What is the time complexity of Binary Tree Pruning?

The optimal solution has a time complexity of O(n).

What data structures are used to solve Binary Tree Pruning?

This problem uses Tree, Depth-First Search, Binary Tree. Understanding these concepts is essential for solving this Medium problem efficiently.

What are the key insights for solving Binary Tree Pruning?

Insight 1: A post-order traversal is essential. We need to process the left and right subtrees *before* deciding whether to prune the current node. Insight 2: Recursion simplifies the process. We can recursively prune the left and right subtrees, and then use the result to determine if the current node's subtree should be pruned.

Which companies ask LeetCode 814. Binary Tree Pruning in interviews?

This problem is frequently asked at Hulu.

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Binary Tree Pruning - LeetCode 814 Solution

Binary Tree Pruning - Complete Solution Guide

Binary Tree Pruning is LeetCode problem 814, a Medium level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

Given the root of a binary tree, return the same tree where every subtree (of the given tree) not containing a 1 has been removed . A subtree of a node node is node plus every node that is a descendant of node . Example 1: Input: root = [1,null,0,0,1] Output: [1,null,0,null,1] Explanation: Only the red nodes satisfy the property "every subtree not containing a 1". The diagram on the right represents the answer. Example 2: Input: root = [1,0,1,0,0,0,1] Output: [1,null,1,null,1] Example 3: Input:

Detailed Explanation

The problem asks us to prune a binary tree. Pruning means removing subtrees that don't contain the value '1'. A subtree is defined as a node and all its descendants. So, we need to traverse the tree and, for each node, check if the subtree rooted at that node contains at least one '1'. If it doesn't, we remove the entire subtree. The input is the root of the binary tree, and the output is the pruned tree.

Solution Approach

The solution uses a recursive post-order traversal of the binary tree. For each node, it first recursively calls the `pruneTree` function on the left and right subtrees. This ensures that the subtrees are pruned before the parent node is considered. After the recursive calls, the function checks if the current node's value is '0' and if both its left and right children are null (meaning they have been pruned or were initially null). If both conditions are true, the current node's subtree doesn't contain '1', so the function returns `null`, effectively pruning the node. Otherwise, it returns the current node, keeping it in the tree.

Step-by-Step Algorithm

Step 1: Base Case: If the current node is null, return null. This handles empty trees and the bottom of the recursion.
Step 2: Recursively prune the left subtree: `root.left = pruneTree(root.left)`.
Step 3: Recursively prune the right subtree: `root.right = pruneTree(root.right)`.
Step 4: Check if the current node should be pruned: If `root.val == 0` AND `root.left is None` AND `root.right is None`, return `None`.
Step 5: Otherwise, return the current node: return `root`.

Key Insights

Insight 1: A post-order traversal is essential. We need to process the left and right subtrees *before* deciding whether to prune the current node.
Insight 2: Recursion simplifies the process. We can recursively prune the left and right subtrees, and then use the result to determine if the current node's subtree should be pruned.
Insight 3: A node can be pruned if it has a value of '0' and its left and right children are null after pruning.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(h)

Topics

This problem involves: Tree, Depth-First Search, Binary Tree.

Companies

Asked at: Hulu.

Binary Tree Pruning | LeetCode 814

Medium

Tree Depth-First Search Binary Tree

Time: O(n)Space: O(h)

Solution Code

Available in:

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode() {}
 *     TreeNode(int val) { this.val = val; }
 *     TreeNode(int val, TreeNode left, TreeNode right) {
 *         this.val = val;
 *         this.left = left;
 *         this.right = right;
 *     }
 * }
 */
class Solution {
    public TreeNode pruneTree(TreeNode root) {
        if (root == null) {
            return null;
        }
        
        root.left = pruneTree(root.left);
        root.right = pruneTree(root.right);
        
        if (root.val == 0 && root.left == null && root.right == null) {
            return null;
        }
        
        return root;
    }
}

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Problem Info

Description

Problem 814: Binary Tree Pruning - Detailed explanation and solution approaches.

Topics

Tree Depth-First Search Binary Tree

Companies

Hulu

Stats

Difficulty:Medium

Languages:4

Companies:1

Problem #:814

Problem Explanation

💡

Think Before You Code

🤔 Ask Yourself

→What is the input? What output do I need?
→Can I solve a smaller version of this problem first?
→What patterns have I seen in similar problems?

✏️ Try This First

Before looking at the solution, try to solve it on paper with a simple example!

🚀 Try on LeetCode

Solution Approach

📋

Step-by-Step Solution

5 steps

1
Step 1: Base Case: If the current node is null, return null. This handles empty trees and the bottom of the recursion.
2
Step 2: Recursively prune the left subtree: `root.left = pruneTree(root.left)`.
3
Step 3: Recursively prune the right subtree: `root.right = pruneTree(root.right)`.
4
Step 4: Check if the current node should be pruned: If `root.val == 0` AND `root.left is None` AND `root.right is None`, return `None`.
5
Step 5: Otherwise, return the current node: return `root`.

💡

Pro Tip for Students

Try tracing through each step with a small example on paper before coding. Understanding "why" each step happens is more important than memorizing the code!

⚡

Complexity Analysis

⏱️

Time Complexity

O(n)

👍 Linear - Good! Visits each element once.

