Invert Binary Tree

Easy Trees & BST Recursion Original on LeetCode

Invert Binary Tree is a easy trees & bst problem solved with the recursion pattern. The best approach, recursive, runs in O(n) time and O(h) space. Below are 2 approaches in Java, from iterative (bfs) up.

Problem

Mirror a binary tree, swapping left and right children at every node, and return its root.

Examples

Example 1

Input: root = [4, 2, 7, 1, 3, 6, 9]
Output: [4, 7, 2, 9, 6, 3, 1]

Example 2

Input: root = []
Output: []

Constraints

The tree has 0 to 100 nodes.

Animated walkthrough

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Solutions

Try it yourself first. Then compare: each approach lists its idea, the steps, its time and space, and the Java code.

Approach	Time	Space
Iterative (BFS)	`O(n)`	`O(w)`
Recursive	`O(n)`	`O(h)`

1Iterative (BFS)

TimeO(n)

SpaceO(w)

Visit nodes with a queue and swap each node's children.

Poll, swap left and right, enqueue the non-null children.

Java

class Solution {
    public TreeNode invertTree(TreeNode root) {
        if (root == null) return null;
        Queue<TreeNode> q = new ArrayDeque<>();
        q.add(root);
        while (!q.isEmpty()) {
            TreeNode n = q.poll();
            TreeNode t = n.left; n.left = n.right; n.right = t;
            if (n.left != null) q.add(n.left);
            if (n.right != null) q.add(n.right);
        }
        return root;
    }
}

2Recursive

TimeO(n)

SpaceO(h)

Invert both subtrees and attach them to the opposite sides.

if root == null return null.
left = invert(root.left); right = invert(root.right).
root.left = right; root.right = left.

Java

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

Edge cases to test

Empty tree
Single node

Hints

Hint 1

Swap the two children of every node. The order you visit nodes in does not matter.

FAQ

What is the best time complexity for Invert Binary Tree?

Recursive runs in O(n) time and O(h) extra space.

Which pattern does Invert Binary Tree use?

It is a trees & bst problem that uses the recursion pattern. Other problems with the same pattern: Binary Tree Inorder Traversal (Recursive), Binary Tree Preorder Traversal (Recursive), Binary Tree Postorder Traversal (Recursive).

Is there a brute force solution for Invert Binary Tree?

Yes. Iterative (BFS) takes O(n) time and O(w) space. Visit nodes with a queue and swap each node's children.

Which edge cases should I test for Invert Binary Tree?

Empty tree; Single node.