja72LNrxPf2BGRCySNAjYAHi1I9/DzOpDU4HAf2e1IZZbOp2ncIHA+lBVspC0JfBXYGOg9JqEIFWlrZqkA4DfAv2B2yRNiIg9SOdBzpG0kHS11QlFj3I1s27k8r/Dwy8U2mce4QKB9aTansVo4C1SMcGpLHmvRZtFxA3ADWXGXwdc1xHvYWb16/FJMPqOQvsbX4GdPpdfPPZp1SaLwcCWEfFSZwRjZo3nnQ/grCvS5bIAW34WvrN3vjHZp1V7n8WzwOqdEYiZNZ6PF8KIy+CDOam9igsE1q1qk8XpwAWSdpO0mqSVi1+dEaCZdV+/uwUmvp6Ge/aAnx0Dq5S9ON7yVu1hqHHZv3ez5PkK0Y4T3GbWeMY9Bdc8UGif8LV0CMrqU7XJYpdOicLMGsrr/4Hz/6/Q3ulzcKS/XepatcniNeCtiFjiKihJAtbpsKjMrNuaOx9GjCkqENgvPUfbBQLrW7XnLF4j3QtRauVsmplZsyLgv6+FV/+d2r17wfnDXCCwK6g2WTSdmyi1PDCv/eGYWXd2w8Nw1xOF9k8Ogg3Wyi8eq1xFh6EkXZgNBnC+pI+KJvckVZ2d0MGxmVk38vyb8JuiW2+/vi3ss21+8Vh1Kj1n0XQvpYBNgAVF0xYATwK/7MC4zKwb+XBOOk/xSYHAteCUA3MNyapUUbKIiF0AJF0KnBQRMzs1KjPrNhYvhpF/LRQIXGGZdJ7CBQK7lqquhoqIYzsrEDPrni69Bx59sdA+44h0BZR1La0mC0k3A9+IiJnZcLMiYt+WpptZY3nsRfjLXYX2UbvCjpvlF4+1XSU9i/eAzSU9kg2bmbXqP+/DWX8tFAjcen04fq98Y7K2azVZRMSxkhYBazQdhpJ0G/CtiJjW2QGaWdfTVCDww6xAYL/PwDkuENilVXqfRem9lTsCvo3GzMr67c3w3BtpuGePVEl25RXyjcnap9qb8pr4xnwzK+ueJ+HaBwvt7+0DW7hAYJdXabIIPn3ndoc8Jc/Muo/SAoE7bw6H75xbONaBKr10VsBfJWWlv1ga+FPJndy+GsqsgX00H4ZfCnOzW3bX7gcjhrpAYHdRabK4rKT9144OxMy6rgj4+TWpZwHQpxecfyws7zOb3Uald3D7Zjwza9Z1D6VzFU1+cjCsv2Z+8VjHa+sJbjMzIF319L83Ftr7fRG+tk1+8VjncLIwszb7YHYqELgwKxC40drwIxcI7JacLMysTRZlBQL/80Fqr7AsnDcsna+w7qcukoWkX0h6UdIzkm6Q1Ldo2nBJkyVNkrRHnnGaWcGld8Njkwrts46ANVfJLx7rXHWRLIB7gM0iYnPgJWA4gKTBwFBgU2BP4PeSXDDALGePvACX3F1oH7Mb7LBpfvFY56uLZBERd0fEwqz5KLB2NrwfcHVEzI+I14DJpKfymVlO/v1+Ovz0SYHADeDbLhDY7dVFsihxHHBHNrwW8FbRtCnZuE+RdLyk8ZLGT58+vZNDNGtMCxamE9ozs9tx+60I5xyV6j9Z91bVw4/aQ9I4YPUyk0ZExE3ZPCOAhcDYpsXKzF+2zEhEjAZGAwwZMsSlSMw6wYU3pWdpQ0oQ57pAYMOoWbKIiN1ami7pGGAfYNeIpg4uU4B1imZbG5jaORGaWUvuegKu+2eh/f2vw+cH5ReP1VZddB4l7QmcCuwbEcX1pm4GhkrqI2k9YAPg8TxiNGtkr/07lfNossvnYeiX84vHaq9mPYtW/A7oA9yjVHXs0Yg4ISKek3QN8Dzp8NT3I2JRjnGaNZw581KBwHlZgcAB/V0gsBHVRbKIiPVbmDYKGFXDcMws01Qg8I13UrtPLxg1DJZbOtewLAd1cRjKzOrT3x6EcU8V2qce4gKBjcrJwszKevZ1uPDmQvuA7WGvL+QWjuXMycLMPuX92fDTywoFAjdZB04+IN+YLF9OFma2hEWL4awr4J2iAoGjhkHvujjDaXlxsjCzJfzlLvjXS4X2yCNhjZXzi8fqg5OFmX3ikRdSNdkmw3aH7QfnF4/VDycLMwNg2oxUILDJFzaEb+2ZXzxWX5wszOxTBQL7rwhnu0CgFfGuYGb8743wQlbfuWePdEJ7peVzDcnqjJOFWYO76wm4/qFC+4f7wucG5haO1SknC7MG9uq0JQsE7roFHLpTfvFY/XKyMGtQc+bB8DFFBQJXheGHuUCgledkYdaAIuC8q+HNrEDg0r3h/GEuEGjNc7Iwa0DXPAD3Pl1on3YoDFojv3is/jlZmDWYZ16D3xYVCDxwB9hj6/zisa7BycKsgcyYBSMuS/WfAAYPgJP2zzcm6xqcLMwaRFOBwHc/TO3PLAvnHuMCgVYZJwuzBvHnO2H8y2lYgpHfcIFAq5yThVkDeOg5GHNPoX3s7rDdJvnFY12Pk4VZNzdtBpx9ZaG97UZw3B75xWNdk5OFWTc2/2M4/VKYlRUIXLVvOvzkAoFWLe8yZt3Yb26AF6ek4aV6wqhjoK8LBFobOFmYdVN3/AtufKTQPnFf2GxgbuFYF+dkYdYNTZ4K/31tob37lnDwjvnFY11fXSQLSb+Q9KKkZyTdIKlvNn6gpLmSJmSvi/OO1azezZkHp49J5ysABq4Gp7lAoLVTXSQL4B5gs4jYHHgJGF407ZWI2CJ7nZBPeGZdQwSMugremp7ay/SG84+FZfvkG5d1fXWRLCLi7ohYmDUfBdbOMx6zrurqf8B9zxTaww9LPQuz9qqLZFHiOOCOovZ6kp6S9A9JzR51lXS8pPGSxk+fPr3zozSrM0+/ChfdUmgf/CXYfav84rHupWZVYSSNA1YvM2lERNyUzTMCWAiMzaZNAwZExHuStgZulLRpRMwsXUlEjAZGAwwZMiQ64zOY1asZs+CnRQUCN10XTtwv35ise6lZsoiI3VqaLukYYB9g14iIbJn5wPxs+AlJrwAbAuM7OVyzLmPhIjjzcng3+wm14nKpQGAvFwi0DlQXh6Ek7QmcCuwbER8Vje8vqWc2PAjYAHg1nyjN6tOf7oQnJqdhCc7+Bqy+Ur4xWfdTL789fnYTwVcAAAwJSURBVAf0Ae5Rur7v0ezKp52AcyQtBBYBJ0TEjPzCNKsvD06Ey8cV2t/8Kmy7cX7xWPdVF8kiItZvZvx1wHU1DsesS3j7XfhZcYHAjeHYr+YXj3VvdXEYysyqM//j9MS7WXNTe7W+MPJI6OH/0dZJvGuZdUG/vh4mFRcIHOYCgda5nCzMupjbHoebHi20T9o/XSpr1pmcLMy6kMlT4YK/Fdpf3QoO2iG/eKxxOFmYdRGz58LwS2FBViBwvdXgtENdINBqw8nCrAuIgHOvginvpvayfeC8Y2EZFwi0GnGyMOsCrrwf/vFsoe0CgVZrThZmde6pV+APtxbah+4Iu22ZXzzWmJwszOrYezPhjKICgZsNhB/sm2tI1qCcLMzq1MJFcMbl8N6s1O67HIxygUDLiZOFWZ0afXs6BAVZgcCjYNW++cZkjcvJwqwOPTgRrri30P7WnrDNRvnFY+ZkYVZnprwL54wttLfbBIa1+DQYs87nZGFWR+YtgNPHwOx5qb36SnCWCwRaHfAuaFZH/ud6ePntNNwrKxC44nK5hmQGOFmY1Y1bH4NbHiu0Tz4ABg/ILx6zYk4WZnXgpbfhF0WP+dpzazhg+/ziMSvlZGGWs1lz03mKpgKBg1aH/zrEBQKtvjhZmOUoAs69Mj0iFVwg0OqXk4VZjsbeCw9MLLRHDIV1V80vHrPmOFmY5eTJyfCH2wrtw3aCr2yRXzxmLXGyMMvBux+muk+LI7U/N9AFAq2+OVmY1djCRXDGFTAjKxC40vJw7jGwVM984zJriZOFWY1dfBtMyAoE9nCBQOsi6iJZSPqZpGckTZB0t6Q1i6YNlzRZ0iRJe+QZp1l7/eNZGHtfof3tveALG+YXj1ml6qUy/i8i4gwASScCZwInSBoMDAU2BdYExknaMCIWdUYQv7kBPu6UNZsldz1RGN5+MBy9a36xmFWjLpJFRMwsai4HZKf92A+4OiLmA69JmgxsAzzSGXHc9Ggq5GbW2dZYGc48wgUCreuoi2QBIGkUcDTwIbBLNnot4NGi2aZk48otfzxwPMCAAS6oY/Wrdy84b5gLBFrXUrNkIWkcsHqZSSMi4qaIGAGMkDQc+AFwFlCu4EGUGUdEjAZGAwwZMqTsPK05cb/Cs47NOkMPwZafhfXK/U8wq2M1SxYRUenjW64EbiMliynAOkXT1gamdnBon3DhNjOz8uriiKmkDYqa+wIvZsM3A0Ml9ZG0HrAB8Hit4zMza3T1cs7i55I2AhYDbwAnAETEc5KuAZ4HFgLf76wroczMrHl1kSwi4qAWpo0CRtUwHDMzK1EXh6HMzKy+OVmYmVmrnCzMzKxVThZmZtYqRbTp/rW6Jmk66aqqtuoHvNtB4XQkx1Udx1Udx1Wd7hjXuhHRv9yEbpks2kvS+IgYknccpRxXdRxXdRxXdRotLh+GMjOzVjlZmJlZq5wsyhuddwDNcFzVcVzVcVzVaai4fM7CzMxa5Z6FmZm1ysnCzMxa1VDJQtKekiZJmizptDLTJenCbPozkraqdNlOjuvILJ5nJD0s6fNF016X9KykCZLG1ziunSV9mL33BElnVrpsJ8f1k6KYJkpaJGnlbFpnbq9LJL0jaWIz0/Pav1qLK6/9q7W48tq/Wour5vuXpHUk3SfpBUnPSTqpzDydu39FREO8gJ7AK8AgoDfwNDC4ZJ69gTtIT+j7IvBYpct2clzbAytlw3s1xZW1Xwf65bS9dgZubcuynRlXyfxfB+7t7O2VrXsnYCtgYjPTa75/VRhXzfevCuOq+f5VSVx57F/AGsBW2fAKwEu1/v5qpJ7FNsDkiHg1IhYAVwP7lcyzH3B5JI8CfSWtUeGynRZXRDwcEe9nzUdJTwzsbO35zLlurxKHA1d10Hu3KCIeAGa0MEse+1erceW0f1WyvZqT6/YqUZP9KyKmRcST2fAs4AVgrZLZOnX/aqRksRbwVlF7Cp/e2M3NU8mynRlXsW+Sfj00CeBuSU9IOr6DYqomru0kPS3pDkmbVrlsZ8aFpGWBPYHrikZ31vaqRB77V7VqtX9Vqtb7V8Xy2r8kDQS2BB4rmdSp+1ddPPyoRlRmXOl1w83NU8mybVXxuiXtQvrP/KWi0TtExFRJqwL3SHox+2VUi7ieJNWSmS1pb+BG0qNv62J7kQ4RPBQRxb8SO2t7VSKP/atiNd6/KpHH/lWNmu9fkpYnJaeTI2Jm6eQyi3TY/tVIPYspwDpF7bWBqRXOU8mynRkXkjYH/gzsFxHvNY2PiKnZv+8AN5C6nDWJKyJmRsTsbPh2oJekfpUs25lxFRlKySGCTtxelchj/6pIDvtXq3Lav6pR0/1LUi9SohgbEdeXmaVz96+OPhFTry9SL+pVYD0KJ3k2LZnnayx5gujxSpft5LgGAJOB7UvGLwesUDT8MLBnDeNancKNndsAb2bbLtftlc23Ium483K12F5F7zGQ5k/Y1nz/qjCumu9fFcZV8/2rkrjy2L+yz3058JsW5unU/athDkNFxEJJPwDuIl0dcElEPCfphGz6xcDtpCsKJgMfAce2tGwN4zoTWAX4vSSAhZGqSq4G3JCNWwq4MiLurGFcBwPflbQQmAsMjbR35r29AA4A7o6IOUWLd9r2ApB0FekKnn6SpgBnAb2K4qr5/lVhXDXfvyqMq+b7V4VxQe33rx2Ao4BnJU3Ixp1OSvQ12b9c7sPMzFrVSOcszMysjZwszMysVU4WZmbWKicLMzNrlZOFmZm1ysnCrIvKKpz+OO84rDE4WVi3Jmk1Sb+W9LKkeVnp6Ycl/TArnVD3JI1splz2F4Df1zoea0wNc1OeNZ6s4NpDwEzgDOAZ0g+kDYGjgfeAK3MKD0m9I1UBbZOImN6R8Zi1xD0L687+ACwGhkTE1RHxfERMjIjrI2J/sro+klaUNDrrdcyS9A9JQ5pWImmYpNmSds0edjMnexDNesVvJunrWbXReZJekzRKUu+i6a9nvYRLJH0AjM3G/zx7MM3cbJ4LJC3d9N6kO4g3lRTZa1jR+n5ctP4Bkm7IPsMsSddLWrto+sgs/qGSXsnmuTGrt2TWIicL65aUnly2B3BRSUmGT0REKNVmuI1UsnkfUunnB4B7lZ4F0KQPMBw4DtgO6As0lX5A0h6kL//fAZtm8x0MnFfytqcALwJDSOUaAOZk828CfI9UoG5ENu3/gF8Bk0gPwFkjG1f6eUWqyroa8BVgF2BN4MZsWpOBwGGkchVfzT7vqHLbx2wJHVl8yy+/6uUFbEsqw3xAyfgpwOzsdTHpi3U2sEzJfBOA/8qGh2Xr2qho+pHAAqBH1n4AOKNkHftn624qq/M6cEsFsZ9AelhNU3skZYraZev7cTa8O7AIGFg0fRCpZ7Vb0XrmASsWzTOi+L388qu5l89ZWKPZkVRMbTSwNLA1sCwwfckf4CwNfLaoPT8iJhW1p5KKy/UlVR/dGthG0qlF8/QAliFVT52WjfvUc5klHQycDKwPLJ/F17PKz7UJMDUiXm8aERGvSpoKDAbGZaPfiIgPSz7HqlW+lzUgJwvrriaTegMbF4+MiNcAJH2UjeoB/IeUREoVP1xmYcm0pgqcPYr+PRu4tsx6ik9EL3FITNIXSY+5PBv4EfABsC/wyzLraYmKYipVPP7jMtN8ONpa5WRh3VJEvCfpbuAHkn4b2UN0yniSdJx/cUS82o63fBLYOCImV7ncDsDbEfGzphGS1i2ZZwGt9zSeB9aSNLCpdyFpEOm8xfNVxmT2Kf5FYd3Z90j7+BOSDpc0WNKGkg4HPk86xj+OdHntTZL2krSepO0knS2pXG+jOecAR0g6R9JmkjaWdLCkC1pZ7iXSl/yRkgZJ+i5weMk8rwPrStpKUj9JfcqsZxzpoTZjJW2dXc01lpTE7q3ic5iV5WRh3VbWU9gSuBP4GfAU6cvzFNLNbCdHRJAeGHMv8CfSVUfXABtRxaMnI+Iu0pPKdgEez16nkZ7u1tJytwC/AH5Dug9kd9LDiIpdR3qwzd9Jh7RKkwnZ59g/m34/cB/wb2D/bJpZu/jhR2Zm1ir3LMzMrFVOFmZm1ionCzMza5WThZmZtcrJwszMWuVkYWZmrXKyMDOzVjlZmJlZq/4/cL8kO2XGIcIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x165b262c5e0>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1008x864 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "req_col = [[2,1], [2,1], [1], [2,1], [2,1]]\n",
    "req_rows = [[2,2], [2,2], [], [1,1], [3]]\n",
    "\n",
    "row = [item for sublist in req_rows for item in sublist]\n",
    "\n",
    "\n",
    "ga_instance = pygad.GA(gene_space=gene_space,\n",
    "                       num_generations=num_generations,\n",
    "                       num_parents_mating=num_parents_mating,\n",
    "                       fitness_func=fitness_function,\n",
    "                       sol_per_pop=sol_per_pop,\n",
    "                       num_genes=len(row),\n",
    "                       parent_selection_type=parent_selection_type,\n",
    "                       keep_parents=keep_parents,\n",
    "                       crossover_type=crossover_type,\n",
    "                       mutation_type=mutation_type,\n",
    "                       mutation_num_genes=1,\n",
    "                      stop_criteria=['reach_0'])\n",
    "ga_instance.run()\n",
    "\n",
    "solution, solution_fitness, solution_idx = ga_instance.best_solution()\n",
