<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 {
    std::unordered_map<int, int> leastNum;
    
    int helper(int n, const std::vector<int>& nums, int maxIdx)
    {
        if(auto itr = leastNum.find(n); itr != leastNum.end())
            return itr->second;
        
        int ans = 100000;
        for (auto i = maxIdx; i < nums.size(); ++i)
        {
            if (nums[i] <= n)
                ans = std::min(ans, 1 + helper(n-nums[i], nums, i));
        }
        
        leastNum.insert({n, ans});
        return ans;
    }
public:
    int numSquares(int n) {
        std::vector<int> nums;
        for(int i=1; i*i <=n; ++i)
        {
            nums.push_back(i*i);
            leastNum.insert({i*i, 1});
                
        }
        
        return helper(n, nums, 0);
        
    }
};
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