<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 solve(int n, vector<int> &arr,vector<int> &dp){ //is function se jo answer return ho rha hai...wo mera ek jyada ho rha hai..isliye jb mai is solution ka answer return krunga toh -1 krke krunga
        if(n < 0){
            return INT_MAX;
        }
        if(n == 0){
            return 1;
        }

        //already existing case
        if(dp[n] != -1){
            return dp[n];
        }

        int mini = INT_MAX;
        for(int i = 0; i < arr.size(); i++){
            n -= arr[i];
            int recKaAns = solve(n, arr,dp);
            if(recKaAns != INT_MAX){
            int ans = 1 + recKaAns;
            mini = min(ans, mini);
            }
            n += arr[i];
        } // Missing closing bracket here

        dp[n] = mini;
        return dp[n];
    }
    
    int numSquares(int n) {
        vector<int> arr;
        for(int i = 1; i <= n; i++){
            arr.push_back(i * i);
        }

        vector<int> arr2;
        for(int i = 0; i < arr.size(); i++){
            if(arr[i] <= n){
                arr2.push_back(arr[i]);
            } else if(arr[i] > n){
                break;
            }
        }

        vector<int>dp(n+1,-1);
        
        int ans = solve(n, arr2,dp);
        return ans-1;
    }
};

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