What is the space complexity of LeetCode 889. Construct Binary Tree from Preorder and Postorder Traversal?

The Python solution on this page uses O(n) auxiliary space.

Construct Binary Tree from Preorder and Postorder Traversal — LeetCode 889 Python Solution

MediumTreeArrayHash TableDivide and ConquerBinary Tree

Problem: #889
Pattern: Tree Traversal
Reading time: 4 min
Source: leetcode.com

The problem

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.

Example

Input: preorder = [1,2,4,5,3,6,7], postorder = [4,5,2,6,7,3,1]
Output: [1,2,3,4,5,6,7]

Python solution

Python

# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right
class Solution:
    def constructFromPrePost(
        self, preorder: List[int], postorder: List[int]
    ) -> Optional[TreeNode]:
        def dfs(a: int, b: int, c: int, d: int) -> Optional[TreeNode]:
            if a > b:
                return None
            root = TreeNode(preorder[a])
            if a == b:
                return root
            i = pos[preorder[a + 1]]
            m = i - c + 1
            root.left = dfs(a + 1, a + m, c, i)
            root.right = dfs(a + m + 1, b, i + 1, d - 1)
            return root

        pos = {x: i for i, x in enumerate(postorder)}
        return dfs(0, len(preorder) - 1, 0, len(postorder) - 1)

Complexity

Measure	Complexity
Time	O(n)
Space	O(n) auxiliary

Pattern: Tree Traversal

Choose the order — preorder, inorder, postorder, level — and the problem solves itself. LeetCode 889. Construct Binary Tree from Preorder and Postorder Traversal is filed here because LeetCode tags it Tree and Binary Tree, which is the vocabulary this hub collects.

The tree traversal guide has the Python template for the pattern and the 225 LeetCode problems that use it.

Frequently asked questions

How hard is LeetCode 889. Construct Binary Tree from Preorder and Postorder Traversal?: LeetCode 889. Construct Binary Tree from Preorder and Postorder Traversal is rated Medium on LeetCode.
What is the time complexity of LeetCode 889. Construct Binary Tree from Preorder and Postorder Traversal?: The Python solution on this page runs in O(n).
What is the space complexity of LeetCode 889. Construct Binary Tree from Preorder and Postorder Traversal?: The Python solution on this page uses O(n) auxiliary space.
What topics does LeetCode 889. Construct Binary Tree from Preorder and Postorder Traversal cover?: LeetCode 889. Construct Binary Tree from Preorder and Postorder Traversal is tagged Tree, Array, Hash Table, Divide and Conquer and Binary Tree on LeetCode.