bzoj1004 HNOI2008—Cards

Posted 2020-08-26 MashiroSky

http://www.lydsy.com/JudgeOnline/problem.php?id=1004 (题目链接)

题意

　　n张卡片，染成3种颜色，每种颜色只能染固定张数。给出一些洗牌方案，问染色方案数。

Solution

　　Burnside引理。

　　左转题解：LCF

代码

// bzoj1004
#include<algorithm>
#include<iostream>
#include<cstdlib>
#include<cstring>
#include<cstdio>
#include<cmath>
#define LL long long
#define inf 1<<30
#define Pi acos(-1.0)
#define free(a) freopen(a".in","r",stdin),freopen(a".out","w",stdout);
using namespace std;

const int maxn=100;
LL f[maxn][maxn][maxn],a[maxn],vis[maxn],size[maxn];
LL n,m,P,R,G,B;

LL power(LL a,LL b) {
	LL res=1;
	while (b) {
		if (b&1) res=res*a%P;
		a=a*a%P;b>>=1;
	}
	return res;
}
LL dp() {
	memset(vis,0,sizeof(vis));
	memset(f,0,sizeof(f));
	int cnt=0;
	for (int i=1;i<=n;i++) if (!vis[i]) {
			size[++cnt]=0;
			for (int j=a[i];!vis[j];j=a[j]) vis[j]=1,size[cnt]++;
		}
	f[0][0][0]=1;
	for (int i=1;i<=cnt;i++)
		for (int r=R;r>=0;r--)
			for (int b=B;b>=0;b--)
				for (int g=G;g>=0;g--) {
					if (r>=size[i]) f[r][b][g]=(f[r][b][g]+f[r-size[i]][b][g])%P;
					if (b>=size[i]) f[r][b][g]=(f[r][b][g]+f[r][b-size[i]][g])%P;
					if (g>=size[i]) f[r][b][g]=(f[r][b][g]+f[r][b][g-size[i]])%P;
				}
	return f[R][B][G]%P;
}
int main() {
	scanf("%lld%lld%lld%lld%lld",&R,&B,&G,&m,&P);
	n=R+B+G;LL ans=0;
	for (int i=1;i<=n;i++) a[i]=i;
	ans=(ans+dp())%P;
	for (int i=1;i<=m;i++) {
		for (int j=1;j<=n;j++) scanf("%lld",&a[j]);
		ans=(ans+dp())%P;
	}
	ans*=power(m+1,P-2);
	printf("%lld",ans%P);
	return 0;
}