re_run_Lista 12.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lista 12\n",
    "\n",
    "Vinicius de Souza Rios\n",
    "\n",
    "William Chalub Cruz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pulp import *\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Questão 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def optimal_wings(menu,asas_desejadas,Show=True):\n",
    "    problem = LpProblem(\"Chicken_Wings\",LpMinimize)  \n",
    "\n",
    "\n",
    "    pedido = []\n",
    "    for qtd in menu:\n",
    "        pedido.append(LpVariable(\"Combo_\"+str(qtd),0,None,LpInteger))\n",
    "\n",
    "    problem += sum([combo*menu[int(combo.name.split(\"Combo_\")[1])] for combo in pedido]),\"Custo total\"\n",
    "    problem +=  sum([combo*int(combo.name.split(\"Combo_\")[1]) for combo in pedido])>=asas_desejadas,\"Minimo compra\"\n",
    "\n",
    "    problem.writeLP(\"Chicken_Wings.lp\")\n",
    "    \n",
    "    problem.solve()\n",
    "    \n",
    "    if Show==True:\n",
    "        print(\"Status:\", LpStatus[problem.status])\n",
    "    \n",
    "    combos_compra = {}\n",
    "    for v in problem.variables():\n",
    "        if v.varValue>0:\n",
    "            combos_compra[int(v.name.split(\"Combo_\")[1])]=v.varValue\n",
    "    #     print(v.name, \"=\", v.varValue)\n",
    "    if Show == True:\n",
    "        print(\"Para um pedido de {} asas de frango, a divisão ótima é:  \".format(asas_desejadas))\n",
    "        for i in combos_compra:\n",
    "            print(\"\\t• Quantidade do Combo_{} = {} \".format(i,combos_compra[i]))\n",
    "        print(\"Custo total = {}\".format(sum([menu[i]*combos_compra[i] for i in combos_compra])))\n",
    "\n",
    "    return sum([menu[i]*combos_compra[i] for i in combos_compra])\n",
    "        \n",
    "        \n",
    "        \n",
    "menu = {4:4.55,    5:5.70,     6:6.80,     7:7.95,     8:9.10,\n",
    "        9:10.20,   10:11.35,   11:12.50,   12:13.60,   13:14.75,\n",
    "        14:15.90,  15:17.00,   16:18.15,   17:19.30,   18:20.40,\n",
    "        19:21.55,  20:22.70,   21:23.80,   22:24.95,   23:26.10,\n",
    "        24:27.25,  25:27.80,   26:28.95,   27:30.10,   28:31.20,\n",
    "        29:32.35,  30:33.50,   35:39.15,   40:44.80,   45:50.50,\n",
    "        50:55.60,  60:67.00,   70:78.30,   75:83.45,   80:89.10,\n",
    "        90:100.45, 100:111.25, 125:139.00, 150:166.85, 200:222.50}  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "otimizado={}\n",
    "for item in menu:\n",
    "    otimizado[item]=optimal_wings(menu,item,Show=False)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1f30cbcb320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1f30cd94080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "o_x,o_y = zip(*sorted(otimizado.items()))\n",
    "m_x,m_y = zip(*sorted(menu.items()))\n",
    "\n",
    "\n",
    "plt.scatter(o_x,o_y,edgecolors=\"k\",facecolors=\"None\",label=\"Custo Otimizado\")\n",
    "plt.plot(m_x,m_y,\"b.\",label=\"Custo Menu\")\n",
    "plt.legend()\n",
    "plt.xlabel(\"Quantidade de 'Chicken Wings'\")\n",
    "plt.ylabel(\"Custo total\")\n",
    "plt.show()\n",
    "\n",
    "economia = []\n",
    "for item in menu:\n",
    "    economia.append((item,menu[item]-otimizado[item]))\n",
    "\n",
    "e_x,e_y = zip(*sorted(economia))\n",
    "\n",
    "plt.plot(e_x,e_y,\"ro-\")\n",
    "plt.xlabel(\"Quantidade de 'Chicken Wings'\")\n",
    "plt.ylabel(\"Economia em relação ao menu\")\n",
    "plt.title(\"Destaque da economia\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Questão 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "SDK = np.kron(np.ones((3,3)),np.zeros((3,3)))\n",
