# 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

``````import Data.List
import Data.Char

main = do
print . maximum . map (product . take 13) . tails \$ map digitToInt \$ filter isDigit a
``````

• 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。