N-Queen.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pyomo.environ import *\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import random \n",
    "import operator\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{(1, 'x'): 1,\n",
       " (1, 'y'): 1,\n",
       " (2, 'x'): 1,\n",
       " (2, 'y'): 2,\n",
       " (3, 'x'): 1,\n",
       " (3, 'y'): 3,\n",
       " (4, 'x'): 1,\n",
       " (4, 'y'): 4,\n",
       " (5, 'x'): 1,\n",
       " (5, 'y'): 5,\n",
       " (6, 'x'): 1,\n",
       " (6, 'y'): 6,\n",
       " (7, 'x'): 1,\n",
       " (7, 'y'): 7,\n",
       " (8, 'x'): 1,\n",
       " (8, 'y'): 8,\n",
       " (9, 'x'): 2,\n",
       " (9, 'y'): 1,\n",
       " (10, 'x'): 2,\n",
       " (10, 'y'): 2,\n",
       " (11, 'x'): 2,\n",
       " (11, 'y'): 3,\n",
       " (12, 'x'): 2,\n",
       " (12, 'y'): 4,\n",
       " (13, 'x'): 2,\n",
       " (13, 'y'): 5,\n",
       " (14, 'x'): 2,\n",
       " (14, 'y'): 6,\n",
       " (15, 'x'): 2,\n",
       " (15, 'y'): 7,\n",
       " (16, 'x'): 2,\n",
       " (16, 'y'): 8,\n",
       " (17, 'x'): 3,\n",
       " (17, 'y'): 1,\n",
       " (18, 'x'): 3,\n",
       " (18, 'y'): 2,\n",
       " (19, 'x'): 3,\n",
       " (19, 'y'): 3,\n",
       " (20, 'x'): 3,\n",
       " (20, 'y'): 4,\n",
       " (21, 'x'): 3,\n",
       " (21, 'y'): 5,\n",
       " (22, 'x'): 3,\n",
       " (22, 'y'): 6,\n",
       " (23, 'x'): 3,\n",
       " (23, 'y'): 7,\n",
       " (24, 'x'): 3,\n",
       " (24, 'y'): 8,\n",
       " (25, 'x'): 4,\n",
       " (25, 'y'): 1,\n",
       " (26, 'x'): 4,\n",
       " (26, 'y'): 2,\n",
       " (27, 'x'): 4,\n",
       " (27, 'y'): 3,\n",
       " (28, 'x'): 4,\n",
       " (28, 'y'): 4,\n",
       " (29, 'x'): 4,\n",
       " (29, 'y'): 5,\n",
       " (30, 'x'): 4,\n",
       " (30, 'y'): 6,\n",
       " (31, 'x'): 4,\n",
       " (31, 'y'): 7,\n",
       " (32, 'x'): 4,\n",
       " (32, 'y'): 8,\n",
       " (33, 'x'): 5,\n",
       " (33, 'y'): 1,\n",
       " (34, 'x'): 5,\n",
       " (34, 'y'): 2,\n",
       " (35, 'x'): 5,\n",
       " (35, 'y'): 3,\n",
       " (36, 'x'): 5,\n",
       " (36, 'y'): 4,\n",
       " (37, 'x'): 5,\n",
       " (37, 'y'): 5,\n",
       " (38, 'x'): 5,\n",
       " (38, 'y'): 6,\n",
       " (39, 'x'): 5,\n",
       " (39, 'y'): 7,\n",
       " (40, 'x'): 5,\n",
       " (40, 'y'): 8,\n",
       " (41, 'x'): 6,\n",
       " (41, 'y'): 1,\n",
       " (42, 'x'): 6,\n",
       " (42, 'y'): 2,\n",
       " (43, 'x'): 6,\n",
       " (43, 'y'): 3,\n",
       " (44, 'x'): 6,\n",
       " (44, 'y'): 4,\n",
       " (45, 'x'): 6,\n",
       " (45, 'y'): 5,\n",
       " (46, 'x'): 6,\n",
       " (46, 'y'): 6,\n",
       " (47, 'x'): 6,\n",
       " (47, 'y'): 7,\n",
       " (48, 'x'): 6,\n",
       " (48, 'y'): 8,\n",
       " (49, 'x'): 7,\n",
       " (49, 'y'): 1,\n",
       " (50, 'x'): 7,\n",
       " (50, 'y'): 2,\n",
       " (51, 'x'): 7,\n",
       " (51, 'y'): 3,\n",
       " (52, 'x'): 7,\n",
       " (52, 'y'): 4,\n",
       " (53, 'x'): 7,\n",
       " (53, 'y'): 5,\n",
       " (54, 'x'): 7,\n",
       " (54, 'y'): 6,\n",
       " (55, 'x'): 7,\n",
       " (55, 'y'): 7,\n",
       " (56, 'x'): 7,\n",
       " (56, 'y'): 8,\n",
       " (57, 'x'): 8,\n",
