bzoj 1079: [SCOI2008]着色方案

思路：按个数分类dp

#include<bits/stdc++.h>
#define LL long long
#define fi first
#define se second
#define mk make_pair
#define pii pair<int,int>
#define piii pair<int, pair<int,int> >

using namespace std;

const int N = 16;
const int M = 10 + 7;
const int inf = 0x3f3f3f3f;
const LL INF = 0x3f3f3f3f3f3f3f3f;
const int mod = 1e9 + 7;

int n, cur, sum, num[6];
int dp[2][6][N][N][N][N][N];

void add(int &a, int b) {
    a += b; if(a >= mod) a-= mod;
}
int main() {
    scanf("%d", &n);
    for(int i = 1; i <= n; i++) {
        int x; scanf("%d", &x);
        num[x]++;
        sum += x;
    }
    dp[cur][0][num[1]][num[2]][num[3]][num[4]][num[5]] = 1;

    for(int i = 0; i < sum; i++) {
        cur ^= 1;
        for(int j = 0; j <= 5; j++)
            for(int a = 0; a <= n; a++)
                for(int b = 0; b <= n; b++)
                    for(int c = 0; c <= n; c++)
                        for(int d = 0; d <= n; d++)
                            for(int e = 0; e <= n; e++)
                                dp[cur][j][a][b][c][d][e] = 0;

        for(int j = 0; j <= 5; j++) {
            for(int a = 0; a <= n; a++) {
                for(int b = 0; b <= n; b++) {
                    for(int c = 0; c <= n; c++) {
                        for(int d = 0; d <= n; d++) {
                            for(int e = 0; e <= n; e++) {
                                if(!dp[cur ^ 1][j][a][b][c][d][e]) continue;
                                if(e) {
                                    LL cnt = e - (5 == j);
                                    add(dp[cur][4][a][b][c][d + 1][e - 1], 1ll * dp[cur ^ 1][j][a][b][c][d][e] * cnt % mod);
                                }

                                if(d) {
                                    LL cnt = d - (4 == j);
                                    add(dp[cur][3][a][b][c + 1][d - 1][e], 1ll * dp[cur ^ 1][j][a][b][c][d][e] * cnt % mod);
                                }

                                if(c) {
                                    LL cnt = c - (3 == j);
                                    add(dp[cur][2][a][b + 1][c - 1][d][e], 1ll * dp[cur ^ 1][j][a][b][c][d][e] * cnt % mod);
                                }

                                if(b) {
                                    LL cnt = b - (2 == j);
                                    add(dp[cur][1][a + 1][b - 1][c][d][e], 1ll * dp[cur ^ 1][j][a][b][c][d][e] * cnt % mod);
                                }

                                if(a) {
                                    LL cnt = a - (1 == j);
                                    add(dp[cur][0][a - 1][b][c][d][e], 1ll * dp[cur ^ 1][j][a][b][c][d][e] * cnt % mod);
                                }
                            }
                        }
                    }
                }
            }
        }
    }
    int ans = dp[cur][0][0][0][0][0][0];
    printf("%d
", ans);
    return 0;
}
/*
*/