扩展欧几里得算法和线性同余方程

1.扩展欧几里得算法

代码:

 1 #include <iostream>
 2 #include <cstdio>
 3 #include <cstring>
 4 #include <string.h>
 5 #include <math.h>
 6 #include <algorithm>
 7 #include <stack>
 8 #include <queue>
 9 #include <vector>
10 #include <map>
11 #include <set>
12 #define ll long long
13 const int N=1e6+10;
14 using namespace std;
15 typedef pair<int,int>PII;
16 
17 int exgcd(int a,int b,int &x1,int &y1){
18    if(b==0){
19      x1=1,y1=0;
20      return a;
21    }
22    int x2,y2;
23    int d=exgcd(b,a%b,x2,y2);
24    x1=y2,y1=x2-a/b*y2;
25    return d;
26 }
27 
28 int main(){
29  ios::sync_with_stdio(false);
30  int t;
31  cin>>t;
32   while(t--){
33    int a,b,x1,y1;
34    cin>>a>>b;
35     exgcd(a,b,x1,y1);
36     
37     printf("%d %d\n",x1,y1);
38   }
39   
40   return 0;
41 }

2.线性同余方程

代码:

 1 #include <iostream>
 2 #include <cstdio>
 3 #include <cstring>
 4 #include <cmath>
 5 #include <algorithm>
 6 #include <stack>
 7 #include <queue>
 8 #include <vector>
 9 #include <map>
10 #include <set>
11 #include <unordered_set>
12 #include <unordered_map>
13 #define ll long long
14 #define fi first
15 #define se second
16 #define pb push_back
17 #define me memset
18 const int N = 1e6 + 10;
19 const int mod = 1e9 + 7;
20 using namespace std;
21 typedef pair<int,int> PII;
22 typedef pair<long,long> PLL;
23 
24 int exgcd(int a,int b,int &x1,int &y1){
25     int x2,y2;
26     if(b==0){
27         x1=1,y1=0;
28         return a;
29     }
30     int d=exgcd(b,a%b,x2,y2);
31     x1=y2,y1=x2-a/b*y2;
32     return d;
33 }
34 
35 
36 int main() {
37     ios::sync_with_stdio(false);
38     int n;
39      cin>>n;
40       while(n--){
41         int a,b,m;
42         int x1,y1;
43           cin>>a>>b>>m;
44             int d=exgcd(a,m,x1,y1);
45             if(b%d) printf("impossible\n");
46             else printf("%lld\n",(ll)x1*(b/d)%m);
47       }
48 
49     return 0;
50 }