<p>Given an integer <code>n</code>, return <em>the least number of perfect square numbers that sum to</em> <code>n</code>.</p>

<p>A <strong>perfect square</strong> is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, <code>1</code>, <code>4</code>, <code>9</code>, and <code>16</code> are perfect squares while <code>3</code> and <code>11</code> are not.</p>

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

<pre>
<strong>Input:</strong> n = 12
<strong>Output:</strong> 3
<strong>Explanation:</strong> 12 = 4 + 4 + 4.
</pre>

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

<pre>
<strong>Input:</strong> n = 13
<strong>Output:</strong> 2
<strong>Explanation:</strong> 13 = 4 + 9.
</pre>

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

<ul>
	<li><code>1 &lt;= n &lt;= 10<sup>4</sup></code></li>
</ul>

class Solution {
public:
    int f(int n,int t,vector<vector<int>>& dp){
        
        if(t==0){
            return 0;
        }
        
        if(n==0){
            return INT_MAX;
        }
        
        if(dp[n][t]!=-1){
            return dp[n][t];
        }
        
        int p=INT_MAX;
        int np=f(n-1,t,dp);
        
        if(n*n<=t){
            p=f(n,t-n*n,dp);
            
            if(p!=INT_MAX)
                p++;
        }
        
        return dp[n][t]=min(p,np);
    }
    int numSquares(int n) {
        float sqt=sqrt(n);
        
        if((int)sqt==sqt){
            return 1;
        }
        
        vector<vector<int>> dp((int)sqt+1,vector<int>(n+1,-1));
        return f((int)sqt,n,dp);
    }
};
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