原題連結：
http://acm.hdu.edu.cn/showproblem.php?pid=2669
The Sky is Sprite.
The Birds is Fly in the Sky.
The Wind is Wonderful.
Blew Throw the Trees
Trees are Shaking, Leaves are Falling.
Lovers Walk passing, and so are You.
…Write in English class by yifenfei

Girls are clever and bright. In HDU every girl like math. Every girl like to solve math problem!
Now tell you two nonnegative integer a and b. Find the nonnegative integer X and integer Y to satisfy Xa + Y

b = 1. If no such answer print “sorry” instead.
Input
The input contains multiple test cases.
Each case two nonnegative integer a,b (0<a, b<=2^31)
Output
output nonnegative integer X and integer Y, if there are more answers than the X smaller one will be choosed. If no answer put “sorry” instead.
Sample Input
77 51
10 44
34 79
Sample Output
2 -3
sorry
7 -3
題意：
輸入a，b，要求找出滿足ax+by=1等式的其中x最小的那一組解。
題解：
利用擴充套件歐幾里得演算法，如果a和b的最小公約數是1，則一定有解，再將其中x最小的一組解輸出。
如果不是1，則sorry。
附上AC程式碼：

#include <iostream>
#include <cstdio>
using namespace std;
int exgcd(int a,int b,int &x,int &y)//擴充套件歐幾里得演算法
{
    if (b==0)
    {
        x=1,y=0;
        return a;
    }
    int q=exgcd(b,a%b,y,x);
    y-=a/b*x;
    return q;
}
int main()
{
    int a,b,x,y;
    while(scanf("%d%d",&a,&b)!=EOF)
    {
        if(exgcd(a,b,x,y)==1)
        {
            while(x<0)//調整至x最小的非負數
            {
                x+=b;
                y-=a;
            }
            printf("%d %d\n",x,y);
        }

        else
            printf("sorry\n");
    }
    return 0;
}

 

歡迎評論！