Flip Equivalent Binary Trees

Problem Description

Given the roots of two binary trees root1 and root2, return true if the two trees are flip equivalent or false otherwise. A binary tree X is flip equivalent to a binary tree Y if we can make X equal to Y after some number of flip operations, where a flip operation allows us to swap the left and right child subtrees of any node.

Key Insights

• The structure of the trees can change through flip operations, meaning the left and right subtrees can be swapped at any node.
• Two trees can be equivalent if their root values are the same and either:
  • The left subtree of one tree is equivalent to the left subtree of the other tree and the right subtree of one tree is equivalent to the right subtree of the other tree, or
  • The left subtree of one tree is equivalent to the right subtree of the other tree and vice versa.
• Both trees can be empty, in which case they are considered equivalent.

Space and Time Complexity

Time Complexity: O(n), where n is the number of nodes in the trees, since we may need to visit each node once. Space Complexity: O(h), where h is the height of the tree, due to the recursion stack.

Solution

To determine if the two trees are flip equivalent, we can use a recursive depth-first search approach. We will compare the root nodes of both trees first. If they are equal, we will check their children recursively. For each node, we will consider both possibilities of flipping the subtrees. If the nodes are not equal, we return false.

The algorithm can be summarized as follows:

1. If both nodes are null, return true.
2. If one node is null and the other is not, return false.
3. If the values of the nodes are not equal, return false.
4. Recursively check the left and right children for both configurations (flipped and non-flipped).

Code Solutions