HDU 5151 Sit sit sit（区间DP)

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HDU 5151 Sit sit sit

题目链接

区间DP+组合计数问题，转移方程为，每次选当前区间最后一个放的位置，然后乘上组合数C[区间长度][左区间长度]

代码：

#include <cstdio>#include <cstring>typedef long long ll;const ll MOD = 1000000007;const int N = 105;int n, a[N];ll dp[N][N], C[N][N];int main() {    C[1][0] = C[1][1] = 1;    for (int i = 2; i <= 100; i++) {C[i][0] = C[i][i] = 1;for (int j = 1; j < i; j++) {    C[i][j] = (C[i - 1][j] + C[i - 1][j - 1]) % MOD;}    }    while (~scanf("%d", &n)) {for (int i = 1; i <= n; i++) scanf("%d", &a[i]);memset(dp, 0, sizeof(dp));for (int i = 1; i <= n; i++) dp[i][i] = 1;for (int len = 1; len < n; len++) {    for (int l = 1; l + len <= n; l++) {int r = l + len;for (int k = l; k <= r; k++) {    if (l == k) dp[l][r] = (dp[l][r] + dp[k + 1][r]) % MOD;    else if (r == k) dp[l][r] = (dp[l][r] + dp[l][k - 1]) % MOD;    else if (a[k - 1] == a[k + 1]) dp[l][r] = (dp[l][r] + (dp[l][k - 1] * dp[k + 1][r] % MOD * C[r - l][k - l]) % MOD) % MOD;}    }}printf("%lld\n", dp[1][n]);    }    return 0;}

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