<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 isSquareNumber(int n) {
    if (n < 0) {
        return false;
    }
    int sqrt_n = static_cast<int>(sqrt(n));
    return sqrt_n * sqrt_n == n;
    }

   
    bool winnerSquareGame(int n) {
        unordered_map<int,bool> um;
        um[1]=true;
        um[2]=false;
        um[3]=true;
        vector<int> ps;
        ps.push_back(1);
        for(int i=4;i<=n;i++)
        {
            if(isSquareNumber(i))
            {
                um[i]=true;
                ps.push_back(i);
            }
            else
            {
                bool flag=false;
                for(int j=0;j<ps.size();j++)
                {
                    
                    if(um.find(i-ps[j])!=um.end() && um[i-ps[j]]==false)
                    {
                       flag=true;
                       break;
                    }
                }
                um[i]=flag;
            }
        }
        // for(int i=1;i<=n;i++)
        //     cout<<i<<" "<<um[i]<<endl;

        return um[n];
    }
};
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