Codeforces 1107E Vasya and Binary String——dp

参考poj1390

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int maxn = 105;
int n;
char s[maxn];
int a[maxn];
int c[maxn], len[maxn], cnt;
ll f[maxn][maxn], cost[maxn];
ll dp[maxn][maxn][maxn];

ll calf(int i, int j) {
    if (f[i][j] != -1) return f[i][j];
    if (j == 1) return a[i];
    if (j == i) return 1LL * i * a[1];
    for (int k = 1; k <= i - j + 1; k++) {
        f[i][j] = max(f[i][j], calf(i-k, j-1) + cost[k]);
    }
    return f[i][j];
}

ll caldp(int i, int j, int k) {
    if (dp[i][j][k] != -1) return dp[i][j][k];
    if (i == j) return cost[len[j] + k];
    ll ans = caldp(i, j-1, 0) + cost[len[j] + k];
    for (int t = i; t < j; t++) {
        if (c[t] == c[j]) {
            ans = max(ans, caldp(i, t, len[j] + k) + caldp(t+1, j-1, 0));
        }
    }
    return dp[i][j][k] = ans;
}

int main() {
    scanf("%d", &n);
    scanf("%s", s);
    for (int i = 1; i <= n; i++) {
        scanf("%d", &a[i]);
    }
    cnt = 1;
    c[cnt] = s[0] - '0';
    len[cnt] = 1;
    for (int i = 1; s[i]; i++) {
        if (s[i] == s[i-1]) {
            len[cnt]++;
        }
        else {
            cnt++;
            c[cnt] = s[i] - '0';
            len[cnt] = 1;
        }
    }
    memset(f, -1, sizeof(f));
    for (int i = 1; i <= n; i++) {
        cost[i] = a[i];
        for (int j = 1; j <= i; j++) {
            cost[i] = max(cost[i], calf(i, j));
        }
    }
    memset(dp, -1, sizeof(dp));
    printf("%lld\n", caldp(1, cnt, 0));
    return 0;
}