<p>Alice and Bob play a game with piles of stones. There are an <strong>even</strong> number of piles arranged in a row, and each pile has a <strong>positive</strong> integer number of stones <code>piles[i]</code>.</p>

<p>The objective of the game is to end with the most stones. The <strong>total</strong> number of stones across all the piles is <strong>odd</strong>, so there are no ties.</p>

<p>Alice and Bob take turns, with <strong>Alice starting first</strong>. Each turn, a player takes the entire pile of stones either from the <strong>beginning</strong> or from the <strong>end</strong> of the row. This continues until there are no more piles left, at which point the person with the <strong>most stones wins</strong>.</p>

<p>Assuming Alice and Bob play optimally, return <code>true</code><em> if Alice wins the game, or </em><code>false</code><em> if Bob wins</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> piles = [5,3,4,5]
<strong>Output:</strong> true
<strong>Explanation:</strong> 
Alice starts first, and can only take the first 5 or the last 5.
Say she takes the first 5, so that the row becomes [3, 4, 5].
If Bob takes 3, then the board is [4, 5], and Alice takes 5 to win with 10 points.
If Bob takes the last 5, then the board is [3, 4], and Alice takes 4 to win with 9 points.
This demonstrated that taking the first 5 was a winning move for Alice, so we return true.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> piles = [3,7,2,3]
<strong>Output:</strong> true
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= piles.length &lt;= 500</code></li>
	<li><code>piles.length</code> is <strong>even</strong>.</li>
	<li><code>1 &lt;= piles[i] &lt;= 500</code></li>
	<li><code>sum(piles[i])</code> is <strong>odd</strong>.</li>
</ul>

class Solution {
private:
    int getAlicePts(int startInd, int endInd, bool aliceTurn, vector<int>& piles) {
        if (startInd > endInd) return 0;

        if (aliceTurn == true) {
            int takeStart = piles[startInd] + getAlicePts(startInd + 1, endInd, false, piles);
            int takeEnd = piles[endInd] + getAlicePts(startInd, endInd - 1, false, piles);

            return max(takeStart, takeEnd);
        } 
        else {
            int takeStart = 0 + getAlicePts(startInd + 1, endInd, true, piles);
            int takeEnd = 0 + getAlicePts(startInd, endInd - 1, true, piles);

            return min(takeStart, takeEnd);
        }
    }
public:
    bool stoneGame(vector<int>& piles) {
        int n = piles.size();
        vector<vector<vector<int>>> alicePts(n, vector<vector<int>>(n, vector<int>(2, 0)));

        for (int startInd = 0; startInd < n; startInd++) {
            alicePts[startInd][startInd][1] = piles[startInd];
        }
        
        for (int startInd = n - 1; startInd >= 0; startInd--) {
            for (int endInd = startInd + 1; endInd < n; endInd++) {
                for (int aliceTurn = 0; aliceTurn <= 1; aliceTurn++) {
                    if (aliceTurn == 1) {
                        int takeStart = piles[startInd] + alicePts[startInd + 1][endInd][0];
                        int takeEnd = piles[endInd] + alicePts[startInd][endInd - 1][0];

                        alicePts[startInd][endInd][aliceTurn] = max(takeStart, takeEnd);
                    } 
                    else {
                        int takeStart = 0 + alicePts[startInd + 1][endInd][1];
                        int takeEnd = 0 + alicePts[startInd][endInd - 1][1];

                        alicePts[startInd][endInd][aliceTurn] = min(takeStart, takeEnd);
                    }
                }
            }
        }

        int alicePoints = alicePts[0][n - 1][1];
        int bobPoints = accumulate(piles.begin(), piles.end(), 0) - alicePoints;

        return (alicePoints > bobPoints);
    }
};
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