代码

#include <bits/stdc++.h>

using namespace std;

unsigned solve(int n, char *s) {
  vector<unsigned> dp = {1};
  for (int i = 0; i < n; ++i) {
    vector<unsigned> pd(min(i + 1, n - i - 1) / 2 + 1);
    if (s[i] != ')') {
      if (i & 1) {
        copy_n(dp.begin(), min(pd.size() - 1, dp.size()), pd.begin() + 1);
      } else {
        copy_n(dp.begin(), min(pd.size(), dp.size()), pd.begin());
      }
    }
    if (s[i] != '(') {
      if (i & 1) {
        for (int j = 0; j < min(pd.size(), dp.size()); ++j) {
          pd[j] += dp[j];
        }
      } else {
        for (int j = 1; j < min(pd.size() + 1, dp.size()); ++j) {
          pd[j - 1] += dp[j];
        }
      }
    }
    dp = pd;
  }
  return dp[0];
}

评测结果