算法竞赛入门 7.1.3 分数拆分

求解的关键是对等式变形，1/x <= 1/y ,1/k = 1/x + 1/y <= 1/y + 1/y = 2/y ,所以y >= 2k；再根据x=(k*y) / (y - k)；求解x，判断x是否为整数即可。根据x的表达式可知：y>k

判断一个数是否为整数，用floor（x+0.5） == x

#include <iostream>
#include <math.h>
#include <vector>

using namespace std;
struct Index{
    int x;
    int y;
};

int main()
{
    int n;

    while(cin >> n){
        vector<Index> result;
        for(int y=n ; y<=2*n ; y++){
            int x = floor(1.0*n*y/(y-n))+0.5;
            if(1.0*n*y/(y-n) == x){
//                cout << "1/" << n << "=1/"<<x << "+1/" << y  << endl;
                Index t = {x,y};
                result.push_back(t);
            }
        }
        cout << result.size() << endl;
        for(int i=0 ; i<result.size() ; i++){
            cout << "1/" << n << "=1/"<<result[i].x << "+1/" << result[i].y  << endl;
        }
    }


    return 0;
}