/*
 * @lc app=leetcode.cn id=312 lang=cpp
 *
 * [312] 戳气球
 */

// @lc code=start
class Solution {
public:
    int maxCoins(vector<int>& nums) {
        int n = nums.size();
        vector<vector<int> > dp (n + 2, vector<int>(n + 2));
        vector<int> val(n + 2);
        val[0] = 1;
        for (int i = 1; i < n + 1; ++i) {
            val[i] = nums[i - 1];
        }
        val[n + 1] = 1;

        for (int i = n - 1; i >= 0; --i) {
            for (int j = i + 2; j <= n + 1; ++j) {
                for (int k = i + 1; k < j; ++k) {
                    int sum = val[k] * val[i] * val[j];
                    sum += dp[i][k] + dp[k][j];
                    dp[i][j] = max(dp[i][j], sum);
                }
            }
        }
        return dp[0][n+1];
    }
};
// @lc code=end