Pots of Gold Game

Two players X and Y are playing a game in which there are pots of gold arranged in a line, each containing some gold coins. They get alternating turns in which the player can pick a pot from one of the ends of the line. The winner is the player who has a higher number of coins at the end. The objective is to maximize the number of coins collected by X, assuming Y also plays optimally.

Return the maximum coins X could get while playing the game. Initially, X starts the game.

• Time : O(n^2)
• Space : O(n^2)

class Solution {
    int dp[505][505];
    int helper(vector<int>& A, int l, int r) {
        if(l > r) return 0;
        if(dp[l][r] != -1) return dp[l][r];
        int& res = dp[l][r] = INT_MIN;
        res = max(res, A[l] - helper(A, l + 1, r));
        res = max(res, A[r] - helper(A, l, r - 1));
        return res;
    }
public:
    int maxCoins(vector<int>&A,int n)
    {
        memset(dp, -1, sizeof dp);
        return (helper(A, 0, n - 1) + accumulate(begin(A), end(A), 0)) / 2;
    }