       " (57, 'y'): 1,\n",
       " (58, 'x'): 8,\n",
       " (58, 'y'): 2,\n",
       " (59, 'x'): 8,\n",
       " (59, 'y'): 3,\n",
       " (60, 'x'): 8,\n",
       " (60, 'y'): 4,\n",
       " (61, 'x'): 8,\n",
       " (61, 'y'): 5,\n",
       " (62, 'x'): 8,\n",
       " (62, 'y'): 6,\n",
       " (63, 'x'): 8,\n",
       " (63, 'y'): 7,\n",
       " (64, 'x'): 8,\n",
       " (64, 'y'): 8}"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N = 8\n",
    "dic = {}\n",
    "counter = 0\n",
    "for x in range(1,1+N):\n",
    "    for y in range(1,1+N):\n",
    "        counter +=1\n",
    "        dic[counter,'x'] = x\n",
    "        dic[counter,'y'] = y\n",
    "dic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = N \n",
    "model = AbstractModel()\n",
    "\n",
    "model.i = RangeSet(n)\n",
    "model.j = Set(initialize = model.i)\n",
    "\n",
    "model.attack_limit = Param(initialize = 0, mutable= True)\n",
    "\n",
    "model.U = Var(model.i,model.j, within= Binary)\n",
    "\n",
    "def rule_c1(model,i):\n",
    "    return  sum(model.U[i,j] for j in model.j) <= 1\n",
    "model.C1 = Constraint(model.i, rule=rule_c1)   \n",
    "\n",
    "\n",
    "def rule_c2(model,j):\n",
    "    return  sum(model.U[i,j] for i in model.i) <= 1\n",
    "model.C2 = Constraint(model.i, rule=rule_c2) \n",
    "\n",
    "def rule_c3(model,i,j):\n",
    "    return  sum(model.U[i,m] for m in model.j if j!=m) + sum(model.U[n,j] for n in model.i if i!=n) +  sum(model.U[n,m] for n in model.i for m in model.j if abs(m-j)==abs(n-i) and m!=j and n!=i )   <= model.attack_limit + (n**2)*(1-model.U[i,j]) \n",
    "model.C3 = Constraint(model.i,model.j, rule=rule_c3) \n",
    "\n",
    "\n",
    "def rule_c4(model,i,j):\n",
    "    return sum(model.U[n,m] for n in model.i for m in model.j if (m-j)==(n-i) and m!=j and n!=i ) + model.U[i,j]  <= 1 \n",
    "model.C4 = Constraint(model.i,model.j, rule=rule_c4)   \n",
    "def rule_c5(model,i,j):\n",
    "    return sum(model.U[n,m] for n in model.i for m in model.j if (m-j)==-(n-i) and m!=j and n!=i ) + model.U[i,j]  <= 1 \n",
    "model.C5 = Constraint(model.i,model.j, rule=rule_c5)   \n",
    "\n",
    "\n",
    "def rule_OF(model):\n",
    "    return  sum(model.U[i,j] for j in model.j for i in model.i)\n",
    "model.obj1 = Objective(rule=rule_OF, sense=maximize)\n",
    "instance = model.create_instance()  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "this is feasible and optimal\n",
      "OF = 8.0 \n"
     ]
    }
   ],
   "source": [
    "instance = model.create_instance()  \n",
    "instance.C3.deactivate()\n",
    "opt = SolverFactory('cbc')\n",
    "results = opt.solve(instance) # solves and updates instance\n",
    "from pyomo.opt import SolverStatus, TerminationCondition\n",
    "if (results.solver.status == SolverStatus.ok) and (results.solver.termination_condition == TerminationCondition.optimal):\n",
    "     print (\"this is feasible and optimal\")\n",
    "elif results.solver.termination_condition == TerminationCondition.infeasible:\n",
    "     print (\"do something about it? or exit?\")\n",
    "else:\n",
    "     print ('ERROR ' + str(results.solver))\n",
    "print(f\"OF = {value(instance.obj1)} \")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,8))\n",
