扩展欧几里得

扩展欧几里得

解释：

扩展欧几里得算法是用来在已知 a, b 的情况下求解一组 x,y,使它们满足等式ax+by=gcd(a,b)=kd(注意：gcd(a, b) | d)该方程的解一定存在

证明：略

模板代码：

include

include

using namespace std;

typedef long long LL;

void extend_Eulid(LL a, LL b, LL &x, LL &y, LL &d){
if (b == 0) {d = a, x = 1, y = 0;}
else{
extend_Eulid(b, a % b, y, x, d);
y -= x * (a / b);
}
}

int main(){
LL a, b, d, x, y;
while(~scanf("%lld%lld", &a, &b)){
extend_Eulid(a, b, x, y, d);
printf("%llda + %lldb = %lld\n", x, y, d);
}
}