<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>

from typing import List
from queue import deque


class Solution:
    def numSquares(self, n: int) -> int:
        nodes = self.generate_nodes(n)

        queue = deque(nodes)
        checked = set()

        minimum = 0

        while queue:
            for i in range(len(queue)):
                current_node = queue.popleft()

                if current_node == n:
                    queue.clear()
                    break

                for node in nodes:
                    next_node = current_node + node

                    if next_node not in checked:
                        queue.append(next_node)
                        checked.add(next_node)
            minimum += 1
        return minimum

    def generate_nodes(self, n):
        nodes = []

        i = 1
        value = i**2
        while value <= n:
            nodes.append(value)
            i += 1
            value = i**2

        return nodes
20671