Project Euler -- 欧拉题集 F#及Haskell 版 - No.5, No.6

No5.

2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder

What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?

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F#：

let rec gcd x y = if y = 0UL then x

                         else gcd y (x % y)

 

let scm x y = ((x*y):uint64) / ((gcd x y) : uint64)

let scmN n = List.fold scm 1UL [2UL..n]

let anwser5 = scmN 20UL

Haskell：

gcd1 x y = if x `mod` y == 0 then y

                  else gcd x (abs $ x-y)

scm x y = (x*y) `div` gcd1 x y

scmN n = foldl scm 1 [2..n]

anwser5 = scmN 20

Answer: [b]232792560[/b]

后语： 求N个数的最小公倍数。

            F# 坑爹了，用int过程中会溢出，改用UL。

No6.

The sum of the squares of the first ten natural numbers is,

12 + 22 + ... + 102 = 385

The square of the sum of the first ten natural numbers is,

(1 + 2 + ... + 10)2 = 552 = 3025

Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 − 385 = 2640.

Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.

Haskell:

-- 1^2+2^2+3^2+...+n^2=n(n+1)(2n+1)/6

-- (1+2+...+n)^2      = (1+n)^2*n^2/4

answer6 = b - a

   where  a = sum . map ( ^2 ) $ [1..100]

          b = flip (^) 2 (sum [1..100])

F#:

略；

答案：25164150

后语： 无聊的一道题。