    "SDK[0,1] = 2\n",
    "SDK[0,4] = 3\n",
    "SDK[0,7] = 4\n",
    "SDK[1,0] = 6\n",
    "SDK[1,8] = 3\n",
    "SDK[2,2] = 4\n",
    "SDK[2,6] = 5\n",
    "SDK[3,3] = 8\n",
    "SDK[3,5] = 6\n",
    "SDK[4,0] = 8\n",
    "SDK[4,4] = 1\n",
    "SDK[4,8] = 6\n",
    "SDK[5,3] = 7\n",
    "SDK[5,5] = 5\n",
    "SDK[6,2] = 7\n",
    "SDK[6,6] = 6\n",
    "SDK[7,0] = 4\n",
    "SDK[7,8] = 8\n",
    "SDK[8,1] = 3\n",
    "SDK[8,4] = 4\n",
    "SDK[8,7] = 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 2., 0., 0., 3., 0., 0., 4., 0.],\n",
       "       [6., 0., 0., 0., 0., 0., 0., 0., 3.],\n",
       "       [0., 0., 4., 0., 0., 0., 5., 0., 0.],\n",
       "       [0., 0., 0., 8., 0., 6., 0., 0., 0.],\n",
       "       [8., 0., 0., 0., 1., 0., 0., 0., 6.],\n",
       "       [0., 0., 0., 7., 0., 5., 0., 0., 0.],\n",
       "       [0., 0., 7., 0., 0., 0., 6., 0., 0.],\n",
       "       [4., 0., 0., 0., 0., 0., 0., 0., 8.],\n",
       "       [0., 3., 0., 0., 4., 0., 0., 2., 0.]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "SDK"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "variaveis = {}\n",
    "\n",
    "prob = LpProblem(\"Sodoku\",LpMinimize)\n",
    "for i in range(9):\n",
    "    variaveis[i]={}\n",
    "    for j in range(9):\n",
    "        variaveis[i][j]=[LpVariable(\"Possivel_\"+str(k)+\"_in_\"+str(i+1)+str(j+1),0,1,LpInteger) for k in range(1,10)]\n",
    "\n",
    "prob +=sum([sum(variaveis[i][j]) for i in range(9) for j in range(9)]) #FO aleatoria = soma de todas as intancias\n",
    "        \n",
    "for i in range(9):\n",
    "    for j in range(9):\n",
    "        prob +=sum(variaveis[i][j])<=1\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "#Restrições:\n",
    "\n",
    "#bloco 1,1 - Só pode haver apenas 1 de cada numero de 1 a 9\n",
    "bloco = {}\n",
    "bloco[1] = {}\n",
    "bloco[1][1] ={}\n",
    "for k in range(1,10):\n",
    "    bloco[1][1][k] = []\n",
    "    for i in range(3):\n",
    "        for j in range(3):\n",
    "            bloco[1][1][k].append(variaveis[i][j][k-1])\n",
    "    prob +=sum(bloco[1][1][k])==1\n",
    "    \n",
    "\n",
    "#bloco 1,2 - Só pode haver apenas 1 de cada numero de 1 a 9\n",
    "bloco[1][2] = {}\n",
    "bloco[1][2][k] = []\n",
    "for k in range(1,10):\n",
    "    bloco[1][2][k] = []\n",
    "    for i in range(3):\n",
    "        for j in range(3,6):\n",
    "            bloco[1][2][k].append(variaveis[i][j][k-1])\n",
    "    prob +=sum(bloco[1][2][k])==1\n",
    "\n",
    "\n",
    "#bloco 1,3 - Só pode haver apenas 1 de cada numero de 1 a 9    \n",
    "bloco[1][3] = {}    \n",
    "for k in range(1,10):\n",
    "    bloco[1][3][k] = []\n",
    "    for i in range(3):\n",
    "        for j in range(6,9):\n",
    "            bloco[1][3][k].append(variaveis[i][j][k-1])\n",
    "    prob +=sum(bloco[1][3][k])==1    \n",
    "\n",
    "\n",
    "#bloco 2,1 - Só pode haver apenas 1 de cada numero de 1 a 9\n",
    "bloco[2] = {}    \n",
    "bloco[2][1] = {}    \n",
    "for k in range(1,10):\n",
    "    bloco[2][1][k] = []\n",
    "    for i in range(3,6):\n",
    "        for j in range(3):\n",
    "            bloco[2][1][k].append(variaveis[i][j][k-1])\n",
    "    prob +=sum(bloco[2][1][k])==1\n",
    "\n",
    "\n",
    "#bloco 2,2 - Só pode haver apenas 1 de cada numero de 1 a 9    \n",
    "bloco[2][2] = {}\n",
    "for k in range(1,10):\n",
    "    bloco[2][2][k] = []\n",
    "    for i in range(3,6):\n",
    "        for j in range(3,6):\n",
    "            bloco[2][2][k].append(variaveis[i][j][k-1])\n",
    "    prob +=sum(bloco[2][2][k])==1\n",
    " \n",
