Codeforces 1107 E

E - Vasya and Binary String

思路：区间dp + 记忆化搜索

转移方程看上一篇博客。

代码：

#pragma GCC optimize(2)
#pragma GCC optimize(3)
#pragma GCC optimize(4)
#include<bits/stdc++.h>
using namespace std;
#define fi first
#define se second
#define y1 y11
#define pi acos(-1.0)
#define LL long long
//#define mp make_pair
#define DEBUG
#define pb push_back
#define ls rt<<1, l, m
#define rs rt<<1|1, m+1, r
#define ULL unsigned LL
#define pll pair<LL, LL>
#define pli pair<LL, int>
#define pii pair<int, int>
#define piii pair<pii, int>
#define pdd pair<long double, long double>
#define mem(a, b) memset(a, b, sizeof(a))
#define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define fopen freopen("in.txt", "r", stdin);freopen("out.txt", "w", stout);
//head

const int N = 105;
LL dp[N][N][N];
string s;
int a[N];
LL dfs(int l, int r, int k) {
    if(l > r) return 0;
    if(l == r) return a[k+1];
    if(~dp[l][r][k]) return dp[l][r][k];
    dp[l][r][k] = dfs(l, r-1, 0) + a[k+1];
    for (int i = l; i < r; i++) {
        if(s[i] == s[r]) {
            dp[l][r][k] = max(dp[l][r][k], dfs(i+1, r-1, 0) + dfs(l, i, k+1));
        }
    }
    return dp[l][r][k];
}
int main() {
    fio;
    int n;
    cin >> n;
    cin >> s;
    for (int i = 1; i <= n; ++i) cin >> a[i];
    mem(dp, -1);
    cout << dfs(0, n-1, 0) << endl;
    return 0;
}