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.
#include <iostream> #include <string> using namespace std; int rc(int n, int d) { int a[10010]; //记录每一次除法的被除数 int b[10010]; memset(a, 0, sizeof(a)); memset(b, 0, sizeof(b)); int count = 0; while (n%d != 0) { while (n < d) n = n * 10; int tmp = n / d; count++; if (a[n] == 1) return count - b[n]; a[n] = 1; b[n] = count; //最近的一次被除数为n时的位置 n = n - tmp*d; } return 0; } int main() { int maxlen = 0, maxn = 0; for (int i = 1; i < 1000; i++) { int tmp = rc(1, i); if (tmp>maxlen) { maxn = i; maxlen = tmp; } } cout << maxn << endl; system("pause"); return 0; }
时间: 2024-11-05 17:27:33