EularProject 71：Ordered fractions

lazy_piger
2017-07-16

Consider the fraction, n/d, where n and d are positive integers. If n<d and HCF(n,d)=1, it is called a reduced proper fraction.

If we list the set of reduced proper fractions for d ≤ 8 in ascending order of size, we get:

1/8, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 3/8, 2/5, 3/7, 1/2, 4/7, 3/5, 5/8, 2/3, 5/7, 3/4, 4/5, 5/6, 6/7, 7/8

It can be seen that 2/5 is the fraction immediately to the left of 3/7.

By listing the set of reduced proper fractions for d ≤ 1,000,000 in ascending order of size, find the numerator of the fraction immediately to the left of 3/7.

Answer:
428570
Completed on Sun, 16 Jul 2017, 14:38
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#include <iostream>using namespace std;#define MAX 1000000int HCF(int a, int b){    int c = a%b;    if (c == 0)        return b;    else        return HCF(b, c);}int main(){    int s_n = 3, s_d = 7;    int t_n = 0, t_d = 1;    int i, j;    for (i = 1; i < MAX; i++)    {        for (j = i * s_d / s_n; j < MAX; j++)        {            if (HCF(i, j) == 1)            {                if (i * s_d < j * s_n)                {                    if (i * t_d > j * t_n)                    {                        t_n = i;                        t_d = j;                    }                    break;                }            }        }    }    cout << t_n << "/" << t_d << endl;    return 0;}