💾

Space Complexity

O(h)

📝

Why?

The time complexity is O(n) because the pruneTree function is called once for each node in the tree. The space complexity is determined by the maximum depth of the recursion stack, which corresponds to the height of the tree.

📖New to Big O? Click to learn more

Big O Notation - Quick Guide

O(1)Best - Instant

O(log n)Excellent - Binary Search

O(n)Good - One loop

O(n log n)OK - Sorting

O(n²)Slow - Nested loops

O(2ⁿ)Very Slow - Recursion

Alternative Approaches

Iterative Approach with Stack

Instead of recursion, we can use a stack to perform a post-order traversal iteratively. This would involve pushing nodes onto the stack and processing them after their children have been visited.

Time: O(n)Space: O(n) in the worst case (skewed tree), as we might need to store all nodes in the stack.

Trade-offs: Avoids recursion overhead, potentially slightly faster for very deep trees, but generally more complex to implement and understand compared to the recursive approach. Recursion is more readable in this case.

✨

Key Insights

1Insight 1: A post-order traversal is essential. We need to process the left and right subtrees *before* deciding whether to prune the current node.
2Insight 2: Recursion simplifies the process. We can recursively prune the left and right subtrees, and then use the result to determine if the current node's subtree should be pruned.
3Insight 3: A node can be pruned if it has a value of '0' and its left and right children are null after pruning.

📚

Key Terms Explained

For Students

Tree

Hierarchical structure with nodes. Like a family tree!

Edge Cases

Edge case 1: Empty tree (root is null). The base case `if not root: return None` handles this correctly.
Edge case 2: A tree where all nodes are 0. The algorithm correctly prunes the entire tree and returns null.
Edge case 3: A tree where the root is 1 and all subtrees are pruned. The algorithm correctly leaves only the root node.
Edge case 4: A tree with a complex mix of 0s and 1s. The recursive nature of the algorithm ensures that all unnecessary 0 subtrees are removed while retaining the necessary 1s.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Using a pre-order or in-order traversal instead of post-order. This would lead to incorrect pruning, as the decision to prune a node needs to be made *after* processing its children.

✗Common mistake 2: Forgetting the base case (handling null nodes). This would result in a stack overflow error.

✗Common mistake 3: Not updating the `left` and `right` pointers after the recursive calls. If the subtrees are pruned, the parent's pointers need to be updated to `null`.

✗Common mistake 4: Incorrectly checking the conditions for pruning a node. The node must have a value of '0' AND both its left and right children must be null.

✅

Learning Tip

Every mistake is a learning opportunity! When you make an error, understand why it happened before moving on.

🌍

Where is This Used in Real Life?

💼Real-world scenario 1: Optimizing decision trees in machine learning. Removing branches that don't contribute significantly to the prediction accuracy can improve performance and reduce complexity.

🏦Real-world scenario 2: Data compression. Removing redundant or unnecessary parts of a data structure (like a tree) can reduce the storage space required.

💡Understanding real-world applications helps you see the "why" behind algorithms. It's not just about passing interviews—these concepts power the apps and websites you use every day!

Author's Notes

💡 Key Insight

Most tree problems can be solved recursively. The base case is usually a null node. Think about what information needs to flow up vs down the tree.

🎯 Interview Tip

If stuck, try working through a small example by hand. The pattern often reveals itself.

⚠️ Watch Out

Not handling null nodes properly. Always check if the current node exists before accessing its children.

Written by Saswata Mondal

Software Engineer • Algorithms Enthusiast • Interview Coach

👨‍💻

About the Author

👨‍💻

Saswata MondalAuthor400+ LC Problems

B.Tech CSE, IEM Kolkata | LeetCode Rating: 1672 (Top 15%)

Certified: IBM Java Developer, NPTEL Programming in Java

Last updated: September 3, 2024LeetCode Profile GitHub

This solution has been crafted based on my experience solving 400+ LeetCode problems. Each explanation is designed to help you understand the underlying concepts, not just memorize the code.

Community Tips & Insights

In a real interview, always clarify constraints first. Ask about input size and value ranges.

@TechLeadJul 14

Don't forget to handle the edge case when the input is empty. Many candidates miss this in interviews.

@DevExpert92Jul 7

❓

Frequently Asked Questions

How do I choose between recursive and iterative tree traversal?

Use recursive traversal for cleaner code when stack depth isn't a concern (tree height < ~1000). Use iterative with explicit stack for very deep trees to avoid stack overflow. Iterative is also preferred when you need fine-grained control over the traversal process.

What techniques are commonly tested in medium-difficulty problems?

Medium problems often require combining multiple techniques: two-pointer with hash maps, BFS/DFS with state tracking, dynamic programming with optimization, or divide-and-conquer approaches. They test your ability to recognize patterns and choose the right combination of techniques.

How should I practice algorithm problems effectively?

Focus on understanding patterns rather than memorizing solutions. After solving a problem, review optimal solutions and understand the intuition. Group similar problems to recognize patterns. Practice explaining your approach out loud. Review problems after a few days to test retention.

What is the optimal approach for "Binary Tree Pruning"?

For this medium-level Tree problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether depth-first search techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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