标签：class using htm gcd floor include hit height space
1.扩展欧几里得：
void Exgcd(ll a, ll b, ll &x, ll &y) {
if (!b) x = 1, y = 0;
else Exgcd(b, a % b, y, x), y -= a / b * x;
}
int main() {
ll x, y;
Exgcd (a, p, x, y);
x = (x % p + p) % p;
printf ("%d\n", x); //x是a在mod p下的逆元
}
2.费马小定理+快速幂：
ll fpm(ll x, ll power, ll mod) {
x %= mod;
ll ans = 1;
for (; power; power >>= 1, (x *= x) %= mod)
if(power & 1) (ans *= x) %= mod;
return ans;
}
int main() {
ll x = fpm(a, p - 2, p); //x为a在mod p意义下的逆元
}
3.线性递推方程：
k∗i+r≡0(modp)
k∗(r的逆元)+(l的逆元)≡0(modp)
(l的逆元)≡−k∗(r的逆元)(modp)
(l的逆元)≡−⌊p/i?⌋∗((p%i)的逆元)(modp)
#include <bits/stdc++.h>
#define p 1000000007
using namespace std;
long long inv[100010];
int main()
{
int n;
cin>>n;
inv[1]=1;
for(int i=2;i<=n;i++){
inv[i]=(p-p/i)*inv[p%i]%p;
}
for(int i=1;i<=n;i++){
cout<<inv[i]<<" ";
}
}
另外，对于阶乘：inv[i+1]*(i+1)=inv[i]
标签：class using htm gcd floor include hit height space
原文地址：https://www.cnblogs.com/kamimxr/p/11634882.html
