[Haskell] Exercise 4.13, 4.14

○ Exercise 4.13
ユークリッドの互除法

import Prelude hiding (gcd)
gcd :: Int -> Int -> Int
gcd m n
  | m < n           = gcd n m
  | m `mod` n == 0  = n
  | otherwise       = gcd n (m `mod` n)

Main> gcd 7 5
1
Main> gcd 12 18
6
Main>

○ Exercise 4.14

power2 :: Int -> Int
power2 n
  | n == 0          = 1
  | n == 1          = 2
  | n `mod` 2 == 0  = square (power2 (n `div` 2))
  | otherwise       = 2 * square (power2 ((n-1) `div` 2))
    where square x = x * x

Main> power2 0
1
Main> power2 1
2
Main> power2 2
4
Main> power2 3
8
Main> power2 4
16
Main> power2 5
32
Main>