【BZOJ】【P1004】【HNOI2008】【Cards】【题解】【Burnside引理+dp】

传送门：http://www.lydsy.com/JudgeOnline/problem.php?id=1004

等价类计数用Burnside定理,需要计算不动点个数

dp计算

Code:

#include<bits/stdc++.h>using namespace std;typedef long long LL;int Sa,Sb,Sc,m,n;LL p;int N;int w[3601],fac[101];int dp[21][21][21],a[61];int power(int x,int k,int p){int ans=1;for(;k;k>>=1){if(k&1)ans=(ans*x)%p;x=(x*x)%p;}return ans;}int inv(int x){return power(x,p-2,p);}int ans;int main(){cin>>Sa>>Sb>>Sc>>m>>p;n=Sa+Sb+Sc;fac[0]=1;for(int i=1;i<=n;i++)fac[i]=fac[i-1]*i%p;ans=fac[n]*inv(fac[Sa])%p*inv(fac[Sb])*inv(fac[Sc])%p;for(int i=1;i<=m;i++){for(int j=1;j<=n;j++)scanf("%d",&a[j]);int vis[61];memset(vis,0,sizeof vis);for(int j=1;j<=n;j++){if(!vis[j]){N++;for(int x=j;!vis[x];x=a[x]){vis[x]=1;w[N]++;}}}}dp[0][0][0]=1;for(int i=1;i<=N;i++)for(int j=Sa;j>=w[i];j--)for(int k=Sb;k>=w[i];k--)for(int l=Sc;l>=w[i];l--)dp[j][k][l]+=dp[j-w[i]][k][l]+dp[j][k-w[i]][l]+dp[j][k][l-w[i]],dp[j][k][l]%=p;cout<<(LL)(ans+dp[Sa][Sb][Sc])*inv(m+1)%p<<endl;return 0;}