bzoj 1272: [BeiJingWc2008]Gate Of Babylon （容斥原理+Lucas定理）

题目描述

传送门

题解

代码

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
#define LL long long
using namespace std;
LL n,m,t,p,a[20];
LL jc[1000003],inv[1000003];
LL quickpow(LL num,int x)
{
LL base=num%p; LL ans=1;
while (x) {
if (x&1) ans=ans*base%p;
x>>=1;
base=base*base%p;
}
return ans;
}
LL C(LL n,LL m)
{
return jc
*inv[m]%p*inv[n-m]%p;
}
LL calc(LL n,LL m)
{
if (m==0) return 1;
return calc(n/p,m/p)*C(n%p,m%p)%p;
}
int main()
{
freopen("a.in","r",stdin);
//freopen("my.out","w",stdout);
scanf("%lld%lld%lld%lld",&n,&t,&m,&p); jc[0]=1;
for (LL i=1;i<=p;i++) jc[i]=(LL)jc[i-1]*i%p;
for (LL i=0;i<=p;i++) inv[i]=quickpow(jc[i],p-2);
for (LL i=1;i<=t;i++) scanf("%lld",&a[i]);
LL ans=0;
for (int i=0;i<(1<<t);i++){
LL sum=0; int cnt=0;
for (int j=0;j<t;j++)
if ((i>>j)&1) sum+=(a[j+1]+1),cnt++;
if (sum>m) continue;
sum=m-sum;
LL c=calc(n+sum,n);
//if (c<0) cout<<"!"<<endl;
//  cout<<c<<endl;
//cout<<n+sum<<" "<<n<<" "<<c<<endl;
if (cnt&1) ans=(ans-c+p)%p;
else ans=(ans+c)%p;
}
printf("%lld\n",(ans%p+p)%p);
}