    "print(\"Fitness value of the best solution = {solution_fitness}\".format(solution_fitness=solution_fitness))\n",
    "ga_instance.plot_fitness()\n",
    "\n",
    "visualisation(solution)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitness value of the best solution = 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x165b2ab2f70>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1008x864 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "req_col = [[1,2], [3], [2], [3], [1,1]]\n",
    "req_rows = [[3], [4], [1,1], [2], [1,1]]\n",
    "\n",
    "row = [item for sublist in req_rows for item in sublist]\n",
    "\n",
    "ga_instance = pygad.GA(gene_space=gene_space,\n",
    "                       num_generations=num_generations,\n",
    "                       num_parents_mating=num_parents_mating,\n",
    "                       fitness_func=fitness_function,\n",
    "                       sol_per_pop=sol_per_pop,\n",
    "                       num_genes=len(row),\n",
    "                       parent_selection_type=parent_selection_type,\n",
    "                       keep_parents=keep_parents,\n",
    "                       crossover_type=crossover_type,\n",
    "                       mutation_type=mutation_type,\n",
    "                       mutation_num_genes=1,\n",
    "                      stop_criteria=['reach_0'])\n",
    "\n",
    "ga_instance.run()\n",
    "\n",
    "solution, solution_fitness, solution_idx = ga_instance.best_solution()\n",
    "print(\"Fitness value of the best solution = {solution_fitness}\".format(solution_fitness=solution_fitness))\n",
    "ga_instance.plot_fitness()\n",
    "\n",
    "visualisation(solution)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitness value of the best solution = 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x165b0ed2f70>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1008x864 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "req_col = [[3], [3], [1,2], [3], [1]]\n",
    "req_rows = [[3], [2], [2,2], [2], [2]]\n",
    "\n",
    "row = [item for sublist in req_rows for item in sublist]\n",
    "\n",
    "ga_instance = pygad.GA(gene_space=gene_space,\n",
    "                       num_generations=num_generations,\n",
    "                       num_parents_mating=num_parents_mating,\n",
    "                       fitness_func=fitness_function,\n",
    "                       sol_per_pop=sol_per_pop,\n",
    "                       num_genes=len(row),\n",
    "                       parent_selection_type=parent_selection_type,\n",
    "                       keep_parents=keep_parents,\n",
    "                       crossover_type=crossover_type,\n",
    "                       mutation_type=mutation_type,\n",
    "                       mutation_num_genes=1,\n",
    "                      stop_criteria=['reach_0'])\n",
    "\n",
    "ga_instance.run()\n",
    "\n",
    "solution, solution_fitness, solution_idx = ga_instance.best_solution()\n",
    "print(\"Fitness value of the best solution = {solution_fitness}\".format(solution_fitness=solution_fitness))\n",
    "ga_instance.plot_fitness()\n",
    "\n",
    "visualisation(solution)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 5) Plus"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitness value of the best solution = 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x165b2901040>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1008x864 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "req_col = [[3], [2,2], [1,1], [2,2], [3]]\n",
    "req_rows = [[3], [2,2], [1,1], [2,2], [3]]\n",
    "\n",
    "row = [item for sublist in req_rows for item in sublist]\n",
    "\n",
    "\n",
    "ga_instance = pygad.GA(gene_space=gene_space,\n",
    "                       num_generations=num_generations,\n",
    "                       num_parents_mating=num_parents_mating,\n",
    "                       fitness_func=fitness_function,\n",
    "                       sol_per_pop=sol_per_pop,\n",
    "                       num_genes=len(row),\n",
    "                       parent_selection_type=parent_selection_type,\n",
    "                       keep_parents=keep_parents,\n",
    "                       crossover_type=crossover_type,\n",
    "                       mutation_type=mutation_type,\n",
    "                       mutation_num_genes=1,\n",
    "                      stop_criteria=['reach_0'])\n",
    "\n",
    "ga_instance.run()\n",
    "\n",
    "solution, solution_fitness, solution_idx = ga_instance.best_solution()\n",
    "print(\"Fitness value of the best solution = {solution_fitness}\".format(solution_fitness=solution_fitness))\n",
    "ga_instance.plot_fitness()\n",
    "\n",
    "visualisation(solution)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test for small inputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitness value of the best solution = 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x165b2dcfa00>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1008x864 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "req_col1 = [[2], [1,3], [4], [2], [1]]\n",
    "req_rows1 = [[1,1], [3], [2], [3], [3]]\n",
    "\n",
    "req_col2 = [[3], [3], [1,2], [3], [1]]\n",
    "req_rows2 = [[3], [2], [2,2], [2], [2]]\n",
    "\n",
    "req_col3 = [[1,2], [3], [2], [3], [1,1]]\n",
    "req_rows3 = [[3], [4], [1,1], [2], [1,1]]\n",
    "\n",
    "req_col4 = [[2,1], [2,1], [1], [2,1], [2,1]]\n",
    "req_rows4 = [[2,2], [2,2], [], [1,1], [3]]\n",
    "\n",
    "req_col5 = [[3], [2,2], [1,1], [2,2], [3]]\n",
    "req_rows5 = [[3], [2,2], [1,1], [2,2], [3]]\n",
    "\n",
    "cols = [req_col1, req_col2, req_col3, req_col4, req_col5]\n",
    "rows = [req_rows1, req_rows2, req_rows3, req_rows4, req_rows5]\n",
    "\n",
    "times = []\n",
    "\n",
    "for j in range(100):\n",
    "    # randomly selecting one of the inputs\n",
    "    i = randint(0, 4)\n",
    "    req_col = cols[i]\n",
    "    req_rows = rows[i]\n",
    "    \n",
    "    row = [item for sublist in req_rows for item in sublist]\n",
    "\n",
    "    ga_instance = pygad.GA(gene_space=gene_space,\n",
    "                       num_generations=num_generations,\n",
    "                       num_parents_mating=num_parents_mating,\n",
    "                       fitness_func=fitness_function,\n",
    "                       sol_per_pop=sol_per_pop,\n",
    "                       num_genes=len(row),\n",
    "                       parent_selection_type=parent_selection_type,\n",
    "                       keep_parents=keep_parents,\n",
    "                       crossover_type=crossover_type,\n",
    "                       mutation_type=mutation_type,\n",
    "                       mutation_num_genes=1,\n",
    "                      stop_criteria=['reach_0'])\n",
    "    \n",
    "    start = time.time()\n",
    "    ga_instance.run()\n",
    "\n",
    "    solution, solution_fitness, solution_idx = ga_instance.best_solution()\n",
    "    end = time.time()\n",
    "    \n",
    "    # saving time for perfect attempts\n",
    "    if solution_fitness == 0:\n",
    "        times.append(end - start)\n",
    "\n",
    "# printing the solution and visualisation for the last input\n",
    "print(\"Fitness value of the best solution = {solution_fitness}\".format(solution_fitness=solution_fitness))\n",
    "ga_instance.plot_fitness()\n",
    "\n",
    "visualisation(solution)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Perfect solution:  100 %\n",
      "Mean time for perfect solution:  0.38391480207443235\n"
     ]
    }
   ],
   "source": [
    "print('Perfect solution: ',len(times), '%')\n",
    "print('Mean time for perfect solution: ', np.mean(times))\n",
    "\n",
    "small_inputes_accuracy = len(times)\n",
    "small_mean_time = np.mean(times)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Note\n",
    "\n",
    "The algorithm works perfectly for 5x5 nonograms. The algorithm works very fast, it can find a solution even in the 2nd generation the average execution time is less than 1 second. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Checking bigger inputs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next step was to check how the algorithm copes with larger inputs."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 7x7\n",
