HDU 2669 Romantic 扩展欧几里得

最新推荐文章于 2019-07-20 00:43:48 发布

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最新推荐文章于 2019-07-20 00:43:48 发布

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分类专栏：数学

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本文介绍了一个数学问题，即给定两个正整数a和b，寻找非负整数X和整数Y，使得X*a+Y*b=1。若无解则输出'sorry'。通过扩展欧几里得算法解决此类问题。

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Romantic

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 2958 Accepted Submission(s): 1160

Problem Description

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 X*a + 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

Sample Output

   
    2 -3
sorry
7 -3

Author

yifenfei

Source

HDU女生专场公开赛——谁说女子不如男

通过扩展欧几里得算法求得x，y之后，要求所有的x和y的解的话，得求得通项公式：(x+k*gx , y-k*gy) gx= b/gcd(a,b),gy = a/gcd(a,b)互素,k为任意整数

//15MS	228K
#include<stdio.h>
#include<string.h>
#include<algorithm>
#include<math.h>
#include<queue>
#include<vector>
#define M 10007
#define inf 0x3f3f3f3f
#define ll long long
using namespace std;
long long extended_euclidean(long long n, long long m, long long &x, long long &y)
{
    if (m == 0)
    {
        x = 1;
        y = 0;
        return n;
    }
    long long g = extended_euclidean(m, n % m, x, y);
    long long t = x - n / m * y;
    x = y;
    y = t;
    return g;
}
int main()
{
    ll a,b,x,y;
    while(scanf("%I64d%I64d",&a,&b)!=EOF)
    {
        ll d=extended_euclidean(a,b,x,y);
        if(1%d)printf("sorry\n");
        else
        {
            while(x<0){x+=b;y-=a;}
            printf("%I64d %I64d\n",x,y);
        }
    }
    return 0;
}