DP preprocesses the value of each interval, and then enumerates the bracket positions.
#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;
years = max(years, res);
}
}
printf("%lld\n", ans);
}