    "record_distance = {}\n",
    "for j in instance.j:\n",
    "    for i in instance.i:\n",
    "        if value(instance.U[i,j]) >0:\n",
    "            x, y = i, j \n",
    "            plt.scatter(x,y, s=0 , c='k')\n",
    "            plt.text(x-0.25,y, s = '\\u2655', fontsize=30 , c= 'k')\n",
    "        else:\n",
    "            x, y = i, j \n",
    "            plt.scatter(x,y, s=50 , c='k', alpha = 0.2)\n",
    "\n",
    "plt.xlim(0.2, N+0.7)\n",
    "plt.ylim(0.2, N+0.7)\n",
    "plt.xticks(fontweight='bold' , c= 'k')\n",
    "plt.yticks(fontweight='bold' , c= 'k')\n",
    "plt.savefig(' Base  '+  ' .png', format='png', dpi=300)\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "this is feasible and optimal\n",
      "OF = 10.0 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "instance = model.create_instance()  \n",
    "instance.C3.activate()\n",
    "instance.C1.deactivate()\n",
    "instance.C2.deactivate()\n",
    "instance.C4.deactivate()\n",
    "instance.C5.deactivate()\n",
    "instance.attack_limit = 1\n",
    "opt = SolverFactory('cbc')\n",
    "results = opt.solve(instance) # solves and updates instance\n",
    "from pyomo.opt import SolverStatus, TerminationCondition\n",
    "if (results.solver.status == SolverStatus.ok) and (results.solver.termination_condition == TerminationCondition.optimal):\n",
    "     print (\"this is feasible and optimal\")\n",
    "elif results.solver.termination_condition == TerminationCondition.infeasible:\n",
    "     print (\"do something about it? or exit?\")\n",
    "else:\n",
    "     print ('ERROR ' + str(results.solver))\n",
    "print(f\"OF = {value(instance.obj1)} \")\n",
    "\n",
    "plt.figure(figsize=(8,8))\n",
    "record_distance = {}\n",
    "for j in instance.j:\n",
    "    for i in instance.i:\n",
    "        if value(instance.U[i,j]) >0:\n",
    "            x, y = i, j \n",
    "            plt.scatter(x,y, s=0 , c='k')\n",
    "            plt.text(x-0.25,y, s = '\\u2655', fontsize=30 , c= 'k')\n",
    "        else:\n",
    "            x, y = i, j \n",
    "            plt.scatter(x,y, s=50 , c='k', alpha = 0.2)\n",
    "\n",
    "plt.xlim(0.2, N+0.7)\n",
    "plt.ylim(0.2, N+0.7)\n",
    "plt.xticks(fontweight='bold' , c= 'k')\n",
    "plt.yticks(fontweight='bold' , c= 'k')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "this is feasible and optimal\n",
      "Limit = 1 , OF = 10.0 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "this is feasible and optimal\n",
      "Limit = 2 , OF = 13.0 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "this is feasible and optimal\n",
      "Limit = 3 , OF = 15.0 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "this is feasible and optimal\n",
      "Limit = 4 , OF = 18.0 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "this is feasible and optimal\n",
      "Limit = 5 , OF = 21.0 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "instance = model.create_instance()  \n",
    "instance.C3.activate()\n",
    "instance.C1.deactivate()\n",
    "instance.C2.deactivate()\n",
    "instance.C4.deactivate()\n",
    "instance.C5.deactivate()\n",
    "for lim in range(1,6):\n",
    "    instance.attack_limit = lim\n",
