<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:
    def numSquares(self, n: int) -> int:
        
        # Create a dp_table containing the 'inf' of float with number of n + 1
        dp_table = [float('inf')] * (n + 1)

        # Set te dp_table first index to 0
        dp_table[0] = 0

        # Loop through the index number 1 to n + 1
        for i in range(1, n + 1):
            
            # Set the min_val as the 'inf' float
            min_val = float('inf')

            # Set j as 1
            j = 1

            # while the square of j smaller or equal to i
            while j * j <= i:
                
                # Update min_val to:
                # minimum of (1) the current min_val
                # (2) the value of dp_table with index i substracted by the square of j, add by 1
                min_val = min(min_val, dp_table[i - j * j] + 1)

                # then increase the j's value
                j += 1
            
            # set the dp_table of index i to the updated min_val
            dp_table[i] = min_val
        
        # Return dp_table of index n which is the minimum number that can be used to form the n
        return dp_table[n]
16560