扩展欧几里得

ax + by  = gcd(a,b) 满足贝祖定理

#include <iostream>
using namespace std;

int exgcd1(int m,int n,int &x,int &y)//非递归版本
{
    int x1,y1,x0,y0;
    x0=1; y0=0;
    x1=0; y1=1;
    x=0; y=1;
    int r=m%n;
    int q=(m-r)/n;
    while(r)
    {
        x=x0-q*x1; y=y0-q*y1;
        x0=x1; y0=y1;
        x1=x; y1=y;
        m=n; n=r; r=m%n;
        q=(m-r)/n;
    }
    return n;
}

int exgcd2(int a,int b,int &x,int &y)//递归版本
{
    if(b==0)
    {
        x=1;
        y=0;
        return a;
    }
    int r=exgcd2(b,a%b,x,y);
    int t=x;
    x=y;
    y=t-a/b*y;
    return r;
}
int main()
{
    int a,b,x,y,res;
    cin >> a >> b;
    res = exgcd1(a,b,x,y);
    //res = exgcd2(a,b,x,y);
    cout << res << endl;
    cout<< "x="<< x << " " << "y=" << y << endl;
    return 0;
}