Construct Binary Tree from Preorder and Postorder Traversal

Problem Description

Given two integer arrays, preorder and postorder where preorder is the preorder traversal of a binary tree of distinct values and postorder is the postorder traversal of the same tree, reconstruct and return the binary tree. If there exist multiple answers, you can return any of them.

Key Insights

• The first element of the preorder array is always the root of the tree.
• The last element of the postorder array is also the root of the tree.
• The elements in preorder can be used to determine the structure of the tree, while postorder helps identify the boundaries of the left and right subtrees.
• The problem can be solved using a recursive approach by dividing the preorder and postorder arrays into subarrays that represent the left and right children of the current root.

Space and Time Complexity

Time Complexity: O(N), where N is the number of nodes in the tree, since we visit each node once. Space Complexity: O(N), for the recursion stack in the worst case.

Solution

To reconstruct the binary tree from preorder and postorder traversals, we can use a recursive function that takes slices of the preorder and postorder arrays. The approach involves:

1. Identifying the root from the preorder array.
2. Finding the left and right children by looking for the root's children in the postorder array.
3. Recursively building the left and right subtrees using the appropriate slices of the arrays.

Code Solutions