The method of seeking multiplicative inverse (four kinds)

First, the extended Euclidean inverse yuan

Board O (logN):

 1 #include<bits/stdc++.h>
 2 typedef long long ll;
 3 ll exgcd(ll a,ll b,ll &x,ll &y) {
 4     if(!b) {
 5         x=1,y=0;
 6         return a;
 7     }
 8     ll res=exgcd(b,a%b,y,x);
 9     y-=a/b*x;       ///x=x1,y=x1-a/b*y1   x1,y1代表下一状态
10     return res;
11 }
12 int main()
13 {
14     ll a,p,x,y;  /// extended Euclidean inverse element calculation of a (P MOD) 
15      Scanf ( " %% LLD LLD " , & a, & P);
 16      LL D = exgcd (a, P, X, Y);
 . 17      the printf (D == 1 ? " % LLD " : " -1 " , (X + P)% P); /// greatest common denominator is not 1, the inverse does not exist, the output of -1 
18 is      return  0 ;
 . 19 }

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Second, Fermat's little theorem inverse yuan (p is a prime number)

Board O (logp):

 1 #include<bits/stdc++.h>
 2 typedef long long ll;
 3 ll quickpowmod(ll a,ll b,ll mod) {
 4     ll ans=1;
 5     while(b) {
 6         if(b&1) ans=(ans*a)%mod;
 7         b>>=1;
 8         a=(a*a)%mod;
 9     }
10     return ans;
11 }
12 int main()
13 {
14     ll a,p;  ///费马小定理计算a的逆元（mod p）
15     scanf("%lld%lld",&a,&p);
16     ll inva=quickpowmod(a,p-2,p);
17     printf("%lld",inva);
18     return 0;
19 }

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