    "\n",
    "With a change in the size of the nonogram, it is necessary to change the gene space."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitness value of the best solution = 0\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x165b2fd2640>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x864 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "req_col = [[1,2,1], [2,3], [1,1,2], [1,2,1], [4,1], [1,2,2], [5,1]]\n",
    "req_rows = [[1,3], [2,2,1], [2,3], [1,4], [4, 1], [2,2], [2,1,2]]\n",
    "\n",
    "row = [item for sublist in req_rows for item in sublist]\n",
    "\n",
    "# changing gene_space\n",
    "gene_space = [0,1,2,3,4,5,6] \n",
    "\n",
    "\n",
    "fitness_function = fitness_func\n",
    "\n",
    "\n",
    "\n",
    "ga_instance = pygad.GA(gene_space=gene_space,\n",
    "                       num_generations=num_generations,\n",
    "                       num_parents_mating=num_parents_mating,\n",
    "                       fitness_func=fitness_function,\n",
    "                       sol_per_pop=sol_per_pop,\n",
    "                       num_genes=len(row),\n",
    "                       parent_selection_type=parent_selection_type,\n",
    "                       keep_parents=keep_parents,\n",
    "                       crossover_type=crossover_type,\n",
    "                       mutation_type=mutation_type,\n",
    "                       mutation_num_genes=1,\n",
    "                      stop_criteria=['reach_0'])\n",
    "\n",
    "#running the algorithm\n",
    "ga_instance.run()\n",
    "\n",
    "#summary: best solution\n",
    "solution, solution_fitness, solution_idx = ga_instance.best_solution()\n",
    "print(\"Fitness value of the best solution = {solution_fitness}\".format(solution_fitness=solution_fitness))\n",
    "ga_instance.plot_fitness()\n",
    "\n",
    "visualisation(solution)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Face"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitness value of the best solution = 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x165b31b1130>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x864 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "req_col = [[3], [3,1], [2,2,1], [5,1], [2,2,1], [3,1], [3]]\n",
    "req_rows = [[3], [5], [2,1,2], [7], [1,3,1], [1,1], [3]]\n",
    "\n",
    "row = [item for sublist in req_rows for item in sublist]\n",
    "\n",
    "# changing gene_space\n",
    "gene_space = [0,1,2,3,4,5,6] \n",
    "\n",
    "\n",
    "fitness_function = fitness_func\n",
    "\n",
    "\n",
    "\n",
    "ga_instance = pygad.GA(gene_space=gene_space,\n",
    "                       num_generations=num_generations,\n",
    "                       num_parents_mating=num_parents_mating,\n",
    "                       fitness_func=fitness_function,\n",
    "                       sol_per_pop=sol_per_pop,\n",
    "                       num_genes=len(row),\n",
    "                       parent_selection_type=parent_selection_type,\n",
    "                       keep_parents=keep_parents,\n",
    "                       crossover_type=crossover_type,\n",
    "                       mutation_type=mutation_type,\n",
    "                       mutation_num_genes=1,\n",
    "                      stop_criteria=['reach_0'])\n",
    "\n",
    "#running the algorithm\n",
    "ga_instance.run()\n",
    "\n",
    "#summary: best solution\n",
    "solution, solution_fitness, solution_idx = ga_instance.best_solution()\n",
    "print(\"Fitness value of the best solution = {solution_fitness}\".format(solution_fitness=solution_fitness))\n",
    "ga_instance.plot_fitness()\n",
    "\n",
    "visualisation(solution)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 8x8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitness value of the best solution = 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x165b2ede370>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x864 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "req_col = [[1], [1,3, 1], [4,3], [2,3], [1,2,1], [2,2,2], [2,1,1], [3,2]]\n",
    "req_rows = [[3,3], [6], [1,1], [2,2], [2,4], [3,1], [2,1], [6]]\n",
    "\n",
    "row = [item for sublist in req_rows for item in sublist]\n",
    "\n",
    "gene_space = [0,1,2,3,4,5,6,7] \n",
    "\n",
    "\n",
    "fitness_function = fitness_func\n",
    "\n",
    "\n",
    "\n",
    "ga_instance = pygad.GA(gene_space=gene_space,\n",
    "                       num_generations=num_generations,\n",
    "                       num_parents_mating=num_parents_mating,\n",
    "                       fitness_func=fitness_function,\n",
    "                       sol_per_pop=sol_per_pop,\n",
    "                       num_genes=len(row),\n",
    "                       parent_selection_type=parent_selection_type,\n",
    "                       keep_parents=keep_parents,\n",
    "                       crossover_type=crossover_type,\n",
    "                       mutation_type=mutation_type,\n",
    "                       mutation_num_genes=1,\n",
    "                      stop_criteria=['reach_0'])\n",
    "\n",
    "#running the algorithm\n",
    "ga_instance.run()\n",
    "\n",
    "#summary: best solution\n",
    "solution, solution_fitness, solution_idx = ga_instance.best_solution()\n",
    "print(\"Fitness value of the best solution = {solution_fitness}\".format(solution_fitness=solution_fitness))\n",
    "ga_instance.plot_fitness()\n",
    "\n",
    "visualisation(solution)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Note\n",
    "\n",
    "Nonograms to size 8x8 are quickly solved by the algorithm without changing population size and number of generations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 10x10 nonograms"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1) House"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "15.575823783874512\n",
      "Fitness value of the best solution = 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x165b264ce20>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x864 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "req_col = [[6],[7],[8],[9],[5,3],[5,3],[9],[8],[7],[6]]\n",
    "req_rows = [[2],[4],[6],[8],[10],[4,4],[4,4],[10],[10],[10]]\n",
    "row = [item for sublist in req_rows for item in sublist]\n",
    "\n",
    "# changing gene_space, beacuse know I have 10 columns\n",
    "gene_space = [0,1,2,3,4,5,6,7,8,9]\n",
    "\n",
    "\n",
    "# population size\n",
    "sol_per_pop = 400\n",
    "\n",
    "\n",
    "# how many parents we choose (about 50% of the population)\n",
    "num_parents_mating = 200\n",
    "# number of generations\n",
    "num_generations = 250\n",
    "\n",
    "keep_parents = 10\n",
    "\n",
    "# initiation of the algorithm with higher parameters stored in attributes\n",
    "ga_instance = pygad.GA(gene_space=gene_space,\n",
    "                       num_generations=num_generations,\n",
    "                       num_parents_mating=num_parents_mating,\n",
    "                       fitness_func=fitness_function,\n",
    "                       sol_per_pop=sol_per_pop,\n",
    "                       num_genes=len(row),\n",
    "                       parent_selection_type=parent_selection_type,\n",
    "                       keep_parents=keep_parents,\n",
    "                       crossover_type=crossover_type,\n",
    "                       mutation_type=mutation_type,\n",
    "                       mutation_num_genes=1,\n",
    "                      stop_criteria=['reach_0'])\n",
    "start = time.time()\n",
    "#running the algorithm\n",
    "ga_instance.run()\n",
    "end = time.time()\n",
    "print(end - start)\n",
    "\n",
    "#summary: best solution\n",
    "solution, solution_fitness, solution_idx = ga_instance.best_solution()\n",
    "print(\"Fitness value of the best solution = {solution_fitness}\".format(solution_fitness=solution_fitness))\n",
    "ga_instance.plot_fitness()\n",
    "\n",
    "visualisation(solution)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Note\n",
    "\n",
    "I tried modifying the fitness function to penalize for the wrong number of colored cells in each column, but it made the time worse.\n",
    "\n",
    "Modified function:\n",
    "\n",
    "def fitness_func(solution, solution_idx):\n",
