题目

Problem 008: Largest product in a series

The four adjacent digits in the 1000-digit number that have the greatest product are 9 × 9 × 8 × 9 = 5832.

73167176531330624919225119674426574742355349194934 96983520312774506326239578318016984801869478851843 85861560789112949495459501737958331952853208805511 12540698747158523863050715693290963295227443043557 66896648950445244523161731856403098711121722383113 62229893423380308135336276614282806444486645238749 30358907296290491560440772390713810515859307960866 70172427121883998797908792274921901699720888093776 65727333001053367881220235421809751254540594752243 52584907711670556013604839586446706324415722155397 53697817977846174064955149290862569321978468622482 83972241375657056057490261407972968652414535100474 82166370484403199890008895243450658541227588666881 16427171479924442928230863465674813919123162824586 17866458359124566529476545682848912883142607690042 24219022671055626321111109370544217506941658960408 07198403850962455444362981230987879927244284909188 84580156166097919133875499200524063689912560717606 05886116467109405077541002256983155200055935729725 71636269561882670428252483600823257530420752963450

Find the thirteen adjacent digits in the 1000-digit number that have the greatest product. What is the value of this product?

解答

本题要求找出 1000 位整数中连续 13 个数字的最大乘积。使用 Haskell 解答如下:

import Data.List
import Data.Char

main = do
  a <- readFile "008.txt"
  print . maximum . map (product . take 13) . tails $ map digitToInt $ filter isDigit a

在上述程序中:

  • 首先使用 readFile 函数将 008.txt 文件的内容(1000 位整数)读入到字符串 a 中。
  • 最后一行从右往左分析,filter isDigit a 过滤掉 \n 等字符,只留下数字字符。
  • map digitToInt 将数字字符转换为(只有一位的)整数,得到的是单个数字的列表:[7,3,1,6,7,...,4,5,0]。
  • tails 函数返回列表中所有尾部元素组成的列表的列表:[ [7,3,1,6,7,...,4,5,0], [3,1,6,7,...,4,5,0], [1,6,7,...,4,5,0], [6,7,...,4,5,0], [7,...,4,5,0], ..., [4,5,0], [5,0], [0], [] ]。
  • map (product . take 13) 对列表中的每个元素(也是列表)进行以下操作:take 13 从列表开头取出 13 个元素(如果不够 13 个则有多少个就取多少个),product 将这些元素全部乘起来。结果是:[ 5000940, 0, 0, 0, 0, ..., 0, 0, 0, 1 ]。
  • maximum 函数找出这些乘积中最大的。
  • print 函数输出结果。大功告成。

这个程序的运行时间是 0.006 秒。

参考资料

  1. Haskell: Prelude: readFile
  2. Haskell: Prelude: filter
  3. Haskell: Prelude: map
  4. Haskell: Prelude: take
  5. Haskell: Prelude: product
  6. Haskell: Prelude: maximum
  7. Haskell: Prelude: print
  8. Haskell: Data.Char: isDigit
  9. Haskell: Data.Char: digitToInt
  10. Haskell: Data.List: tails