hdu4180 数论

一个分数假如 3/5=1/(1+2/3)=1/(1+1/(1+1/2));

当分子出现1的时候，只要让分母减一。

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#define EX(a, b) (a = a ^ b, b = a ^ b, a = a ^ b)
using namespace std;

int gcd(int a, int b)
{
    return (b == 0) ? a : gcd(b, a % b);
}

class fenshu
{
    public:
    int x, y;

    fenshu friend operator + (fenshu n, fenshu m)
    {
        m.x *= n.y;
        n.x *= m.y;
        m.y *= n.y;
        n.y = m.y;
        n.x += m.x;
        int k = gcd(n.x, n.y);
        n.x /= k;
        n.y /= k;
        return n;
    }

    fenshu friend operator / (int k, fenshu n)
    {
        EX(n.x, n.y);
        n.x *= k;
        return n;
    }
};

fenshu ans_get(fenshu now)
{
    if(now.x <= 1)
    {
        --now.y;
        return now;
    }
    else
    {
        EX(now.x, now.y);  //小数倒置

        fenshu s;
        s.x = now.x / now.y;
        s.y = 1;  //分离出来的整数

        now.x = now.x % now.y;
        return 1 / (s + ans_get(now));
    }//继续分离
}

void solve()
{
    int T;
    scanf("%d", &T);
    while(T--)
    {
        fenshu now, s;
        scanf("%d/%d", &now.x, &now.y);
        now = ans_get(now);
        printf("%d/%d
", now.x, now.y);
    }
}

int main()
{
    solve();
    return 0;
}