Code : Remove Boxes

class Solution {
  public:
    int removeBoxes(vector<int> &boxes);
};

int Solution::removeBoxes(vector<int> &a) {
    int n = a.size();

    vector<vector<vector<int>>> dp(
        n + 1, vector<vector<int>>(n + 1, vector<int>(n + 2, 0)));

    // dp[i][j][f] is the maximum points for the subarray [i...j]
    // when f boxes with color a[i] are added at the start.

    for (int i = n - 1; i >= 0; i--) {
        for (int j = i; j < n; j++) {
            for (int f = 0; f <= n; f++) {
                int nf = f + 1;

                // Collapse whatever has been accumulated so far.
                dp[i][j][f] = nf * nf + dp[i + 1][j][0];

                // Merge it with an identical colored box.
                for (int k = i + 1; k <= j; k++) {
                    if (a[i] != a[k]) {
                        continue;
                    }
                    dp[i][j][f] =
                        max(dp[i][j][f], dp[i + 1][k - 1][0] + dp[k][j][nf]);
                }
            }
        }
    }

    return dp[0][n - 1][0];
}