    "\n",
    "    \"\"\"\n",
    "    Fitness function - checks the quality of the solution\n",
    "    \n",
    "    Inputs:\n",
    "    solution, solution_idx\n",
    "    \n",
    "    Description:\n",
    "    penalty function for invalid values of shaded cells in each row and column\n",
    "    \n",
    "    Max value: 0\n",
    "    \"\"\"\n",
    "    nono = nonogram(solution)[0]\n",
    "    penalty = nonogram(solution)[1]\n",
    "    if len(nono) < 10:\n",
    "        for i in range(len(nono)):\n",
    "            if columns(nono)[i] != req_col[i]:\n",
    "                 penalty += 10\n",
    "    else:\n",
    "        for i in range(len(nono)):\n",
    "            if columns(nono)[i] != req_col[i]:\n",
    "                    penalty += 10\n",
    "            if np.sum(columns(nono)[i]) != np.sum(req_col[i]):\n",
    "                penalty += 10\n",
    "    return -penalty\n",
    "    \n",
    "Time for house example exceed 2 minutes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2) Musical note"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "45.1681022644043\n",
      "Fitness value of the best solution = 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x165b2ed2f40>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x864 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "req_col = [[2],[4],[4],[8],[1,1],[1,1],[1,1,2],[1,1,4],[1,1,4],[8]]\n",
    "req_rows = [[4],[3,1],[1,3],[4,1],[1,1],[1,3],[3,4],[4,4],[4,2],[2]]\n",
    "row = [item for sublist in req_rows for item in sublist]\n",
    "\n",
    "\n",
    "gene_space = [0,1,2,3,4,5,6,7,8,9]\n",
    "\n",
    "\n",
    "# initiation of the algorithm with higher parameters stored in attributes\n",
    "ga_instance = pygad.GA(gene_space=gene_space,\n",
    "                       num_generations=num_generations,\n",
    "                       num_parents_mating=num_parents_mating,\n",
    "                       fitness_func=fitness_function,\n",
    "                       sol_per_pop=sol_per_pop,\n",
    "                       num_genes=len(row),\n",
    "                       parent_selection_type=parent_selection_type,\n",
    "                       keep_parents=keep_parents,\n",
    "                       crossover_type=crossover_type,\n",
    "                       mutation_type=mutation_type,\n",
    "                       mutation_num_genes=1,\n",
    "                      stop_criteria=['reach_0'])\n",
    "\n",
    "start = time.time()\n",
    "#running the algorithm\n",
    "ga_instance.run()\n",
    "end = time.time()\n",
    "print(end - start)\n",
    "\n",
    "#summary: best solution\n",
    "solution, solution_fitness, solution_idx = ga_instance.best_solution()\n",
    "print(\"Fitness value of the best solution = {solution_fitness}\".format(solution_fitness=solution_fitness))\n",
    "ga_instance.plot_fitness()\n",
    "\n",
    "visualisation(solution)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3) Alarm clock"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "26.57246232032776\n",
      "Fitness value of the best solution = 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x165b2d8ae80>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x864 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "req_col = [[2], [2, 4], [1,6,1], [5,3], [4,3], [1,4], [9], [1,6,1], [2,4], [2]]\n",
    "req_rows = [[2,2], [2,4,2], [1,3,2,1], [4,3], [4,3], [3,4], [2,5], [6], [4], [2,2]]\n",
    "\n",
    "row = [item for sublist in req_rows for item in sublist]\n",
    "\n",
    "# initiation of the algorithm with higher parameters stored in attributes\n",
    "ga_instance = pygad.GA(gene_space=gene_space,\n",
    "                       num_generations=num_generations,\n",
    "                       num_parents_mating=num_parents_mating,\n",
    "                       fitness_func=fitness_function,\n",
    "                       sol_per_pop=sol_per_pop,\n",
    "                       num_genes=len(row),\n",
    "                       parent_selection_type=parent_selection_type,\n",
    "                       keep_parents=keep_parents,\n",
    "                       crossover_type=crossover_type,\n",
    "                       mutation_type=mutation_type,\n",
    "                       mutation_num_genes=1,\n",
    "                      stop_criteria=['reach_0'])\n",
    "\n",
    "start = time.time()\n",
    "#running the algorithm\n",
    "ga_instance.run()\n",
    "end = time.time()\n",
    "print(end - start)\n",
    "\n",
    "#summary: best solution\n",
    "solution, solution_fitness, solution_idx = ga_instance.best_solution()\n",
    "print(\"Fitness value of the best solution = {solution_fitness}\".format(solution_fitness=solution_fitness))\n",
    "ga_instance.plot_fitness()\n",
    "\n",
    "visualisation(solution)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test for medium inputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitness value of the best solution = 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x165b35dc280>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x864 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "req_col1 = [[6],[7],[8],[9],[5,3],[5,3],[9],[8],[7],[6]]\n",
    "req_rows1 = [[2],[4],[6],[8],[10],[4,4],[4,4],[10],[10],[10]]\n",
    "\n",
    "req_col2 = [[2],[4],[4],[8],[1,1],[1,1],[1,1,2],[1,1,4],[1,1,4],[8]]\n",
    "req_rows2 = [[4],[3,1],[1,3],[4,1],[1,1],[1,3],[3,4],[4,4],[4,2],[2]]\n",
    "\n",
    "req_col4 = [[2], [2, 4], [1,6,1], [5,3], [4,3], [1,4], [9], [1,6,1], [2,4], [2]]\n",
    "req_rows4 = [[2,2], [2,4,2], [1,3,2,1], [4,3], [4,3], [3,4], [2,5], [6], [4], [2,2]]\n",
    "\n",
    "cols = [req_col1, req_col2,  req_col4]\n",
    "rows = [req_rows1, req_rows2,  req_rows4]\n",
    "\n",
    "raffled_numbers = []\n",
    "\n",
    "times = []\n",
    "\n",
    "# saving which example gets perfect solution\n",
    "perfect = []\n",
    "\n",
    "for j in range(10):\n",
    "    # randomly selecting one of the inputs\n",
    "    i = randint(0,2)\n",
    "    raffled_numbers.append(i)\n",
    "    req_col = cols[i]\n",
    "    req_rows = rows[i]\n",
    "    \n",
    "    row = [item for sublist in req_rows for item in sublist]\n",
    "\n",
    "    ga_instance = pygad.GA(gene_space=gene_space,\n",
    "                       num_generations=num_generations,\n",
    "                       num_parents_mating=num_parents_mating,\n",
    "                       fitness_func=fitness_function,\n",
    "                       sol_per_pop=sol_per_pop,\n",
    "                       num_genes=len(row),\n",
    "                       parent_selection_type=parent_selection_type,\n",
    "                       keep_parents=keep_parents,\n",
    "                       crossover_type=crossover_type,\n",
    "                       mutation_type=mutation_type,\n",
    "                       mutation_num_genes=1,\n",
    "                      stop_criteria=['reach_0'])\n",
    "    \n",
    "    start = time.time()\n",
    "    ga_instance.run()\n",
    "\n",
    "    solution, solution_fitness, solution_idx = ga_instance.best_solution()\n",
    "    end = time.time()\n",
    "    \n",
    "    # saving time for perfect attempts\n",
    "    if solution_fitness == 0:\n",
    "        times.append(end - start)\n",
    "        perfect.append(i)\n",
    "\n",
    "# printing the solution and visualisation for the last input\n",
    "print(\"Fitness value of the best solution = {solution_fitness}\".format(solution_fitness=solution_fitness))\n",
    "ga_instance.plot_fitness()\n",
    "\n",
    "visualisation(solution)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Perfect solution:  90 %\n",
      "Mean time for perfect solution:  63.5061043103536\n"
     ]
    }
   ],
   "source": [
    "print('Perfect solution: ',len(times) * 10, '%')\n",
    "print('Mean time for perfect solution: ', np.mean(times))\n",
    "\n",
    "medium_inputes_accuracy = len(times)\n",
    "medium_mean_time = np.mean(times)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Printing list to see which example didnt get the best solution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 1, 1, 2, 2, 0, 0, 1, 1, 0]\n",
      "[1, 1, 1, 2, 2, 0, 0, 1, 0]\n"
     ]
    }
   ],
   "source": [
    "print(raffled_numbers)\n",