    "    results = opt.solve(instance) # solves and updates instance\n",
    "    from pyomo.opt import SolverStatus, TerminationCondition\n",
    "    if (results.solver.status == SolverStatus.ok) and (results.solver.termination_condition == TerminationCondition.optimal):\n",
    "         print (\"this is feasible and optimal\")\n",
    "    elif results.solver.termination_condition == TerminationCondition.infeasible:\n",
    "         print (\"do something about it? or exit?\")\n",
    "    else:\n",
    "         print ('ERROR ' + str(results.solver))\n",
    "    print(f\"Limit = {lim} , OF = {value(instance.obj1)} \")\n",
    "\n",
    "    plt.figure(figsize=(8,8))\n",
    "    record_distance = {}\n",
    "    for j in instance.j:\n",
    "        for i in instance.i:\n",
    "            if value(instance.U[i,j]) >0:\n",
    "                x, y = i, j \n",
    "                plt.scatter(x,y, s=0 , c='k')\n",
    "                plt.text(x-0.25,y, s = '\\u2655', fontsize=30 , c= 'k')\n",
    "            else:\n",
    "                x, y = i, j \n",
    "                plt.scatter(x,y, s=50 , c='k', alpha = 0.2)\n",
    "\n",
    "    plt.xlim(0.2, N+0.7)\n",
    "    plt.ylim(0.2, N+0.7)\n",
    "    plt.xticks(fontweight='bold' , c= 'k')\n",
    "    plt.yticks(fontweight='bold' , c= 'k')\n",
    "    plt.text(N/2-2,N/2-0.5, s = 'Limit = ' + str(int(lim))+  ' OF = ' + str(int(value(instance.obj1))) , fontsize=20 , c= 'r', alpha=0.5)\n",
    "    plt.savefig(' Chess lim ' + str(int(lim))+  ' .png', format='png', dpi=300)\n",
    "\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "this is feasible and optimal\n",
      "OF = 5.0 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "this is feasible and optimal\n",
      "OF = 5.0 \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# We are allowed to define how many of the data lines can be used as the training set \n",
    "n = N \n",
    "model = AbstractModel()\n",
    "\n",
    "model.i = RangeSet(n)\n",
    "model.j = Set(initialize = model.i)\n",
    "\n",
    "model.attack_limit = Param(initialize = 0, mutable= True)\n",
    "\n",
    "model.U = Var(model.i,model.j, within= Binary)\n",
    "\n",
    "def rule_c1(model,i):\n",
    "    return  sum(model.U[i,j] for j in model.j) <= 1\n",
    "model.C1 = Constraint(model.i, rule=rule_c1)   \n",
    "\n",
    "\n",
    "def rule_c2(model,j):\n",
    "    return  sum(model.U[i,j] for i in model.i) <= 1\n",
    "model.C2 = Constraint(model.i, rule=rule_c2) \n",
    "\n",
    "def rule_c3(model,i,j):\n",
    "    return  sum(model.U[i,m] for m in model.j if j!=m) + sum(model.U[n,j] for n in model.i if i!=n) +  sum(model.U[n,m] for n in model.i for m in model.j if abs(m-j)==abs(n-i) and m!=j and n!=i ) + model.U[i,j] >= 1 \n",
    "model.C3 = Constraint(model.i,model.j, rule=rule_c3) \n",
    "\n",
    "\n",
    "def rule_c4(model,i,j):\n",
    "    return sum(model.U[n,m] for n in model.i for m in model.j if (m-j)==(n-i) and m!=j and n!=i ) + model.U[i,j]  <= 1 \n",
    "model.C4 = Constraint(model.i,model.j, rule=rule_c4)   \n",
    "def rule_c5(model,i,j):\n",
    "    return sum(model.U[n,m] for n in model.i for m in model.j if (m-j)==-(n-i) and m!=j and n!=i ) + model.U[i,j]  <= 1 \n",
