<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 dp[10000+1][10000+1];
bool f(int n){
    int b=sqrt(n);
    if(b*b==n)return true;
    return false;
}
int func(int n,int sum,int m, vector<vector<int>>&dp){
    if(sum>m)return 1e9;
    if(sum==m)return 0;
    if(n==0)return 1e9;
    if(dp[n][sum]!=-1)return dp[n][sum];
    // bool a=f(n);
    int b=1e9;
    int c=1e9;
    int d=1e9;
    //  b=func(n-1,sum,m,dp);
    // else {
      c=func(n-1,sum,m,dp);
      d=1+func(n,sum+n*n,m,dp);
    // }
    return dp[n][sum]=min(d,min(b,c));
}
    int numSquares(int n) {
        int m=n;
        if(f(n))return 1;
        vector<vector<int>>dp(sqrt(n)+1,vector<int>(n+1,-1));
        return func(sqrt(n),0,n,dp);
     
    }
};
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