ACM常用模板合集
代码语言：javascript复制#include<cstdio>
const int N = 2000 5;
const int MOD = (int)1e9 7;
int comb[N][N];//comb[n][m]就是C(n,m)
void init(){
for(int i = 0; i < N; i ){
comb[i][0] = comb[i][i] = 1;
for(int j = 1; j < i; j ){
comb[i][j] = comb[i-1][j] comb[i-1][j-1];
comb[i][j] %= MOD;
}
}
}
int main(){
init();
} Lucas
代码语言：javascript复制#include<iostream>
using namespace std;
typedef long long LL;
const LL N=1e5 2;
LL a[N];
void init(LL p)
{
a[1]=1;
for(int i=2;i<=p; i)a[i]=a[i-1]*i%p;
}
void exgcd(LL a,LL b,LL &x,LL &y)
{
if(!b){
x=1;
y=0;
return;
}
exgcd(b,a%b,y,x);
y-=a/b*x;
}
LL ksm(LL x,LL n,LL mod)
{
LL ans=1;
while(n){
if(n&1)ans=ans*x%mod;
n>>=1;
x=x*x%mod;
}
return ans;
}
LL C(LL n,LL m,LL p)
{
if(n==m||m==0)return 1;
if(n<m)return 0;
if(m*2>n)m=n-m; /*C(n,m)=c(n,n-m)*/
return a[n]*ksm(a[m]*a[n-m],p-2,p)%p; /*求(a[m]*a[n-m])在(mod p)意义下的乘法逆元*/
/*拓展欧几里得与费马小定理均可*/
/*LL x,y;
exgcd(a[m]*a[n-m],p,x,y);
return (a[n]*x%p p)%p;*/
}
LL lucas(LL n,LL m,LL p)
{
if(!m)return 1;
return lucas(n/p,m/p,p)*C(n%p,m%p,p)%p;
}
int main()
{
ios::sync_with_stdio(false);
LL T,n,m,p;
cin>>T;
while(T--){
cin>>n>>m>>p;
init(p);
cout<<lucas(n m,m,p)<<endl;
}
return 0;
}ExLucas
代码语言：javascript复制#include<bits/stdc .h>
using namespace std;
typedef long long LL;
const LL N=1e5 9;
LL A[N],M[N];
LL ksm(LL x,LL n,LL mod)
{
LL ans=1;
while(n){
if(n&1)ans=ans*x%mod;
n>>=1,x=x*x%mod;
}
return ans;
}
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;
}
LL inv(LL a,LL p)
{
LL x,y;
exgcd(a,p,x,y);
return (x p)%p?x:x p;
}
LL get(LL n,LL pi,LL p) /*求(与pi互素后的n!)%M[i]*/
{
if(!n)return 1;
LL ans=1;
if(n/p){ /*判断有无循环节 */
for(LL i=2;i<=p; i)if(i%pi)ans=ans*i%p;
ans=ksm(ans,n/p,p);
}
for(LL i=2;i<=n%p; i)if(i%pi)ans=ans*i%p; /*循环节剩余部分*/
return ans*get(n/pi,pi,p)%p;
}
LL exlucas(LL n,LL m,LL pi,LL p) /*求A[i]*/
{
LL nn=get(n,pi,p); /*求(与pi互素后的n)%M[i]*/
LL mm=get(m,pi,p); /*求(m!与pi互素后的m!)%M[i]*/
LL nm=get(n-m,pi,p); /*求(与pi互素后的(n-m)!)%M[i]*/
LL k=0; /*含质因数pi的数量*/
for(LL i=n;i;i/=pi)k =i/pi;
for(LL i=m;i;i/=pi)k-=i/pi;
for(LL i=n-m;i;i/=pi)k-=i/pi;
return nn*inv(mm,p)*inv(nm,p)*ksm(pi,k,p)%p;
}
LL crt(LL len,LL Lcm)
{
LL ans=0;
for(LL i=1;i<=len; i){
LL Mi=Lcm/M[i];
ans=((ans A[i]*inv(Mi,M[i])*Mi)%Lcm Lcm)%Lcm;
}
return ans;
}
int main()
{
ios::sync_with_stdio(false);
LL n,m,P,num;
while(cin>>n>>m>>P){
if(n<m){
cout<<0<<endl;
continue;
}
num=0;
memset(A,0,sizeof(A));
memset(M,0,sizeof(M));
for(LL x=P,i=2;i<=P; i)
if(x%i==0){
M[ num]=1;
while(x%i==0){
M[num]*=i;
x/=i;
}
A[num]=exlucas(n,m,i,M[num])%P;
}
cout<<crt(num,P)<<endl;
}
return 0;
}
