ZOJ 3609 Modular Inverse（擴充歐幾裡德）

標籤：exgcd   gcd   擴充   

題目連結：http://acm.zju.edu.cn/onlinejudge/showProblem.do?problemId=4712

The modular modular multiplicative inverse of an integer a modulo m is an integer x such that a-1≡x (modm). This is equivalent to ax≡1 (modm).

Input

There are multiple test cases. The first line of input is an integer T ≈ 2000 indicating the number of test cases.

Each test case contains two integers 0 < a ≤ 1000 and 0 < m ≤ 1000.

Output

For each test case, output the smallest positive x. If such x doesn‘t exist, output "Not Exist".

Sample Input

33 114 125 13

Sample Output

4Not Exist8

References

• http://en.wikipedia.org/wiki/Modular_inverse

代碼如下:

#include <cstdio>#include <cstring>#include <cmath>typedef long long LL;LL exgcd(LL a,LL b,LL &x,LL &y){    if(b == 0)    {        x = 1;        y = 0;        return a;    }    else    {        LL r = exgcd(b,a%b,x,y);        LL t = x;        x = y;        y = t-a/b*y;        return r;    }}LL cal(LL a, LL b, LL c){    LL x, y;    LL tt = exgcd(a, b, x, y);    if(c%tt)//無整數解    {        return -1;    }    x*=c/tt;    b/=tt;    if(b<0)        b=-b;    LL ans=x%b;    if(ans<=0)        ans+=b;    return ans;}int main(){    LL a, b, t;    scanf("%lld",&t);    while(t--)    {        scanf("%lld%lld",&a,&b);        LL ans = cal(a, b, 1);        if(ans == -1)        {            printf("Not Exist\n");            continue;        }        printf("%lld\n",ans);    }    return 0;}

ZOJ 3609 Modular Inverse（擴充歐幾裡德）