Codeforces 898 B（拓展欧几里得）

Proper Nutrition

题意:有n元钱，有2种单价不同的商品，是否存在一种购买方式使得钱恰好花光，如果有输入任意一种方式，如果没有输出“NO”

题解：可以使用拓展欧几里得快速求解。

#include<iostream>
using namespace std;
#define ll long long
ll gcd(ll a, ll b)
{
    return b? gcd(b, a%b) : a;
}

void ex_gcd(ll a, ll b, ll &x, ll &y, ll &d)
{
    if(!b)
    {
        x = 1, y = 0, d = a;
        return ;
    }
    ex_gcd(b, a%b, y, x, d);
    y -= a/b * x;
    return ;
}
int main()
{
    ll m, a, b, x, y;
    cin >> m >> a >> b;
    ll d = gcd(a, b);
    if(m%d)
    {
        cout << "NO
";
        return 0;
    }
    ex_gcd(a, b, x, y, d);
    x *= m/d, y *= m/d;
    a /= d, b /= d;
    if(x<0 && y <0)
    {
        cout << "NO
";
    }
    else if(x < 0)
    {
        x = -x;
        ll z;
        if(x%b) z = x/b+1; //找到最小的正数x
        else z = x/b;
        x = -x + z * b;
        y = y  -  z*a;
        if(y < 0)
            cout << "NO
";
        else cout << "YES
" << x << ' ' << y << endl;
    }
    else if(y < 0)
    {
        y = -y;
        ll z;
        if(y%a) z = y/a+1;
        else z = y/a;
        y = -y + z*a;
        x = x - z*b;
        if(x < 0)
            cout << "NO
";
        else cout << "YES
" << x << ' ' << y << endl;
    }
    else
        cout << "YES
" << x << ' ' << y << endl;
    return 0;
}