Given the root of a binary tree, invert the tree and return its root (Invert Binary Tree).

Optimal Recursive / Depth-First Search Approach:
- Recursively swap the left and right child pointers for every node in the binary tree.

class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right
def invert_tree(root: TreeNode) -> TreeNode:
    if not root:
        return None
    # Swap left and right children
    root.left, root.right = root.right, root.left
    # Recurse down subtrees
    invert_tree(root.left)
    invert_tree(root.right)
    return root

Complexity & Key Logic:
- Time Complexity: O(N) visiting each of the N nodes exactly once.
- Space Complexity: O(H) call stack space, where H is tree height (O(log N) for balanced trees, O(N) for degenerate trees).
- Algorithm Details:
- Base Case: If node is None, return None.
- Swap current node's left and right pointers.
- Recursively invert the newly swapped subtrees.
- Return original root node.