<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::optional<int> explore(int target, const set<int>& squares, unordered_map<int, int>& dp) {
        if(target < 0) return -1;
        if(squares.count(target))
            return 1;
        auto it = dp.find(target);
        if(it != dp.end()) return it->second == -1 ? std::optional<int>() : it->second;

        int range_max = sqrt(target) + 1;
        std::optional<int> minCount;
        auto sIt = squares.rbegin();
        while(sIt != squares.rend() ) {
            std::optional<int> res = explore(target - *sIt, squares, dp);
            if(res && res.value() >= 0) {
                if (!minCount)
                    minCount = INT_MAX;
                minCount = std::min(minCount.value(), res.value());
            }
            sIt++;
        }

        dp[target] = minCount ? minCount.value() + 1 : -1;
        return dp[target];
    }

public:
    int numSquares(int n) {
        int max_range = sqrt(n) + 1;
        std::set<int> squares;

        for(int i = 1; i <= max_range; ++i)
            squares.insert(i*i);

        unordered_map<int, int> dp;
        
        return explore(n, squares, dp).value();
    }
};
45113