    "\n",
    "print(perfect)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Note\n",
    "\n",
    "For a long time of operation of the algorithm, I tested it only for 10 randomly selected examples. Despite the long running time, the algorithm has good performance."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Large inputs - 15x15"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1) Sun"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "503.6780152320862\n",
      "Fitness value of the best solution = 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x165b4cf2820>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x864 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "req_col = [[15],[7,7],[2,4,4,2],[3,7,3],[5,5],[4,4],[4,1,1,4],[1,1,1,1,1],[4,1,1,4],[4,4],[5,5],[3,7,3],[2,4,4,2],[7,7],[15]]\n",
    "req_rows = [[15],[7,7],[2,4,4,2],[3,7,3],[5,5],[4,4],[4,1,1,4],[1,1,1,1],[4,4],[4,3,4],[5,5],[3,7,3],[2,4,4,2],[7,7],[15]]\n",
    "\n",
    "row = [item for sublist in req_rows for item in sublist]\n",
    "\n",
    "\n",
    "gene_space = [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14]\n",
    "\n",
    "# population size\n",
    "sol_per_pop = 1000\n",
    "\n",
    "\n",
    "# how many parents we choose (about 50% of the population)\n",
    "num_parents_mating = 500\n",
    "# number of generations\n",
    "num_generations = 350\n",
    "\n",
    "keep_parents = 25\n",
    "\n",
    "# initiation of the algorithm with higher parameters stored in attributes\n",
    "ga_instance = pygad.GA(gene_space=gene_space,\n",
    "                       num_generations=num_generations,\n",
    "                       num_parents_mating=num_parents_mating,\n",
    "                       fitness_func=fitness_function,\n",
    "                       sol_per_pop=sol_per_pop,\n",
    "                       num_genes=len(row),\n",
    "                       parent_selection_type=parent_selection_type,\n",
    "                       keep_parents=keep_parents,\n",
    "                       crossover_type=crossover_type,\n",
    "                       mutation_type=mutation_type,\n",
    "                       mutation_num_genes=1,\n",
    "                      stop_criteria=['reach_0'])\n",
    "start = time.time()\n",
    "#running the algorithm\n",
    "ga_instance.run()\n",
    "end = time.time()\n",
    "print(end - start)\n",
    "\n",
    "#summary: best solution\n",
    "solution, solution_fitness, solution_idx = ga_instance.best_solution()\n",
    "print(\"Fitness value of the best solution = {solution_fitness}\".format(solution_fitness=solution_fitness))\n",
    "ga_instance.plot_fitness()\n",
    "\n",
    "visualisation(solution)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2) Castle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1585.7438378334045\n",
      "Fitness value of the best solution = -82\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x165b79a4970>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x864 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "req_col = [[12],[2,1],[1,2,1,1],[2,4,1],[5,1,1],[1,1],[8,4],[2,1,5],[1,1,4],[1,1],[5,1,1],[2,4,1],[1,2,1,1],[2,1],[12]]\n",
    "req_rows = [[1],[2],[3],[2,2,1,2,2],[5,1,5],[1,1,1,1,1],[1,1,1,1,1,1,1],[1,1,7,1,1],[1,1],[1,1,1,1],[1,3,1,3,1],[1,1,3,1,1],[1,1,3,1,1],[1,3,1],[15]]\n",
    "\n",
    "row = [item for sublist in req_rows for item in sublist]\n",
    "\n",
    "\n",
    "gene_space = [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14]\n",
    "\n",
    "# population size\n",
    "sol_per_pop = 1000\n",
    "\n",
    "\n",
    "# how many parents we choose (about 50% of the population)\n",
    "num_parents_mating = 500\n",
    "# number of generations\n",
    "num_generations = 350\n",
    "\n",
    "keep_parents = 25\n",
    "\n",
    "# initiation of the algorithm with higher parameters stored in attributes\n",
    "ga_instance = pygad.GA(gene_space=gene_space,\n",
    "                       num_generations=num_generations,\n",
    "                       num_parents_mating=num_parents_mating,\n",
    "                       fitness_func=fitness_function,\n",
    "                       sol_per_pop=sol_per_pop,\n",
    "                       num_genes=len(row),\n",
    "                       parent_selection_type=parent_selection_type,\n",
    "                       keep_parents=keep_parents,\n",
    "                       crossover_type=crossover_type,\n",
    "                       mutation_type=mutation_type,\n",
    "                       mutation_num_genes=1,\n",
    "                      stop_criteria=['reach_0'])\n",
    "start = time.time()\n",
    "#running the algorithm\n",
    "ga_instance.run()\n",
    "end = time.time()\n",
    "print(end - start)\n",
    "\n",
    "#summary: best solution\n",
    "solution, solution_fitness, solution_idx = ga_instance.best_solution()\n",
    "print(\"Fitness value of the best solution = {solution_fitness}\".format(solution_fitness=solution_fitness))\n",
    "ga_instance.plot_fitness()\n",
    "\n",
    "visualisation(solution)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Note\n",
    "The algorithm did not find a solution and the execution time was too long."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3) Flowers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "req_col = [[15],[1,1,11],[1,10],[2,8,2],[5,1,1],[1,1,3],[4],[7],[6,2],[5,1,1,1],[2,1,5,2,1],[1,1,5,2],[3,11],[1,1,9],[2,1,10]]\n",
    "req_rows = [[2,1,10],[1,1,5,1,1],[3,6,1],[1,1,6,2],[2,1,1,3,1],[6,2,1,1,1],[6,1,6],[5,5],[5,1,5],[5,1,5],[4,1,4],[3,1,3],[3,1,3],[4,1,4],[5,5]]\n",
    "\n",
    "row = [item for sublist in req_rows for item in sublist]\n",
    "\n",
    "\n",
    "gene_space = [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14]\n",
    "\n",
    "# population size\n",
    "sol_per_pop = 1000\n",
    "\n",
    "\n",
    "# how many parents we choose (about 50% of the population)\n",
    "num_parents_mating = 500\n",
    "# number of generations\n",
    "num_generations = 350\n",
    "\n",
    "keep_parents = 25\n",
    "\n",
    "# initiation of the algorithm with higher parameters stored in attributes\n",
    "ga_instance = pygad.GA(gene_space=gene_space,\n",
    "                       num_generations=num_generations,\n",
    "                       num_parents_mating=num_parents_mating,\n",
    "                       fitness_func=fitness_function,\n",
    "                       sol_per_pop=sol_per_pop,\n",
    "                       num_genes=len(row),\n",
    "                       parent_selection_type=parent_selection_type,\n",
    "                       keep_parents=keep_parents,\n",
    "                       crossover_type=crossover_type,\n",
    "                       mutation_type=mutation_type,\n",
    "                       mutation_num_genes=1,\n",
    "                      stop_criteria=['reach_0'])\n",
    "start = time.time()\n",
    "#running the algorithm\n",
    "ga_instance.run()\n",
    "end = time.time()\n",
    "print(end - start)\n",
    "\n",
    "#summary: best solution\n",
    "solution, solution_fitness, solution_idx = ga_instance.best_solution()\n",
    "print(\"Fitness value of the best solution = {solution_fitness}\".format(solution_fitness=solution_fitness))\n",
    "ga_instance.plot_fitness()\n",
    "\n",
    "visualisation(solution)"
   ]
  },
  {
   "attachments": {
    "image.png": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Note\n",
    "\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "The algorithm does not find a solution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.2 Second method\n",
    "\n",
    "The chromosome is the whole field of the nonogram. Genes are 0, 1 depending on whether the place is painted over"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Small inputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitness value of the best solution = 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x28c0dea5100>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# coding inputs\n",
    "# req_col - list of lists with requirements for each column\n",
    "# for example: in first column 2 cells must be colored\n",
    "req_col = [[2], [1,3], [4], [2], [1]]\n",
    "# req_rows - same as req_col\n",
    "req_rows = [[1,1], [3], [2], [3], [3]]\n",
