<p>You are given the <code>root</code> of a binary tree with <strong>unique values</strong>.</p>

<p>In one operation, you can choose any two nodes <strong>at the same level</strong> and swap their values.</p>

<p>Return <em>the minimum number of operations needed to make the values at each level sorted in a <strong>strictly increasing order</strong></em>.</p>

<p>The <strong>level</strong> of a node is the number of edges along the path between it and the root node<em>.</em></p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img src="https://assets.leetcode.com/uploads/2022/09/18/image-20220918174006-2.png" style="width: 500px; height: 324px;" />
<pre>
<strong>Input:</strong> root = [1,4,3,7,6,8,5,null,null,null,null,9,null,10]
<strong>Output:</strong> 3
<strong>Explanation:</strong>
- Swap 4 and 3. The 2<sup>nd</sup> level becomes [3,4].
- Swap 7 and 5. The 3<sup>rd</sup> level becomes [5,6,8,7].
- Swap 8 and 7. The 3<sup>rd</sup> level becomes [5,6,7,8].
We used 3 operations so return 3.
It can be proven that 3 is the minimum number of operations needed.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img src="https://assets.leetcode.com/uploads/2022/09/18/image-20220918174026-3.png" style="width: 400px; height: 303px;" />
<pre>
<strong>Input:</strong> root = [1,3,2,7,6,5,4]
<strong>Output:</strong> 3
<strong>Explanation:</strong>
- Swap 3 and 2. The 2<sup>nd</sup> level becomes [2,3].
- Swap 7 and 4. The 3<sup>rd</sup> level becomes [4,6,5,7].
- Swap 6 and 5. The 3<sup>rd</sup> level becomes [4,5,6,7].
We used 3 operations so return 3.
It can be proven that 3 is the minimum number of operations needed.
</pre>

<p><strong class="example">Example 3:</strong></p>
<img src="https://assets.leetcode.com/uploads/2022/09/18/image-20220918174052-4.png" style="width: 400px; height: 274px;" />
<pre>
<strong>Input:</strong> root = [1,2,3,4,5,6]
<strong>Output:</strong> 0
<strong>Explanation:</strong> Each level is already sorted in increasing order so return 0.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li>The number of nodes in the tree is in the range <code>[1, 10<sup>5</sup>]</code>.</li>
	<li><code>1 &lt;= Node.val &lt;= 10<sup>5</sup></code></li>
	<li>All the values of the tree are <strong>unique</strong>.</li>
</ul>

from queue import Queue

class Solution:
    def _classify_nodes_by_level(self, root: TreeNode) -> list[list[TreeNode]]:
        queue, result = Queue(), []
        queue.put(root)

        while not queue.empty():
            count, nodes = queue.qsize(), []

            for _ in range(count):
                node = queue.get()

                if node.left is not None:
                    queue.put(node.left)

                if node.right is not None:
                    queue.put(node.right)

                nodes.append(node.val)

            result.append(nodes)

        return result

    def _swap_count_to_sort(self, nums: list[TreeNode]):
        indices, result = {num: i for i, num in enumerate(nums)}, 0

        for i, (elem1, elem2) in enumerate(zip(nums, sorted(nums))):
            if elem1 != elem2:
                nums[i], nums[indices[elem2]] = nums[indices[elem2]], nums[i]
                indices[elem1], indices[elem2] = indices[elem2], i
                result += 1

        return result

    def minimumOperations(self, root: TreeNode) -> int:
        result = 0
        nums_by_level = self._classify_nodes_by_level(root)

        for nums in nums_by_level:
            result += self._swap_count_to_sort(nums)

        return result
        
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