    "model.C5 = Constraint(model.i,model.j, rule=rule_c5)   \n",
    "\n",
    "\n",
    "def rule_OF(model):\n",
    "    return  sum(model.U[i,j] for j in model.j for i in model.i)\n",
    "model.obj1 = Objective(rule=rule_OF, sense=minimize)\n",
    "instance = model.create_instance()  \n",
    "\n",
    "instance.C1.deactivate()\n",
    "instance.C2.deactivate()\n",
    "opt = SolverFactory('cbc')\n",
    "results = opt.solve(instance) # solves and updates instance\n",
    "from pyomo.opt import SolverStatus, TerminationCondition\n",
    "if (results.solver.status == SolverStatus.ok) and (results.solver.termination_condition == TerminationCondition.optimal):\n",
    "     print (\"this is feasible and optimal\")\n",
    "elif results.solver.termination_condition == TerminationCondition.infeasible:\n",
    "     print (\"do something about it? or exit?\")\n",
    "else:\n",
    "     print ('ERROR ' + str(results.solver))\n",
    "print(f\"OF = {value(instance.obj1)} \")\n",
    "\n",
    "plt.figure(figsize=(8,8))\n",
    "record_distance = {}\n",
    "for j in instance.j:\n",
    "    for i in instance.i:\n",
    "        if value(instance.U[i,j]) >0:\n",
    "            x, y = i, j \n",
    "            plt.scatter(x,y, s=0 , c='k')\n",
    "            plt.text(x-0.25,y, s = '\\u2655', fontsize=30 , c= 'k')\n",
    "        else:\n",
    "            x, y = i, j \n",
    "            plt.scatter(x,y, s=50 , c='k', alpha = 0.2)\n",
    "\n",
    "plt.xlim(0.2, N+0.7)\n",
    "plt.ylim(0.2, N+0.7)\n",
    "plt.xticks(fontweight='bold' , c= 'k')\n",
    "plt.yticks(fontweight='bold' , c= 'k')\n",
    "plt.savefig(' Min Coverage with attack' +  ' .png', format='png', dpi=300)\n",
    "\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n",
    "instance.C1.activate()\n",
    "instance.C2.activate()\n",
    "opt = SolverFactory('cbc')\n",
    "results = opt.solve(instance) # solves and updates instance\n",
    "from pyomo.opt import SolverStatus, TerminationCondition\n",
    "if (results.solver.status == SolverStatus.ok) and (results.solver.termination_condition == TerminationCondition.optimal):\n",
    "     print (\"this is feasible and optimal\")\n",
    "elif results.solver.termination_condition == TerminationCondition.infeasible:\n",
    "     print (\"do something about it? or exit?\")\n",
    "else:\n",
    "     print ('ERROR ' + str(results.solver))\n",
    "print(f\"OF = {value(instance.obj1)} \")\n",
    "\n",
    "plt.figure(figsize=(8,8))\n",
    "record_distance = {}\n",
    "for j in instance.j:\n",
    "    for i in instance.i:\n",
    "        if value(instance.U[i,j]) >0:\n",
    "            x, y = i, j \n",
    "            plt.scatter(x,y, s=0 , c='k')\n",
    "            plt.text(x-0.25,y, s = '\\u2655', fontsize=30 , c= 'k')\n",
    "        else:\n",
    "            x, y = i, j \n",
    "            plt.scatter(x,y, s=50 , c='k', alpha = 0.2)\n",
    "\n",
    "plt.xlim(0.2, N+0.7)\n",
    "plt.ylim(0.2, N+0.7)\n",
    "plt.xticks(fontweight='bold' , c= 'k')\n",
    "plt.yticks(fontweight='bold' , c= 'k')\n",
    "plt.savefig(' Min Coverage without attack' +  ' .png', format='png', dpi=300)\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}