読者です 読者をやめる 読者になる 読者になる

mu chance or much chance ?

日々の戯れ言

Project Euler 26

Project Euler

Problem26を解きました.

  • Reciprocal cycles

A unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given:

1/2 = 0.5
1/3 = 0.(3)
1/4 = 0.25
1/5 = 0.2
1/6 = 0.1(6)
1/7 = 0.(142857)
1/8 = 0.125
1/9 = 0.(1)
1/10 = 0.1
Where 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be seen that 1/7 has a 6-digit recurring cycle.

Find the value of d < 1000 for which 1/d contains the longest recurring cycle in its decimal fraction part.

https://projecteuler.net/problem=26

問題は「自然数 d < 1000を満たす1/dの中で小数部の循環節が最も長くなるdを求めよ」.

num = 1
max = 0
maxID = 1
for d in 1..999 do
	list = Array.new()
	while (amari = num % d) != 0 do
		if list.include?(amari) then
			if max < list.length then
				maxID = d
				max = list.length
			end
			break
		else
			list.push(amari)
		end
		num = amari * 10
	end
end

p maxID

余りを配列に格納して,同じ余りが再度発生したら,
そこまで小数部の循環節となります.