uva 1362 - Exploring Pyramids(区间dp)

题目连接:uva 1362 - Exploring Pyramids

题目大意：给出一个字符串，问有多少种多叉树德前序遍历（这里每经过一个节点，该节点的值即要被算入，回溯的也要）满足该字符串。

解题思路：dp[i][j]表示从i到j的位置可以用多少种多叉树表示。转移方程：dp[i][j]=∑k=i+2jdp[i+1][k−1]∗dp[k][j]。

#include <cstdio>
#include <cstring>

typedef long long ll;
const int N = 305;
const ll MOD = 1e9;

char s[N];
ll dp[N][N];

ll solve (int x, int y) {

    if (x == y)
        return dp[x][y] = 1;

    if (s[x] != s[y])
        return dp[x][y] = 0;

    ll& ans = dp[x][y];

    if (ans >= 0)
        return ans;
    ans = 0;

    for (int i = x+2; i <= y; i++) {
        if (s[x] == s[i])
            ans = (ans + solve(x+1, i-1) * solve(i, y))%MOD;
    }
    return ans;
}

int main () {
    while (scanf("%s", s) == 1) {
        memset(dp, -1, sizeof(dp));
        printf("%lld\n", solve(0, strlen(s)-1));
    }
    return 0;
}