<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>

#include <array>
#include <cstddef> // For std::size_t

// constexpr function to calculate the square of a number
constexpr int square(int n) {
    return n * n;
}

// Generate an array of squares from 1 to 10000 at compile-time
constexpr std::array<int, 10000> generateSquareArray() {
    std::array<int, 10000> squares = {};
    for (std::size_t i = 0; i < squares.size(); ++i) {
        squares[i] = square(static_cast<int>(i) + 1);
    }
    return squares;
}

// Array of squares, calculated at compile-time
constexpr std::array<int, 10000> c_squares = generateSquareArray();


class Solution {
public:
    int numSquares(int n) {
        vector<int> dp(n+1, INT_MAX);
        dp[0] = 0;
    
        int maxSqrtIdx = ceil(sqrt(n)) + 1;
        vector<int> squares(10000, 0);

        for (int idx = 0; idx < 10000; idx ++) 
            squares[idx] = idx * idx;
        
        //squares.assign(c_squares, maxSqrtIdx);

        for (int idx = 1; idx <= n; idx ++) {
            for (int sIdx = 1; sIdx < maxSqrtIdx; sIdx ++) {
                if (idx < squares[sIdx])
                    break;
                dp[idx] = min(dp[idx], dp[idx - squares[sIdx]] + 1);
            }
        }
        return dp[n];
    }

};
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