zjuoj 3609 Modular Inverse

http://acm.zju.edu.cn/onlinejudge/showProblem.do?problemCode=3609

Modular Inverse

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Time Limit: 2 Seconds      Memory Limit: 65536 KB

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

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

3
3 11
4 12
5 13

Sample Output

4
Not Exist
8

References

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

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Author: WU, Zejun
Contest: The 9th Zhejiang Provincial Collegiate Programming Contest

分析：
题目要求给出a和m的值 ， 求出 ax % m == 1 % m成立时的x 的最小值 ， 直接x枚举到m即可。

一开始写的时候没有想到是枚举到m， 后来队友推出m。

AC代码：

#include<cstdio>
#include<algorithm>
#include<cstring>
#include<queue>
#include<iostream>
#include<stack>
#include<map>
#include<string>
using namespace std;
int main(){
    int n, x, a, m;
    scanf("%d", &n);
    while(n--){
        bool flag = true;
        scanf("%d%d", &a, &m);
        for(x = 1; x <= m; x++){
            if((a*x)%m == 1%m){
                flag = false;
                printf("%d
", x);
                break;
            }
        }
        if(flag){
            printf("Not Exist
");
        }
    }
    return 0;
}