[BZOJ 1004][HNOI2008]Cards
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肉肉肉肉,,,
碰置换群啥的不是第一次了……这个题就是给你一堆置换(不要忘记还有一个幺元啊),然后限制颜色数量,求本质不同解个数。那么考虑使用Burnside引理,接下来考虑怎么计算每个置换的不动点数量,这个要求每个循环的颜色一致(不就事Polya定理了吗),所以说可以用背包DP搞一搞。
代码:
/**************************************************************
Problem: 1004
User: danihao123
Language: C++
Result: Accepted
Time:156 ms
Memory:3172 kb
****************************************************************/
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <algorithm>
#include <utility>
#include <vector>
int sr, sb, sg, m, p;
int pow_mod(int a, int b) {
int ans = 1, res = a;
while(b) {
if(1 & b) ans = (ans * res) % p;
res = (res * res) % p; b >>= 1;
}
return ans;
}
int inv(int x) {
return pow_mod(x % p, p - 2);
}
int d[65][21][21][21];
std::vector<int> len;
int dp() {
int n = len.size();
d[0][0][0][0] = 1;
for(int i = 1; i <= n; i ++) {
int l = len[i - 1];
for(int j = 0; j <= sr; j ++) {
for(int k = 0; k <= sb; k ++) {
for(int t = 0; t <= sg; t ++) {
d[i][j][k][t] = 0;
if(j >= l) d[i][j][k][t] += d[i - 1][j - l][k][t];
if(k >= l) d[i][j][k][t] += d[i - 1][j][k - l][t];
if(t >= l) d[i][j][k][t] += d[i - 1][j][k][t - l];
d[i][j][k][t] %= p;
}
}
}
}
return d[n][sr][sb][sg];
}
int next[65]; bool vis[65];
int main() {
scanf("%d%d%d%d%d", &sr, &sb, &sg, &m, &p);
int n = sr + sb + sg;
int ans = 0;
for(int i = 1; i <= n; i ++) {
len.push_back(1);
}
ans = dp();
for(int i = 1; i <= m; i ++) {
memset(vis, 0, sizeof(vis));
for(int i = 1; i <= n; i ++) {
scanf("%d", &next[i]);
}
len.clear();
for(int i = 1; i <= n; i ++) {
if(!vis[i]) {
int p = i, cnt = 0;
do {
vis[p] = true; cnt ++;
p = next[p];
} while(p != i);
len.push_back(cnt);
}
}
ans = (ans + dp()) % p;
}
ans = (ans * inv(m + 1)) % p;
printf("%d\n", ans);
return 0;
}
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