<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,vector<vector<int>>&dp,vector<int>v,int i){
        if(n==0||i==0)
        return n;
        if(dp[i][n]!=-1) return dp[i][n];
        int notPick=f(n,dp,v,i-1);
        int pick=1e6;
        if(n>=v[i])
        pick= n/v[i] + f(n - (n/v[i])*v[i],dp,v,i); 
        return dp[i][n]=min(pick,notPick);
    }
    int numSquares(int n){
        // int sq_range=sqrt(n);
        // if(sq_range*sq_range==n) return 1;
        // vector<int>v(sq_range);
        // for(int i=1;i<=sq_range;i++)
        // v[i-1] = i*i;
        // vector<vector<int>>dp(sq_range,vector<int>(n+1,-1));
        // return f(n,dp,v,sq_range-1);
        int sq_range=sqrt(n);
        if(sq_range*sq_range==n) return 1;
        vector<int>v(sq_range);
        for(int i=1;i<=sq_range;i++)
        v[i-1] = i*i;
        vector<vector<int>>dp(sq_range,vector<int>(n+1));
        for(int i=0;i<=n;i++)
        dp[0][i]=i;
        for(int i=1;i<sq_range;i++){
            for(int j=0;j<=n;j++){
            int notPick=dp[i-1][j];
            int pick=1e6;
            if(j>=v[i])
            pick= j/v[i] + dp[i][j-(j/v[i])*v[i]]; 
            dp[i][j]=min(pick,notPick);
            }
        }
        return dp[sq_range-1][n];
    }
};
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