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

<p>Initially, there are <code>n</code> stones in a pile. On each player&#39;s turn, that player makes a <em>move</em> consisting of removing <strong>any</strong> non-zero <strong>square number</strong> of stones in the pile.</p>

<p>Also, if a player cannot make a move, he/she loses the game.</p>

<p>Given a positive integer <code>n</code>, return <code>true</code> if and only if Alice wins the game otherwise return <code>false</code>, assuming both players play optimally.</p>

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

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> true
<strong>Explanation: </strong>Alice can remove 1 stone winning the game because Bob doesn&#39;t have any moves.</pre>

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

<pre>
<strong>Input:</strong> n = 2
<strong>Output:</strong> false
<strong>Explanation: </strong>Alice can only remove 1 stone, after that Bob removes the last one winning the game (2 -&gt; 1 -&gt; 0).
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> n = 4
<strong>Output:</strong> true
<strong>Explanation:</strong> n is already a perfect square, Alice can win with one move, removing 4 stones (4 -&gt; 0).
</pre>

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

<ul>
	<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>
</ul>

class Solution {
public:
    bool solve(int n, int turn, vector<vector<int>>& dp) {
        if (n == 0) {
            return false;
        }

        if (dp[n][turn] != -1) {
            return dp[n][turn];
        }

        bool canWin = false;
        for (int i = 1; i * i <= n; ++i) {

            if (turn == 1) {
                // If it's the Alice turn, he wins if Bob loses in next turn,ie
                // it returns false;
                if (!solve(n - (i * i), 0, dp)) {
                    canWin = true;
                    break;
                }
            } else {
                // If it's Bobs turn,he wins if alice loses in next turn ie it
                // returns false;
                if (!solve(n - (i * i), 1, dp)) {
                    canWin = true;
                    break;
                }
            }
        }

        dp[n][turn] = canWin;
        return canWin;
    }

    bool winnerSquareGame(int n) {
        vector<vector<int>> dp(n + 1, vector<int>(2, -1));
        return solve(n, 1, dp);
    }
};

31524