180. Invert Binary Tree

Inverting a tree means mirroring it: swap every node's left and right children. Recurse into both subtrees and swap on the way, and the whole tree flips.

Idea

Inverting (mirroring) a binary tree just means that at every node, its left and right children trade places. Because this must happen at every node, a simple recursion suffices: invert each subtree, then swap the two children pointers.

Algorithm

1. If root is None, return None.
2. Recursively invert the left subtree and the right subtree.
3. Swap: root.left, root.right = inverted_right, inverted_left.
4. Return root.

(The order of swapping vs. recursing doesn't matter, as long as both children are swapped.)

Worked example: [4,2,7,1,3,6,9]

     4                 4
    / \               / \
   2   7    ->       7   2
  / \ / \           / \ / \
 1  3 6  9         9  6 3  1

Every node's children are swapped, producing [4,7,2,9,6,3,1].

Complexity

• Time: O(n) — each node visited once.
• Space: O(h) recursion depth.

class Solution {
    public TreeNode invertTree(TreeNode root) {
        if (root == null) {
            return null;
        }
        TreeNode left = invertTree(root.left);
        TreeNode right = invertTree(root.right);
        root.left = right;
        root.right = left;
        return root;
    }
}