Construct Binary Tree
Detailed guide and Python implementation for the 'Construct Binary Tree' problem.
1. Concept Overview
The 'Construct Binary Tree' problem is a key challenge in the Trees section.
This implementation focuses on medium-level logic in Python.
We prioritize technical accuracy and code readability in our provided solutions.
2. Real-World Applications
3. Visual Intuition
Visualizing the logic flow for Construct Binary Tree.
4. Prerequisites
5. Step-by-Step Thinking
1. Understand the problem
Read the problem statement for Construct Binary Tree carefully.
2. Formulate brute force
Draft a simple iterative solution.
3. Identify inefficiency
Look for redundant calculations.
4. Optimize search path
Use hashing or sorting to speed up the process.
5. Final Implementation
Clean up the code for production standards.
Problem Statement
Given two integer arrays preorder and inorder where preorder is the preorder traversal of a binary tree and inorder is the inorder traversal of the same tree, construct and return the binary tree.
The tree should be returned as a level-order list. Implement a function buildTree(preorder: list, inorder: list) -> list.
- •1 <= preorder.length <= 3000
- •inorder.length == preorder.length
- •-3000 <= preorder[i], inorder[i] <= 3000
- •preorder and inorder consist of unique values
- •Each value of inorder also appears in preorder
- •preorder is guaranteed to be the preorder traversal of the tree
- •inorder is guaranteed to be the inorder traversal of the tree
Examples
[3,9,20,15,7], [9,3,15,20,7]
[3,9,20,None,None,15,7]
Preorder: root is 3. In inorder, 9 is to the left of 3 (left subtree) and [15,20,7] is to the right (right subtree). Recursively build: left subtree is just [9], right subtree has root 20 with children 15 and 7.
[-1], [-1]
[-1]
Single node tree.
Need a Hint?
Edge Cases to Watch
- Empty input structures
- Single element inputs
- Large numerical bounds
Ready to Solve?
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Interview Insights & Variations
Complexity Analysis Breakdown
Why Time: Directly evaluates all possibilities.
Why Space: Uses standard local memory.
Why Time: Optimized paths reduce total operations.
Why Space: May trade memory for speed.
Optimized Solution Python Code
Optimized Solution Python Code
def build_tree_opt(preorder, inorder):
if isinstance(preorder, list):
r = build_tree_opt_helper(preorder, inorder)
return tree_to_list(r)
return build_tree_opt_helper(preorder, inorder)
def build_tree_opt_helper(preorder: list, inorder: list) -> TreeNode:
if not preorder or not inorder:
return None
root_val = preorder[0]
root = TreeNode(root_val)
mid = inorder.index(root_val)
root.left = build_tree_opt_helper(preorder[1:mid+1], inorder[:mid])
root.right = build_tree_opt_helper(preorder[mid+1:], inorder[mid+1:])
return rootBrute Force Code (Spoiler Guarded)
Brute Force Code (Spoiler Guarded)
def build_tree_brute(preorder, inorder):
if isinstance(preorder, list):
r = build_tree_brute_helper(preorder, inorder)
return tree_to_list(r)
return build_tree_brute_helper(preorder, inorder)
def build_tree_brute_helper(preorder: list, inorder: list) -> TreeNode:
if not preorder or not inorder: return None
root = TreeNode(preorder[0])
mid = inorder.index(preorder[0])
root.left = build_tree_brute_helper(preorder[1:mid+1], inorder[:mid])
root.right = build_tree_brute_helper(preorder[mid+1:], inorder[mid+1:])
return rootAlgorithm Pattern Checklist
When dealing with Trees data patterns.
Core Prerequisites
Revision Key Notes
Common Mistakes & Pitfalls
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