leetcode 312. Burst Balloons

class Solution {
public:
    int maxCoins(vector<int>& nums) {
        int n = nums.size();
        nums.insert(nums.begin(),1);
        nums.push_back(1);
        vector<vector<int>> dp(n+2,vector<int>(n+2,0));
        for(int len = 1;len <= n;len++){
            for(int i = 1;i <= n - len + 1;i++){
                int j = i + len - 1;
                for(int k = i;k <= j;k++){
                    dp[i][j] = max(dp[i][j],nums[i-1]*nums[k]*nums[j+1] + dp[i][k-1] + dp[k+1][j]);
                }
            }
        }
        return dp[1][n];
    }
};