The Balance POJ - 2142

Posted 2020-11-24 yangxuejian

首先，可以知道题目要求解一个(ax+by=c)的方程，且(x+y)最小。
感性证明:
当(a>b)时，(y)取最小正整数解，(b)减的多，(a)增的少，此时(x+y)取最小值。（类似比热容与温度之间）
反之亦然。

#include<iostream>
#include<cmath>
#include<cstdlib>
using namespace std;
int a, b, c;
int exgcd(int a, int b, int &x, int &y) {
    if(b == 0) {
        x = 1, y = 0;
        return a;
    }
    int g = exgcd(b, a % b, x, y);
    int tmp = x;
    x = y;
    y = tmp - (a / b) * y;
    return g;
}
void solve(int &x, int &y, int a, int b, int c) {
    int g = exgcd(a, b, x, y); 
    x *= (c / g);
    int t = b / g;
    x = (x % t + t) % t;
    y = (a * x - c) / b;
    y = abs(y);
}
int main() {
    while(cin >> a >> b >> c) {     
        if(!a && !b && !c) break;
        int x1, y1, x2, y2;
        solve(x1, y1, a, b, c); 
        solve(x2, y2, b, a, c);
        if(x1 + y1 < x2 + y2) cout << x1 << " " << y1 << "
";
        else cout << y2 << " " << x2 << "
";
    }
    return 0;
}