【AHOI2009】中国象棋

【题目链接】

点击打开链接

【算法】

动态规划

f[i][j][k]表示前i行，有j列放了1个，有k列放了两个

分六种情况讨论即可

【代码】

#include<bits/stdc++.h>
using namespace std;
#define MAXN 110
const long long MOD = ;

long long i,j,k,n,m,ans;
long long dp[MAXN][MAXN][MAXN];

template <typename T> inline void read(T &x) {
        int f = ; x = ;
        char c = getchar();
        for (; !isdigit(c); c = getchar()) { if (c == '-') f = -f; }
        for (; isdigit(c); c = getchar()) x = (x << ) + (x << ) + c - '';
        x *= f;
}
template <typename T> inline void write(T x) {
    if (x < ) { putchar('-'); x = -x; }
    if (x > ) write(x/);
    putchar(x%+'');
}
template <typename T> inline void writeln(T x) {
    write(x);
    puts("");
}

int main() {

        read(n); read(m);

        dp[][][] = ;
        for (i = ; i <= n; i++) {
                for (j = ; j <= m; j++) {
                        for (k = ; k <= m - j; k++) {
                                dp[i][j][k] = dp[i-][j][k];
                                if (j) dp[i][j][k] += dp[i-][j-][k] * (m - j - k + );
                                if (j < m && k) dp[i][j][k] += dp[i-][j+][k-] * (j + );
                                if (j && k) dp[i][j][k] += dp[i-][j][k-] * j * (m - j - k + );
                                if (j >= ) dp[i][j][k] += dp[i-][j-][k] * (m - j - k + ) * (m - j - k + ) >> ;
                                if (j +  <= m && k >= ) dp[i][j][k] += dp[i-][j+][k-] * (j + ) * (j + ) >> ;
                                dp[i][j][k] %= MOD;
                        }
                }
        }
        for (i = ; i <= m; i++) {
                for (j = ; j <= m - i; j++) {
                        ans = (ans + dp[n][i][j]) % MOD;
                }
        }
        writeln(ans);

        return ;

}