    "\n",
    "# genes are numbers: 0 - unpainted cell, 1 - colored cell\n",
    "gene_space = [0,1] \n",
    "\n",
    "\n",
    "def nonogram(solution):\n",
    "    \"\"\"\n",
    "    a function that converts the solution into a matrix representing a filled nonogram\n",
    "    \n",
    "    Inputs:\n",
    "    - solution - given by genetic algorithm solution\n",
    "    \n",
    "    Returns:\n",
    "    - completed nonogram as matrix\n",
    "    \"\"\"\n",
    "    # changing the shape of the solution to a matrix with dimensions req_rows x req_col\n",
    "    nonogram = solution.reshape((len(req_rows), len(req_col)))\n",
    "    return nonogram\n",
    "\n",
    "\n",
    "def rows(matrix):\n",
    "    \"\"\"\n",
    "    a function that counts the number of 1 (collored cells) in each row\n",
    "    \n",
    "    Inputs:\n",
    "    - matrix - completed nonogram\n",
    "    \n",
    "    Returns:\n",
    "    - l - list of lists of the length of the sequence of colored cells in each row\n",
    "    \"\"\"\n",
    "    # l - an empty list to which I will add the results for each row\n",
    "    l = []\n",
    "    for j in range(len(matrix)):\n",
    "        # row - list with values for current row\n",
    "        row = matrix[j]\n",
    "        # l_row - a list containing the length of the consecutive painted cell sequences for the current row\n",
    "        l_row = []\n",
    "        # seq - counts the length of occurrences of 1 in a row in each row\n",
    "        seq = 0\n",
    "        for i in range(len(row)):\n",
    "            # if current element is equal to 1, adds one to the length of the sequence\n",
    "            if row[i] == 1:\n",
    "                seq += 1\n",
    "            else:\n",
    "                # if element of the list is equal to 0:\n",
    "                if seq!=0:\n",
    "                    # if seq is different from 0, adding length of this sequence to list for current row\n",
    "                    l_row.append(seq)\n",
    "                    # changing seq value to 0\n",
    "                    seq = 0\n",
    "        # # if seq is different from 0, adding length of last sequence to list for current row\n",
    "        if seq != 0:\n",
    "            l_row.append(seq)\n",
    "        # adding values for the current row to the main list\n",
    "        l.append(l_row)\n",
    "    return l\n",
    "\n",
    "def columns(matrix):\n",
    "    \"\"\"\n",
    "    a function that counts the number of 1 (collored cells) in each column\n",
    "    \n",
    "    Inputs:\n",
    "    - matrix - completed nonogram\n",
    "    \n",
    "    Returns:\n",
    "    - l - list of lists of the length of the sequence of colored cells in each column\n",
    "    \"\"\"\n",
    "    # l - an empty list to which I will add the results for each column\n",
    "    l = []\n",
    "    for j in range(len(matrix)):\n",
    "        # column - list with values for current column\n",
    "        column = matrix[:, j]\n",
    "        # l_col - a list containing the length of the consecutive painted cell sequences for the current column\n",
    "        l_col = []        \n",
    "        # seq - counts the length of occurrences of 1 in a row in each row\n",
    "        seq = 0\n",
    "        for i in range(len(column)):\n",
    "             # if current element is equal to 1, adds one to the length of the sequence\n",
    "            if column[i] == 1:\n",
    "                seq += 1\n",
    "            else:\n",
    "                # if element of the list is equal to 0:\n",
    "                if seq!=0:\n",
    "                    # if seq is different from 0, adding length of this sequence to list for current column\n",
    "                    l_col.append(seq)\n",
    "                    # changing seq value to 0\n",
    "                    seq = 0\n",
    "        # if seq is different from 0, adding length of last sequence to list for current column\n",
    "        if seq != 0:\n",
    "            l_col.append(seq)\n",
    "        # adding values for the current row to the main list\n",
    "        l.append(l_col)\n",
    "    return l\n",
    "\n",
    "\n",
    "def fitness_func(solution, solution_idx):\n",
    "    \"\"\"\n",
    "    Fitness function - checks the quality of the solution\n",
    "    \n",
    "    Inputs:\n",
    "    solution, solution_idx\n",
    "    \n",
    "    Description:\n",
    "    penalty function for invalid values of shaded cells in each row and column\n",
    "    \n",
    "    Max value: 0\n",
    "    Min value: -100 * 2 * len(req_rows)\n",
    "    \"\"\"\n",
    "    # nono is filled nonogram\n",
    "    nono = solution.reshape((len(req_col), len(req_col)))\n",
    "    fitness = 0\n",
    "    # penalty for wrong value of collored cells\n",
    "    if np.sum(solution == 1) != np.sum(np.sum(columns(nono))):\n",
    "        fitness += 1000\n",
    "    for i in range(len(nono)):\n",
    "        # checking if the requirements for each row and column are met\n",
    "        if rows(nono)[i] != req_rows[i]:\n",
    "            fitness += 100\n",
    "        if columns(nono)[i] != req_col[i]:\n",
    "            fitness += 100\n",
    "    return -fitness\n",
    "\n",
    "fitness_function = fitness_func\n",
    "\n",
    "# population size\n",
    "sol_per_pop = 100\n",
    "\n",
    "# how many genes in a chromosome -the number of rows of the matrix squared, beacuse the dimension of the matrix is n x n\n",
    "num_genes = len(req_rows) ** 2\n",
    "\n",
    "# how many parents we choose (about 50% of the population)\n",
    "num_parents_mating = 50\n",
    "# number of generations\n",
    "num_generations = 100\n",
    "# how many parents to keep\n",
    "keep_parents = 5\n",
    "\n",
    "# parent selection\n",
    "#sss = steady\n",
    "parent_selection_type = \"sss\"\n",
    "\n",
    "# crossover\n",
    "crossover_type = \"single_point\"\n",
    "\n",
    "# mutation set to minimum value\n",
    "# 1/num_genes\n",
    "mutation_type = \"random\"\n",
    "# I set the percentage corresponding to one gene\n",
    "mutation_percent_genes = math.ceil(1/num_genes*100)\n",
    "\n",
    "\n",
    "# initiation of the algorithm with higher parameters stored in attributes\n",
    "ga_instance = pygad.GA(gene_space=gene_space,\n",
    "                       num_generations=num_generations,\n",
    "                       num_parents_mating=num_parents_mating,\n",
    "                       fitness_func=fitness_function,\n",
    "                       sol_per_pop=sol_per_pop,\n",
    "                       num_genes=len(req_rows) ** 2,\n",
    "                       parent_selection_type=parent_selection_type,\n",
    "                       keep_parents=keep_parents,\n",
    "                       crossover_type=crossover_type,\n",
    "                       mutation_type=mutation_type,\n",
    "                       mutation_percent_genes=math.ceil(1/num_genes*100),\n",
    "                      stop_criteria=['reach_0'])\n",
    "\n",
    "#running the algorithm\n",
    "ga_instance.run()\n",
    "\n",
    "#summary: best solution\n",
    "solution, solution_fitness, solution_idx = ga_instance.best_solution()\n",
    "print(\"Fitness value of the best solution = {solution_fitness}\".format(solution_fitness=solution_fitness))\n",
    "ga_instance.plot_fitness()\n",
    "\n",
    "# visualisation\n",
    "def visualisation(solution):\n",
    "    plt.figure(figsize=(10, 8))\n",
    "    # the black color corresponds to the painted ones, white - blank \n",
    "    # row and column captions match the requirements of the nonogram\n",
    "    ax = sns.heatmap(nonogram(solution), cmap = ['white', 'black'], linewidths=0.1, linecolor = 'black',xticklabels=req_col, yticklabels=req_rows)\n",
    "    plt.yticks(rotation=0)\n",
    "    ax.xaxis.tick_top() # x axis on top\n",
    "    ax.xaxis.set_label_position('top')\n",
    "    return ax\n",
    "\n",
    "visualisation(solution)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test for small inputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitness value of the best solution = 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x28c0dfb3040>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "req_col1 = [[2], [1,3], [4], [2], [1]]\n",
