PE_problem_8.ipynb

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    "# Problem 8\n",
    "\n",
    "## Largest product in a series\n",
    "\n",
    "\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",
    "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",
    "```\n",
    "Find the thirteen adjacent digits in the 1000-digit number that have the greatest product. What is the value of this product?\n"
   ]
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   "source": [
    "<br/>\n",
    "The solution is pretty streightforward function that examines every substring of length 13.\n",
    "This is probably the most boring problem from the first eight."
   ]
  },
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   "source": [
    "```Python\n",
    "\n",
    "def calc():\n",
    "\tans = max(prod(digits[i : i + 13]) for i in range(len(digits) - 13 + 1))\n",
    "\treturn str(ans)\n",
    "\n",
    "\n",
    "def prod(x):\n",
    "\tresult = 1\n",
    "\tfor y in x:\n",
    "\t\tresult *= int(y)\n",
    "\treturn result\n",
    "\n",
    "\n",
    "digits = \"7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450\"\n",
    "\n",
    "print('Answer is: {}'.format(calc()))\n",
    "\n",
    "```"
   ]
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   "source": [
    "Answer is: 23514624000"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solution in C\n"
   ]
  },
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   "source": [
    "```C\n",
    "#include <stdio.h>\n",
    "#include <stdint.h>\n",
    "#include <math.h>\n",
    "#include <string.h>\n",
    "#include <stdlib.h>\n",
    "\n",
    "int main() {\n",
    "\tchar *digits = \"73167176531330624919225119674426574742355349194934\" \\\n",
    "\t\t\"96983520312774506326239578318016984801869478851843\" \\\n",
    "\t\t\"85861560789112949495459501737958331952853208805511\" \\\n",
    "\t\t\"12540698747158523863050715693290963295227443043557\" \\\n",
    "\t\t\"66896648950445244523161731856403098711121722383113\" \\\n",
    "\t\t\"62229893423380308135336276614282806444486645238749\" \\\n",
    "\t\t\"30358907296290491560440772390713810515859307960866\" \\\n",
    "\t\t\"70172427121883998797908792274921901699720888093776\" \\\n",
    "\t\t\"65727333001053367881220235421809751254540594752243\" \\\n",
    "\t\t\"52584907711670556013604839586446706324415722155397\" \\\n",
    "\t\t\"53697817977846174064955149290862569321978468622482\" \\\n",
    "\t\t\"83972241375657056057490261407972968652414535100474\" \\\n",
    "\t\t\"82166370484403199890008895243450658541227588666881\" \\\n",
    "\t\t\"16427171479924442928230863465674813919123162824586\" \\\n",
    "\t\t\"17866458359124566529476545682848912883142607690042\" \\\n",
    "\t\t\"24219022671055626321111109370544217506941658960408\" \\\n",
    "\t\t\"07198403850962455444362981230987879927244284909188\" \\\n",
    "\t\t\"84580156166097919133875499200524063689912560717606\" \\\n",
    "\t\t\"05886116467109405077541002256983155200055935729725\" \\\n",
    "\t\t\"71636269561882670428252483600823257530420752963450\";\n",
    "\n",
    "\tuint64_t largest = 0;\n",
    "\n",
    "\tint length = strlen(digits);\n",
    "\tfor (int i = 0; i < (length - 13); i++) {\n",
    "\t\tuint64_t prod = 1;\n",
    "\t\tfor (int j = 0; j < 13; j++) prod *= (*(char *)(digits + i + j)) - '0';\n",
    "\t\tif (prod > largest) largest = prod;\n",
    "\t\telse if (prod == 0) continue;\n",
    "\t}\n",
    "\n",
    "\tprintf(\"%llu\", largest);\n",
    "\treturn 0;\n",
    "}\n",
    "\n",
    "```"
   ]
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