<p>Alice and Bob continue their games with piles of stones. There are a number of piles <strong>arranged in a row</strong>, and each pile has a positive integer number of stones <code>piles[i]</code>. The objective of the game is to end with the most stones.</p>

<p>Alice and Bob take turns, with Alice starting first.</p>

<p>On each player&#39;s turn, that player can take <strong>all the stones</strong> in the <strong>first</strong> <code>X</code> remaining piles, where <code>1 &lt;= X &lt;= 2M</code>. Then, we set <code>M = max(M, X)</code>. Initially, M = 1.</p>

<p>The game continues until all the stones have been taken.</p>

<p>Assuming Alice and Bob play optimally, return the maximum number of stones Alice can get.</p>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">piles = [2,7,9,4,4]</span></p>

<p><strong>Output:</strong> <span class="example-io">10</span></p>

<p><strong>Explanation:</strong></p>

<ul>
	<li>If Alice takes one pile at the beginning, Bob takes two piles, then Alice takes 2 piles again. Alice can get <code>2 + 4 + 4 = 10</code> stones in total.</li>
	<li>If Alice takes two piles at the beginning, then Bob can take all three piles left. In this case, Alice get <code>2 + 7 = 9</code> stones in total.</li>
</ul>

<p>So we return 10 since it&#39;s larger.</p>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">piles = [1,2,3,4,5,100]</span></p>

<p><strong>Output:</strong> <span class="example-io">104</span></p>
</div>

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

<ul>
	<li><code>1 &lt;= piles.length &lt;= 100</code></li>
	<li><code>1 &lt;= piles[i]&nbsp;&lt;= 10<sup>4</sup></code></li>
</ul>

class Solution {
    public:
        int f(int p, int i, int m, int n, vector<int>& piles, vector<vector<vector<int>>>& dp) {
                if (i >= n) {
                            return 0;
                                    }
                                            if (dp[p][i][m] != -1) {
                                                        return dp[p][i][m];
                                                                }
                                                                        int stones = 0;
                                                                                int maxi = (p == 0) ? -1 : INT_MAX; // Alice wants to maximize, Bob wants to minimize

                                                                                        for (int x = 1; x <= min(2 * m, n - i); x++) {
                                                                                                    stones += piles[i + x - 1]; // Accumulate stones picked in this move

                                                                                                                if (p == 0) {
                                                                                                                                // Alice's turn
                                                                                                                                                maxi = max(maxi, stones + f(1, i + x, max(m, x), n, piles, dp));
                                                                                                                                                            } else {
                                                                                                                                                                            // Bob's turn
                                                                                                                                                                                            maxi = min(maxi, f(0, i + x, max(m, x), n, piles, dp));
                                                                                                                                                                                                        }
                                                                                                                                                                                                                }
                                                                                                                                                                                                                        return dp[p][i][m] = maxi;
                                                                                                                                                                                                                            }

                                                                                                                                                                                                                                int stoneGameII(vector<int>& piles) {
                                                                                                                                                                                                                                        int n = piles.size();
                                                                                                                                                                                                                                                vector<vector<vector<int>>> dp(2, vector<vector<int>>(n + 1, vector<int>(n + 1, -1)));
                                                                                                                                                                                                                                                        return f(0, 0, 1, n, piles, dp);
                                                                                                                                                                                                                                                            }
                                                                                                                                                                                                                                                            };






15568