    "\n",
    "#bloco 2,3 - Só pode haver apenas 1 de cada numero de 1 a 9\n",
    "bloco[2][3] = {}\n",
    "for k in range(1,10):\n",
    "    bloco[2][3][k] = []\n",
    "    for i in range(3,6):\n",
    "        for j in range(6,9):\n",
    "            bloco[2][3][k].append(variaveis[i][j][k-1])\n",
    "    prob +=sum(bloco[2][3][k])==1    \n",
    "    \n",
    "\n",
    "#bloco 3,1 - Só pode haver apenas 1 de cada numero de 1 a 9\n",
    "bloco[3] = {}    \n",
    "bloco[3][1] ={}\n",
    "for k in range(1,10):\n",
    "    bloco[3][1][k] = []\n",
    "    for i in range(6,9):\n",
    "        for j in range(3):\n",
    "            bloco[3][1][k].append(variaveis[i][j][k-1])\n",
    "    prob +=sum(bloco[3][1][k])==1\n",
    "    \n",
    "\n",
    "#bloco 3,2 - Só pode haver apenas 1 de cada numero de 1 a 9    \n",
    "bloco[3][2] = {}\n",
    "for k in range(1,10):\n",
    "    bloco[3][2][k] = []\n",
    "    for i in range(6,9):\n",
    "        for j in range(3,6):\n",
    "            bloco[3][2][k].append(variaveis[i][j][k-1])\n",
    "    prob +=sum(bloco[3][2][k])==1\n",
    "    \n",
    "\n",
    "#bloco 3,3 - Só pode haver apenas 1 de cada numero de 1 a 9    \n",
    "bloco[3][3] = {}\n",
    "linha = {}\n",
    "for k in range(1,10):\n",
    "    bloco[3][3][k] = []\n",
    "    for i in range(6,9):\n",
    "        for j in range(6,9):\n",
    "            bloco[3][3][k].append(variaveis[i][j][k-1])\n",
    "    prob +=sum(bloco[3][3][k])==1 \n",
    "    \n",
    "    \n",
    "#cada linha e cada coluna só pode ter apenas um de cada número de 1 a 9    \n",
    "linha = {}\n",
    "coluna = {}\n",
    "for k in range(1,10):\n",
    "    for i in range(9):\n",
    "        linha[i]={}\n",
    "        linha[i][k]=[]\n",
    "        for j in range(9):\n",
    "            linha[i][k].append(variaveis[i][j][k-1])\n",
    "            \n",
    "        prob +=sum(linha[i][k])==1 \n",
    "    for j in range(9):\n",
    "        coluna[j]={}\n",
    "        coluna[j][k]=[]\n",
    "        for i in range(9):\n",
    "            coluna[j][k].append(variaveis[i][j][k-1])\n",
    "        prob +=sum(coluna[j][k])==1\n",
    "        \n",
    "#fixando os número já fornecidos no Sudoku\n",
    "for i in range(9):\n",
    "    for j in range(9):\n",
    "        if SDK[i][j]>0:\n",
    "            prob +=variaveis[i][j][int(SDK[i][j])-1]==1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "     0    1    2    3    4    5    6    7    8\n",
       "0  9.0  2.0  5.0  6.0  3.0  1.0  8.0  4.0  7.0\n",
       "1  6.0  1.0  8.0  5.0  7.0  4.0  2.0  9.0  3.0\n",
       "2  3.0  7.0  4.0  9.0  8.0  2.0  5.0  6.0  1.0\n",
       "3  7.0  4.0  9.0  8.0  2.0  6.0  1.0  3.0  5.0\n",
       "4  8.0  5.0  2.0  4.0  1.0  3.0  9.0  7.0  6.0\n",
       "5  1.0  6.0  3.0  7.0  9.0  5.0  4.0  8.0  2.0\n",
       "6  2.0  8.0  7.0  3.0  5.0  9.0  6.0  1.0  4.0\n",
       "7  4.0  9.0  1.0  2.0  6.0  7.0  3.0  5.0  8.0\n",
       "8  5.0  3.0  6.0  1.0  4.0  8.0  7.0  2.0  9.0"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob.writeLP(\"Soduko.lp\")\n",
    "\n",
    "prob.solve()\n",
    "\n",
    "solucao = []\n",
    "for v in prob.variables():\n",
    "    if v.varValue>0:\n",
    "        solucao.append(v.name)\n",
    "        i=v.name.split(\"Possivel_\")[1].split(\"_in_\")[1][0]\n",
    "        j=v.name.split(\"Possivel_\")[1].split(\"_in_\")[1][1]\n",
    "        num=v.name.split(\"Possivel_\")[1].split(\"_in_\")[0]\n",
    "        SDK[int(i)-1][int(j)-1]=int(num)\n",
    "pd.DataFrame(SDK)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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