Project Euler Problem 31

問題

In England the currency is made up of pound, £, and pence, p, and there are eight
coins in general circulation:

    1p, 2p, 5p, 10p, 20p, 50p, £1 (100p) and £2 (200p).

It is possible to make £2 in the following way:

    1×£1 + 1×50p + 2×20p + 1×5p + 1×2p + 3×1p

How many different ways can £2 be made using any number of coins?

ソース

coin = [200, 100, 50, 20, 10, 5, 2, 1]

@cache = {}
def solv(c, pence)
	return 1 if c.size == 1
	return @cache[[c.size, pence]] unless @cache[[c.size, pence]].nil?
	@cache[[c.size, pence]] = (0..pence / c[0]).map{|i| i * c[0]}.inject(0){|count, n|
		count + solv(c[1...c.size], pence - n)
	}
end

puts solv(coin, 200)

解答

73682

感想

普通に全探索でも求められる問題だった
今回はキャッシュを使っているので計算は一瞬で終わる！