{
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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 34:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Enunciado:\n",
    "\n",
    "145 é um numero curioso pois 1! + 4! + 5! = 1 + 24 + 120 = 145.\n",
    "\n",
    "Encontre a soma de todos os números que são iguais a soma dos fatoriais de seus dígitos.\n",
    "\n",
    "Nota: como 1! = 1 e 2! = 2 não são somas, eles não são incluídos.\n",
    "\n",
    "https://projecteuler.net/index.php?section=problems&id=34"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Resolução:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def fatorial(n):\n",
    "    fat = 1\n",
    "    for i in range(1,n+1):\n",
    "        fat *= i\n",
    "    return fat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "40320\n"
     ]
    }
   ],
   "source": [
    "x = fatorial(8)\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: 1, 1: 1, 2: 2, 3: 6, 4: 24, 5: 120, 6: 720, 7: 5040, 8: 40320, 9: 362880}"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fatoriais = {num:fatorial(num) for num in range(10)}\n",
    "fatoriais"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "def soma_fat(n):\n",
    "    soma = 0\n",
    "    for num in str(n):\n",
    "        #soma += fatorial(int(num))\n",
    "        soma += fatoriais[int(num)]\n",
    "    return soma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "145\n"
     ]
    }
   ],
   "source": [
    "y = soma_fat(145)\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[145, 40585]\n",
      "29.7142000198\n"
     ]
    }
   ],
   "source": [
    "t0 = time.time()\n",
    "l = []\n",
    "for numero in range(3,2540161):\n",
    "    if soma_fat(numero) == numero:\n",
    "        l.append(numero)\n",
    "print(l)\n",
    "tempo = time.time() - t0\n",
    "print(tempo)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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