题解 | #将真分数分解为埃及分数#

//核心就是(b-y)/a = x;
//a/b = 1/(1+x) * (1+(a-y)/b)
//可以自己推一推为什么相等

#include<iostream>
#include<string>
using namespace std;

int main(){
    string inputstr;
    while(getline(cin,inputstr)){
        //找出分母的公约数，然后和为分子
        long long up,down;
        string tmp;
        for(int i = 0;i<inputstr.size();++i){
            if(inputstr[i] == '/'){
                up = stoi(tmp);
                tmp = "";
                while(i<inputstr.size()){
                    ++i;
                    tmp+=inputstr[i];
                }
                break;
            }
            tmp+=inputstr[i];
        }
        down = stoi(tmp);
        while(down%up != 0){
            long long x = down/up,y = down%up;
            down = (x+1)*down;
            up = up-y;
            cout << "1/" << x+1 << "+";
        }
        cout << "1/" << down/up << endl;
    }
    return 0;
}