    "req_rows1 = [[1,1], [3], [2], [3], [3]]\n",
    "\n",
    "req_col2 = [[3], [3], [1,2], [3], [1]]\n",
    "req_rows2 = [[3], [2], [2,2], [2], [2]]\n",
    "\n",
    "req_col3 = [[1,2], [3], [2], [3], [1,1]]\n",
    "req_rows3 = [[3], [4], [1,1], [2], [1,1]]\n",
    "\n",
    "req_col4 = [[2,1], [2,1], [1], [2,1], [2,1]]\n",
    "req_rows4 = [[2,2], [2,2], [], [1,1], [3]]\n",
    "\n",
    "req_col5 = [[3], [2,2], [1,1], [2,2], [3]]\n",
    "req_rows5 = [[3], [2,2], [1,1], [2,2], [3]]\n",
    "\n",
    "list_cols = [req_col1, req_col2, req_col3, req_col4, req_col5]\n",
    "list_rows = [req_rows1, req_rows2, req_rows3, req_rows4, req_rows5]\n",
    "\n",
    "times = []\n",
    "\n",
    "for j in range(100):\n",
    "    # randomly selecting one of the inputs\n",
    "    i = randint(0, 4)\n",
    "    req_col = list_cols[i]\n",
    "    req_rows = list_rows[i]\n",
    "    \n",
    "    row = [item for sublist in req_rows for item in sublist]\n",
    "\n",
    "    ga_instance = pygad.GA(gene_space=gene_space,\n",
    "                       num_generations=num_generations,\n",
    "                       num_parents_mating=num_parents_mating,\n",
    "                       fitness_func=fitness_function,\n",
    "                       sol_per_pop=sol_per_pop,\n",
    "                       num_genes=len(req_rows) ** 2,\n",
    "                       parent_selection_type=parent_selection_type,\n",
    "                       keep_parents=keep_parents,\n",
    "                       crossover_type=crossover_type,\n",
    "                       mutation_type=mutation_type,\n",
    "                       mutation_num_genes=1,\n",
    "                      stop_criteria=['reach_0'])\n",
    "    \n",
    "    start = time.time()\n",
    "    ga_instance.run()\n",
    "\n",
    "    solution, solution_fitness, solution_idx = ga_instance.best_solution()\n",
    "    end = time.time()\n",
    "    \n",
    "    # saving time for perfect attempts\n",
    "    if solution_fitness == 0:\n",
    "        times.append(end - start)\n",
    "\n",
    "# printing the solution and visualisation for the last input\n",
    "print(\"Fitness value of the best solution = {solution_fitness}\".format(solution_fitness=solution_fitness))\n",
    "ga_instance.plot_fitness()\n",
    "\n",
    "visualisation(solution)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Perfect solution:  86 %\n",
      "Mean time for perfect solution:  0.5239754194437072\n"
     ]
    }
   ],
   "source": [
    "print('Perfect solution: ',len(times), '%')\n",
    "print('Mean time for perfect solution: ', np.mean(times))\n",
    "\n",
    "small_inputes_accuracy_2 = len(times)\n",
    "small_mean_time_2 = np.mean(times)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Note\n",
    "The percentage of obtaining a perfect solution is lower than in the case of method 1. After firing the above loop with changed parameters: \n",
    "\n",
    "sol_per_pop = 200\n",
    "\n",
    "num_parents_mating = 100\n",
    "\n",
    "The percentage of perfect solutions increased, however, this resulted in an average time of 1.77 (over a second longer on average per 1 solution)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Medium inputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "81.74845504760742\n",
      "Fitness value of the best solution = 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x28c0f63c130>"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "req_col = [[6],[7],[8],[9],[5,3],[5,3],[9],[8],[7],[6]]\n",
    "req_rows = [[2],[4],[6],[8],[10],[4,4],[4,4],[10],[10],[10]]\n",
    "\n",
    "# changing gene_space, beacuse know I have 10 columns\n",
    "gene_space = [0,1]\n",
    "\n",
    "# population size\n",
    "sol_per_pop = 200\n",
    "\n",
    "# how many genes in a chromosome -the number of rows of the matrix squared, beacuse the dimension of the matrix is n x n\n",
    "num_genes = len(req_rows) ** 2\n",
    "\n",
    "# how many parents we choose (about 50% of the population)\n",
    "num_parents_mating = 100\n",
    "# number of generations\n",
    "num_generations = 250\n",
    "# how many parents to keep\n",
    "keep_parents = 5\n",
    "\n",
    "# initiation of the algorithm with higher parameters stored in attributes\n",
    "ga_instance = pygad.GA(gene_space=gene_space,\n",
    "                       num_generations=num_generations,\n",
    "                       num_parents_mating=num_parents_mating,\n",
    "                       fitness_func=fitness_function,\n",
    "                       sol_per_pop=sol_per_pop,\n",
    "                       num_genes=len(req_rows) ** 2,\n",
    "                       parent_selection_type=parent_selection_type,\n",
    "                       keep_parents=keep_parents,\n",
    "                       crossover_type=crossover_type,\n",
    "                       mutation_type=mutation_type,\n",
    "                       mutation_num_genes=1,\n",
    "                      stop_criteria=['reach_0'])\n",
    "start = time.time()\n",
    "#running the algorithm\n",
    "ga_instance.run()\n",
    "end = time.time()\n",
    "print(end - start)\n",
    "\n",
    "#summary: best solution\n",
    "solution, solution_fitness, solution_idx = ga_instance.best_solution()\n",
    "print(\"Fitness value of the best solution = {solution_fitness}\".format(solution_fitness=solution_fitness))\n",
    "ga_instance.plot_fitness()\n",
    "\n",
    "visualisation(solution)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "95.20984506607056\n",
      "Fitness value of the best solution = 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x28c0f3d1bb0>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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3JHl6N/+qJI8muaKPOiRJ0uzpc8/NA1W1M8lpwG8Bu6rqJcA24GKAqnoXcHWPNUiSpBkzqcNSc8AzkswBJwOPTGhcSZI0Y3oPN1X1HeD3gYeAg8D3q+ovVlsuyXySu5Lc1XeNkiSpHb2HmyTPBfYAZwI/CTwzyaWrLVdVC1W1q6p29V2jJElqxyQOS/0S8K2q+l5V/RD4JPDzExhXkiTNoEmEm4eAVyU5OUmA84B9ExhXkiTNoEmcc/Ml4CbgK8DXuzEX+h5XkiTNprlJDFJV7wHeM4mxJEnSbOtrz81RYPvSTfyOJ8lVwKXAkz3VIUmSZkyqato1rCpJDaHOJYunFkmStoohfYd0JvpFkqSXX1BVTeUL0WdLSZKkphhuJElSUww3kiSpKYYbSZLUFMONJElqiuFGkiQ1xXAjSZKaYriRJElNMdxIkqSmGG4kSVJTDDeSJGlqklyQ5L4k+5NceZw2r02yN8k9Sf5y1T6H8LwNny0lSdqIIX2HdGbi2VJJtgHfBM4HDgB3ApdU1b0jbZ4DfB64oKoeSvKCqjo0rl/33EiSpGk5B9hfVQ9W1RHgRmDPsja/Cnyyqh4CWC3YAMxtepk9cW+IJOlEDe07ZIB7mk7UacDDI9MHgFcua/OPgKcluQN4FvCBqvrouE4HE24kSdKwJJkH5kdmLVTVwmiTFRZbnuzmgH8CnAc8A/hCki9W1TePN67hRpIk9aILMgtjmhwAzhiZPh14ZIU2j1XVk8CTST4LvJTFc3VW5Dk3kiRpWu4EzkpyZpKTgIuBm5e1+RRwbpK5JCezeNhq37hO3XMjSZKmoqqeSnI5cCuwDbi2qu5J8rbu/aural+SzwBfA34EXFNVd4/rdzCXgk+7BkmSJmW1S6g327QuBe+Lh6UkSVJTDDeSJKkphhtJktQUw40kSWqK4UaSJDXFcCNJkppiuJEkSU0x3EiSpKYYbiRJUlMMN5IkqSmGG0mS1BTDjSRJaorhRpIkNcVwI0mSmnLC4SbJjiSHk+ztpq9NcijJ3cvaPS/JbUnu734+t5t/bpJ7l7eXJEnaiI3uuXmgqnZ2r68DLlihzZXA7VV1FnB7N01VfQ7YvcHxJUmSjrFph6Wq6rPAEyu8tQe4vnt9PfCGzRpTkiRpubkJjPHCqjoIUFUHk7xgLQslmQfme61MkiQ1ZxLh5oRU1QKwAJCkplyOJEkaiElcLfXdJKcCdD8PTWBMSZI0oyYRbm4GLuteXwZ8agJjSpKkGbVp4SbJDcAXgLOTHEjy1u6t9wLnJ7kfOL+bliRJ6sWmnXNTVZccZ/7jwHmbNY4kSdI4G9lzcxTYvnQTv/VKci7waeCxDdQgSZJ0jFRt/QuRvFpKkjRLqiqTHK+v79lJ/z2W+GwpSZLUFMONJElqiuFGkiQ1xXAjSZKaYriRJElNMdxIkqSmGG4kSVJTDDeSJKkphhtJktQUw40kSWqK4UaSJDXFcCNJkppiuJEkSU0x3EiSpKbMTbsAaZZU1bRLWJckg6o5ybRLkAZpSOv5WrjnRpIkNcVwI0mSmmK4kSRJTTHcSJKkphhuJElSUww3kiSpKYYbSZLUFMONJElqiuFGkiQ1xXAjSZKaYriRJElNMdxIkqSmGG4kSVJTDDeSJKkphhtJktQUw40kSWqK4UaSJDVlbLhJsiPJ4SR7l83fluSrSW5Z60BJXpHkaJI3ddPPSLI3yZEkp5xY+ZIkScday56bB6pq57J57wD2rXWQJNuA9wG3Ls2rqsNdv4+stR9JkqTVrPuwVJLTgV8GrlnHYm8HPgEcWu94kiRJ63Ei59y8H/hd4EdraZzkNOCNwNXrGSTJfJK7kty1/hIlSdKsWle4SXIRcKiqvryOxd4PvLuqjq5nrKpaqKpdVbVrPctJkqTZNrfO9q8GXp9kN/B04NlJPlZVl45ZZhdwYxKAU4DdSZ6qqj89oYolSZLGSFUd/81kB3BLVb1khfdeC1xRVRd105cDVNUHx/R3XdffTSPzvg3sqqrHxix3/CKlARm3vm1FSQZVc/efKGnwqmrSH+a+VvSprJSbeZ+bFwGPb2J/kiRJ67bew1J/q6ruAO4YmbUDeOcqy7z5RMeTJElai9X23BwFti+/id9Kquqiqjqy1oGXbuIHPI01XnklSZK0mrHn3GwVnnOjVgxhfRvlOTfSdHjOzcb4bClJktQUw40kSWqK4UaSJDXFcCNJkppiuJEkSU0x3EiSpKYYbiRJUlMMN5IkqSmGG0mS1BTDjSRJaorhRpIkTU2SC5Lcl2R/kivHtHtFkqNJ3rRan4YbSZI0FUm2AX8IXAi8GLgkyYuP0+59wK1r6ddwI0mSpuUcYH9VPVhVR4AbgT0rtHs78Ang0Fo6ndu8+iStZohPrR5izZIG4zTg4ZHpA8ArRxskOQ14I/A64BVr6dRwI01QVU27hHVJMqiaDWLS1pJkHpgfmbVQVQujTVZYbPlG5/3Au6vq6FrXccONJEnqRRdkFsY0OQCcMTJ9OvDIsja7gBu7YHMKsDvJU1X1p8frNEP4X1mSrV+ktAZDWN9GuedGmo6qmvSHua8VfezfI8kc8E3gPOA7wJ3Ar1bVPcdpfx1wS1XdNK5f99xIkqSpqKqnklzO4lVQ24Brq+qeJG/r3r/6RPp1z400QUNY30a550aajlnZc9MXLwWXJElNMdxIkqSmGG4kSVJTDDeSJKkphhtJktQUw40kSWqK4UaSJDXFcCNJkppiuJEkSU0x3EiSpKYYbiRJUlMMN5IkqSmGG0mS1BTDjSRJasrYcJNkR5LDSfYum78tyVeT3LLWgZK8IsnRJG/qpp+RZG+SI0lOObHyJUmSjrWWPTcPVNXOZfPeAexb6yBJtgHvA25dmldVh7t+H1lrP5IkSatZ92GpJKcDvwxcs47F3g58Aji03vEkSZLW40TOuXk/8LvAj9bSOMlpwBuBq9czSJL5JHcluWv9JUqSpFm1rnCT5CLgUFV9eR2LvR94d1UdXc9YVbVQVbuqatd6lpMkSbNtbp3tXw28Pslu4OnAs5N8rKouHbPMLuDGJACnALuTPFVVf3pCFUuSJI2Rqjr+m8kO4JaqeskK770WuKKqLuqmLweoqg+O6e+6rr+bRuZ9G9hVVY+NWe74RUoDMm5924qSDKrm7j9R0uBV1aQ/zH2t6FNZKTfzPjcvAh7fxP4kSZLWbb2Hpf5WVd0B3DEyawfwzlWWefOJjidJkrQWq+25OQpsX34Tv5VU1UVVdWStAy/dxA94Gmu88kqSJGk1Y8+52So850atGML6NspzbqTp8JybjfHZUpIkqSmGG0mS1BTDjSRJaorhRpIkNcVwI0mSmmK4kSRJTTHcSJKkphhuJElSUww3kiSpKYYbSZLUFMONJElqiuFGkiQ1xXAjSZKaMjftAqRZMsSnVg+xZkmzzT03kiSpKYYbSZLUFMONJElqiuFGkiQ1xXAjSZKaYriRJElNMdxIkqSmGG4kSVJTDDeSJKkphhtJktQUw40kSWqK4UaSJDXFcCNJkppiuJEkSU0x3EiSpKYYbiRJUlMMN5IkqSmGG0mS1JQTDjdJdiQ5nGRvN31tkkNJ7l7W7nlJbktyf/fzud38c5Pcu7y9JEnSRmx0z80DVbWze30dcMEKba4Ebq+qs4Dbu2mq6nPA7g2OL0mSdIxNOyxVVZ8FnljhrT3A9d3r64E3bNaYkiRJy81NYIwXVtVBgKo6mOQFa1koyTww32tlkiSpOZMINyekqhaABYAkNeVyJEnSQEziaqnvJjkVoPt5aAJjSpKkGTWJcHMzcFn3+jLgUxMYU5IkzahNCzdJbgC+AJyd5ECSt3ZvvRc4P8n9wPndtCRJUi827ZybqrrkOPMfB87brHEkSZLG2ciem6PA9qWb+K1XknOBTwOPbaAGSZKkY6Rq61+I5NVSkqRZUlWZ9JA99Tvpvwfgs6UkSVJjDDeSJKkphhtJktQUw40kSWqK4UaSJDXFcCNJkppiuJEkSU0x3EiSpKYYbiRJUlMMN5IkqSmGG0mSNDVJLkhyX5L9Sa5c4f1/meRr3Z/PJ3npqn36bClJkraWWXm2VJJtwDeB84EDwJ3AJVV170ibnwf2VdVfJ7kQ+A9V9cpx/brnRpIkTcs5wP6qerCqjgA3AntGG1TV56vqr7vJLwKnr9ap4UaSJE3LacDDI9MHunnH81bgv67W6dwGi5IkSVpRknlgfmTWQlUtjDZZYbEVD5El+UUWw80vrDau4UaSJPWiCzILY5ocAM4YmT4deGR5oyQ/C1wDXFhVj682roelJEnStNwJnJXkzCQnARcDN482SPJTwCeBX6uqb66lU/fcSJKkqaiqp5JcDtwKbAOurap7kryte/9q4N8Dzwf+UxKAp6pq17h+vRRckqQtZlYuBe+Lh6UkSVJTDDeSJKkphhtJktQUw40kSWqK4UaSJDXFcCNJkppiuJEkSU0x3EiSpKYYbiRJUlMMN5IkqSmGG0mS1BTDjSRJaorhRpIkNcVwI0mSmnLC4SbJjiSHk+ztpq9NcijJ3cvaPS/JbUnu734+t5t/bpJ7l7eXJEnaiI3uuXmgqnZ2r68DLlihzZXA7VV1FnB7N01VfQ7YvcHxJUmSjrFph6Wq6rPAEyu8tQe4vnt9PfCGzRpTkiRpubkJjPHCqjoIUFUHk7xgLQslmQfme61MkiQ1ZxLh5oRU1QKwAJCkplyOJEkaiElcLfXdJKcCdD8PTWBMSZI0oyYRbm4GLuteXwZ8agJjSpKkGbVp4SbJDcAXgLOTHEjy1u6t9wLnJ7kfOL+bliRJ6sWmnXNTVZccZ/7jwHmbNY4kSdI4G9lzcxTYvnQTv/VKci7waeCxDdQgSZJ0jFRt/QuRvFpKkjRLqiqTHrKnfif99wB8tpQkSWqM4UaSJDXFcCNJkppiuJEkSU0x3EiSpKYYbiRJUlMMN5IkqSmGG0mS1BTDjSRJaorhRpIkNcVwI0mSmmK4kSRJTTHcSJKkphhuJElSUww3kiSpKYYbSZLUFMONJElqiuFGkiQ1xXAjSZKaYriRJElNMdxIkqSmGG4kSVJTDDeSJKkphhtJktQUw40kSWqK4UaSJDXFcCNJkppiuJEkSU0x3EiSpKYYbiRJUlMMN5IkqSmGG0mS1JQTDjdJdiQ5nGRvN31tkkNJ7l7W7nlJbktyf/fzud38c5Pcu7y9JEnSRmx0z80DVbWze30dcMEKba4Ebq+qs4Dbu2mq6nPA7g2OL0mSdIxNOyxVVZ8FnljhrT3A9d3r64E3bNaYkiRJy81NYIwXVtVBgKo6mOQFa1koyTww32tlkiSpOZMINyekqhaABYAkNeVyJEnSQEziaqnvJjkVoPt5aAJjSpKkGTWJcHMzcFn3+jLgUxMYU5IkzahNCzdJbgC+AJyd5ECSt3ZvvRc4P8n9wPndtCRJUi827ZybqrrkOPMfB87brHEkSZLG2ciem6PA9qWb+K1XknOBTwOPbaAGSZKkY6Rq61+I5NVSkqRZUlWZ9JA99Tvpvwfgs6UkSVJjDDeSJKkphhtJktQUw40kSWqK4UaSJDXFcCNJkppiuJEkSU0x3EiSpKYYbiRJUlMMN5IkqSmGG0mSNDVJLkhyX5L9Sa5c4f0k+YPu/a8leflqfRpuJEnSVCTZBvwhcCHwYuCSJC9e1uxC4KzuzzzwodX6NdxIkqRpOQfYX1UPVtUR4EZgz7I2e4CP1qIvAs9Jcuq4Tg03kiRpWk4DHh6ZPtDNW2+bY8xtSmk9m8Kj3yVJmiW9fM8mmWfxUNKShapaWGXcWt7NGtocYxDhRpIkDU8XZBbGNDkAnDEyfTrwyAm0OYaHpSRJ0rTcCZyV5MwkJwEXAzcva3Mz8OvdVVOvAr5fVQfHdeqeG0mSNBVV9VSSy4FbgW3AtVV1T5K3de9fDfw5sBvYD/wAeMtq/aZq7GErSZKkQfGwlCRJaorhRpIkNcVwI0mSmmK4kSRJTTHcSJKkphhuJElSUww3kiSpKYYbSZLUlP8PjppYbmp1F5gAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "req_col = [[6],[7],[8],[9],[5,3],[5,3],[9],[8],[7],[6]]\n",
    "req_rows = [[2],[4],[6],[8],[10],[4,4],[4,4],[10],[10],[10]]\n",
    "\n",
    "# changing gene_space, beacuse know I have 10 columns\n",
    "gene_space = [0,1]\n",
    "\n",
    "# population size\n",
    "sol_per_pop = 220\n",
    "\n",
    "# how many genes in a chromosome -the number of rows of the matrix squared, beacuse the dimension of the matrix is n x n\n",
    "num_genes = len(req_rows) ** 2\n",
    "\n",
    "# how many parents we choose (about 50% of the population)\n",
    "num_parents_mating = 110\n",
    "# number of generations\n",
    "num_generations = 250\n",
    "# how many parents to keep\n",
    "keep_parents = 5\n",
    "\n",
    "# initiation of the algorithm with higher parameters stored in attributes\n",
    "ga_instance = pygad.GA(gene_space=gene_space,\n",
    "                       num_generations=num_generations,\n",
    "                       num_parents_mating=num_parents_mating,\n",
    "                       fitness_func=fitness_function,\n",
    "                       sol_per_pop=sol_per_pop,\n",
    "                       num_genes=len(req_rows) ** 2,\n",
    "                       parent_selection_type=parent_selection_type,\n",
    "                       keep_parents=keep_parents,\n",
    "                       crossover_type=crossover_type,\n",
    "                       mutation_type=mutation_type,\n",
    "                       mutation_num_genes=1,\n",
    "                      stop_criteria=['reach_0'])\n",
    "start = time.time()\n",
    "#running the algorithm\n",
    "ga_instance.run()\n",
    "end = time.time()\n",
    "print(end - start)\n",
    "\n",
    "#summary: best solution\n",
    "solution, solution_fitness, solution_idx = ga_instance.best_solution()\n",
    "print(\"Fitness value of the best solution = {solution_fitness}\".format(solution_fitness=solution_fitness))\n",
    "ga_instance.plot_fitness()\n",
    "\n",
    "visualisation(solution)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The algorithm works for 10x10 nonograms but is much slower than for 5x5 nonograms"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Due to the long execution time of the algorithm, I did not test for average inputs."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. Summary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first method works perfectly for 5x5 nonograms and the execution time of the algorithm is very short. At 10x10 nonograms, the performance drops, but is still very good, but the execution time increases significantly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Percent [%]')"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6,6))\n",
    "plt.bar([5,10], [small_inputes_accuracy,medium_inputes_accuracy*10], width=2, color = 'green')\n",
    "plt.xticks([5,10])\n",
    "plt.xlim(2,12,)\n",
    "plt.title('Percent of perfect solution')\n",
    "plt.xlabel('Size of nonogram')\n",
    "plt.ylabel('Percent [%]')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Time [s]')"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6,6))\n",
    "plt.bar([5,10], [small_mean_time,medium_mean_time], width=2, color = 'green')\n",
    "plt.xticks([5,10])\n",
    "plt.xlim(2,12,)\n",
    "plt.title('Average time of finding a perfect solution')\n",
    "plt.xlabel('Size of nonogram')\n",
    "plt.ylabel('Time [s]')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the case of 15x15 nonograms, the efficiency drops sharply and the execution time of the algorithm is much longer than human completion of the nonogram.\n",
    "\n",
    "Conclusion: the algorithm can be used to solve many 5x5 nonograms or a small number of examples of 10x10 nonograms."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The second algorithm performs worse than 1 for 5x5 nonograms with maintaining a similar execution time. But its performance is still satisfactory.\n",
    "\n",
    "For 10x10 nonograms, the execution time of a single example is much longer than the execution time of a single example with 1 algorithm and the average time of 10 examples. I can assume that with a larger sample it would perform worse than 1 algorithm.\n",
    "\n",
    "Waiting time for 15x15 nonogram execution was too long."
   ]
  },
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   "source": [
    "# 4. Bibliography"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "https://en.wikipedia.org/wiki/Nonogram - rules\n",
    "\n",
    "https://www.puzzle-nonograms.com/ - inputs\n",
    "\n",
    "https://www.puzzles-mobile.com/nonograms/random/10x10 - inputs\n",
    "\n",
    "https://nonograms-katana.fandom.com/wiki/Black-and-White_Nonograms_(1) - inputs"
   ]
  }
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