<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 winnerSquareGame(int n) {
        vector<int> perfectSquares;

        for(int num = 1; num * num <= n; ++num)
            perfectSquares.push_back(num * num);
            
        vector<vector<bool>> dp(n + 1, vector<bool>(2, false));

        for(int num = 1; num <= n; ++num) {
            for(int aliceTurn = 0; aliceTurn <= 1; ++aliceTurn) {
                if(aliceTurn) {
                    bool canWin = false;
        
                    for(int sq : perfectSquares) {
                        if(sq > num) break;
                        canWin = (num - sq > 0) ? dp[num - sq][false] : true;
                        if(canWin) break;
                    }
        
                    dp[num][aliceTurn] = canWin;
                }
                else {
                    bool canWin = true;
        
                    for(int sq : perfectSquares) {
                        if(sq > num) break;
                        canWin = (num - sq > 0) ? dp[num - sq][true] : false;
                        if(!canWin) break;
                    }
        
                    dp[num][aliceTurn] = canWin;
                }
            }
        }

        return dp[n][true];
    }
};
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