51NOD 1452 - 加括号

DP预处理每个区间的值，再枚举括号位置就好了

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N = 5005;
char s[N];
int pre[N], nxt[N], n;
ll dp[N][N];
void init() {
    pre[0] = 0;
    for (int i = 1; i <= n; i++)
        if (s[i] == '+') pre[i] = i;
        else pre[i] = pre[i-1];
    nxt[n+1] = n+1;
    for (int i = n; i >= 1; i--)
        if (s[i] == '+') nxt[i] = i;
        else nxt[i] = nxt[i+1];
    for (int i = 1; i <= n; i += 2) dp[i][i] = s[i]-'0';
    for (int l = 3; l <= n; l += 2) {
        for (int i = 1; i <= n-l+1; i += 2) {
            int j = i+l-1;
            if (pre[j] < i) dp[i][j] = dp[i][j-2]*(s[j]-'0');
            else dp[i][j] = dp[i][pre[j]-1] + dp[pre[j]+1][j];
        }
    }
}
int main() {
    scanf("%s", s+1);
    n = strlen(s+1);
    init();
    ll ans = dp[1][n];
    for (int i = 1; i <= n; i += 2) {
        for (int j = i+2; j <= n; j += 2) {
            if (s[i-1] != '*' && s[j+1] != '*') continue;
            ll res = 0;
            if (pre[i] > 0) res += dp[1][pre[i]-1];
            if (nxt[j] < n+1) res += dp[nxt[j]+1][n];
            ll tmp = dp[i][j];
            if (pre[i]+1 <= i-2) tmp *= dp[pre[i]+1][i-2];
            if (nxt[j]-1 >= j+2) tmp *= dp[j+2][nxt[j]-1];
            res += tmp;
            ans = max(ans, res);
        }
    }
    printf("%lld\n", ans);
}