Exercises/PT-BR/Project_Euler_8.ipynb

{
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   "source": [
    "FGV - Escola de Matemática Aplicada\n",
    "==\n",
    "Curso de Verão - Introdução à Programação com a Linguagem Python\n",
    "--"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Project Euler:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Resolução do problema 8:"
   ]
  },
  {
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   "metadata": {},
   "source": [
    "Enunciado: \n",
    "\n",
    "The four adjacent digits in the 1000-digit number that have the greatest product are 9 × 9 × 8 × 9 = 5832.\n",
    "\n",
    "73167176531330624919225119674426574742355349194934\n",
    "96983520312774506326239578318016984801869478851843\n",
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    "53697817977846174064955149290862569321978468622482\n",
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    "24219022671055626321111109370544217506941658960408\n",
    "07198403850962455444362981230987879927244284909188\n",
    "84580156166097919133875499200524063689912560717606\n",
    "05886116467109405077541002256983155200055935729725\n",
    "71636269561882670428252483600823257530420752963450\n",
    "\n",
    "Find the thirteen adjacent digits in the 1000-digit number that have the greatest product. What is the value of this product?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "https://projecteuler.net/problem=8  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Resolução: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "numero = 7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450"
   ]
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  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open('../Dados/numero_mil_digitos.txt', mode='r') as f:\n",
    "    numero = f.read()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "numero = numero.replace('\\n','')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(numero)"
   ]
  },
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   "execution_count": 2,
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   "source": [
    "numero2 = '''\n",
    "73167176531330624919225119674426574742355349194934\n",
    "96983520312774506326239578318016984801869478851843\n",
    "85861560789112949495459501737958331952853208805511\n",
    "12540698747158523863050715693290963295227443043557\n",
    "66896648950445244523161731856403098711121722383113\n",
    "62229893423380308135336276614282806444486645238749\n",
    "30358907296290491560440772390713810515859307960866\n",
    "70172427121883998797908792274921901699720888093776\n",
    "65727333001053367881220235421809751254540594752243\n",
    "52584907711670556013604839586446706324415722155397\n",
    "53697817977846174064955149290862569321978468622482\n",
    "83972241375657056057490261407972968652414535100474\n",
    "82166370484403199890008895243450658541227588666881\n",
    "16427171479924442928230863465674813919123162824586\n",
    "17866458359124566529476545682848912883142607690042\n",
    "24219022671055626321111109370544217506941658960408\n",
    "07198403850962455444362981230987879927244284909188\n",
    "84580156166097919133875499200524063689912560717606\n",
    "05886116467109405077541002256983155200055935729725\n",
    "71636269561882670428252483600823257530420752963450\n",
    "'''"
   ]
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   "execution_count": 3,
   "metadata": {
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "1000"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(numero2.replace('\\n',''))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
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   },
   "outputs": [],
   "source": [
    "numero_string = str(numero)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "#Criando o arquivo:\n",
    "with open ('numero_mil_digitos_a.txt', mode='w', encoding='utf-8') as arquivo:\n",
    "    arquivo.write(numero_string)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "#Lendo o arquivo:\n",
    "with open ('numero_mil_digitos_a.txt', mode='r', encoding='utf-8') as arquivo:\n",
    "    leitura = arquivo.readlines()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
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     "data": {
      "text/plain": [
       "'7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450'"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "leitura[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1000\n"
     ]
    }
   ],
   "source": [
    "print(len(leitura[0])) #Conferindo o tamanho"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "23514624000\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "#Calculando o valor:\n",
    "x = leitura[0]\n",
    "produtos = [] #Aqui armazenaremos todos os produtos possiveis gerados\n",
    "for a in range(len(x)-12): #o menos 12 é para que não acessemos índice fora da faixa\n",
    "    produto = int(x[a])\n",
    "    contador = 1\n",
    "    indice = a\n",
    "    while contador <= 12: #loop que faz com que o produto'caminhe' pelos 13 numeros consecutivos\n",
    "        indice+=1 #isso faz com que o indice 'ande' para o proximo numero\n",
    "        produto*=int(x[indice])\n",
    "        contador+=1\n",
    "    produtos.append(produto)\n",
    "#print(produtos)\n",
    "print(max(produtos))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Outra versão  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "%%time\n",
    "lista = [int(char) for char in list(numero)]\n",
    "i = 0\n",
    "maior = 0\n",
    "while i+13 <= 1000:\n",
    "    temp = lista[i:i+13]\n",
    "    mult = 1\n",
    "    for elemento in temp:\n",
    "        mult *= elemento\n",
    "    if mult > maior:\n",
    "        maior = mult\n",
    "    i +=1\n",
    "print(maior)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Outra versão (utilizando programação funcional):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "from functools import reduce"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "with open ('numero_mil_digitos.txt', mode='w', encoding='utf-8') as arquivo:\n",
    "    arquivo.write(numero_string)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "23514624000"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "with open('numero_mil_digitos.txt', mode='r') as n:\n",
    "    num = n.read()\n",
    "num = num.replace('\\n','')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "%%time\n",
    "\n",
    "mult = lambda x,y:int(x)*int(y)\n",
    "i = 0\n",
    "indice = 0\n",
    "maior = 0\n",
    "while i < (len(num)-12):\n",
    "    i += 1\n",
    "    numero = reduce(mult,num[i:i+13])\n",
    "    if numero > maior:\n",
    "        maior = numero\n",
    "        indice = i\n",
    "maior"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "23514624000"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reduce(mult,num[indice:indice+13])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'5576689664895'"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "num[indice:indice+13]"
   ]
  }
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