What is the time complexity of Check Completeness of a Binary Tree?

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

What data structures are used to solve Check Completeness of a Binary Tree?

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

What are the key insights for solving Check Completeness of a Binary Tree?

Insight 1: A complete binary tree can be validated by performing a level-order traversal (Breadth-First Search). Insight 2: The key to identifying incompleteness is detecting a `null` node before all nodes on the last level have been visited. If we encounter a `null` node, any subsequent non-null nodes imply the tree is not complete.

Which companies ask LeetCode 958. Check Completeness of a Binary Tree in interviews?

This problem is frequently asked at Lyft.

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Check Completeness of a Binary Tree - LeetCode 958 Solution

Check Completeness of a Binary Tree - Complete Solution Guide

Check Completeness of a Binary Tree is LeetCode problem 958, 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, determine if it is a complete binary tree . In a complete binary tree , every level, except possibly the last, is completely filled, and all nodes in the last level are as far left as possible. It can have between 1 and 2 h nodes inclusive at the last level h . Example 1: Input: root = [1,2,3,4,5,6] Output: true Explanation: Every level before the last is full (ie. levels with node-values {1} and {2, 3}), and all nodes in the last level ({4, 5, 6}) are as far lef

Detailed Explanation

The problem asks us to determine if a given binary tree is a 'complete binary tree'. A complete binary tree is one where all levels are completely filled except possibly the last level, and all nodes in the last level are as far left as possible. This means there should be no gaps in the tree when read level by level from left to right. The input is the root node of the binary tree, and the output is a boolean value: `true` if the tree is complete, and `false` otherwise. The constraints specify that the tree has between 1 and 100 nodes, and node values are between 1 and 1000.

Solution Approach

The solution uses a Breadth-First Search (BFS) algorithm implemented using a queue. The algorithm traverses the tree level by level. A boolean variable `found_null` is used to track whether a `null` node has been encountered. If we encounter a node after already having found a `null` node, then the tree is not a complete binary tree, and we return `false`. If we reach the end of the traversal without finding any non-null nodes after encountering a null node, then the tree is complete, and we return `true`.

Step-by-Step Algorithm

Step 1: Initialize a queue and enqueue the root node.
Step 2: Initialize a boolean variable `found_null` to `false`.
Step 3: While the queue is not empty:
Step 4: Dequeue a node from the queue.
Step 5: If the dequeued node is `null`:
Step 6: Set `found_null` to `true`.
Step 7: Else (the dequeued node is not `null`):
Step 8: If `found_null` is `true`:
Step 9: Return `false` (because we found a non-null node after a null node).
Step 10: Enqueue the left child of the dequeued node.
Step 11: Enqueue the right child of the dequeued node.
Step 12: After the queue is empty, return `true` (because we did not find any non-null nodes after a null node).

Key Insights

Insight 1: A complete binary tree can be validated by performing a level-order traversal (Breadth-First Search).
Insight 2: The key to identifying incompleteness is detecting a `null` node before all nodes on the last level have been visited. If we encounter a `null` node, any subsequent non-null nodes imply the tree is not complete.
Insight 3: We can use a queue to efficiently manage the level-order traversal.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(n)

Topics

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

Companies

Asked at: Lyft.

Check Completeness of a Binary Tree | LeetCode 958

Medium

Tree Breadth-First Search Binary Tree

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

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;
 *     }
 * }
 */
import java.util.LinkedList;
import java.util.Queue;

class Solution {
    public boolean isCompleteTree(TreeNode root) {
        if (root == null) {
            return true;
        }

        Queue<TreeNode> q = new LinkedList<>();
        q.offer(root);
        boolean found_null = false;

        while (!q.isEmpty()) {
            TreeNode node = q.poll();

            if (node == null) {
                found_null = true;
            } else {
                if (found_null) {
                    return false;
                }
                q.offer(node.left);
                q.offer(node.right);
            }
        }

        return true;
    }
}

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Problem Info

Description

Problem 958: Check Completeness of a Binary Tree - Detailed explanation and solution approaches.

Topics

Tree Breadth-First Search Binary Tree

Companies

Lyft

Stats

Difficulty:Medium

Languages:4

Companies:1

Problem #:958

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

12 steps

1
Step 1: Initialize a queue and enqueue the root node.
2
Step 2: Initialize a boolean variable `found_null` to `false`.
3
Step 3: While the queue is not empty:
4
Step 4: Dequeue a node from the queue.
5
Step 5: If the dequeued node is `null`:
6
Step 6: Set `found_null` to `true`.
7
Step 7: Else (the dequeued node is not `null`):
8
Step 8: If `found_null` is `true`:
9
Step 9: Return `false` (because we found a non-null node after a null node).
10
Step 10: Enqueue the left child of the dequeued node.
11
Step 11: Enqueue the right child of the dequeued node.
12
Step 12: After the queue is empty, return `true` (because we did not find any non-null nodes after a null node).

💡

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(n)

📦 Linear space - Memory grows with input size.

📝

Why?

The time complexity is determined by the number of nodes visited during the BFS, which is directly proportional to 'n'. The space complexity is dictated by the maximum size of the queue during the BFS, which is, in the worst case, proportional to the number of nodes on the last level of a complete tree, or roughly n/2, therefore O(n).

📖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

Recursive Approach with Node Counting

Determine the number of nodes and then check if the index of each node in a level order traversal is within the expected range of a complete tree. More complex to implement correctly than the BFS approach.

Time: O(n)Space: O(h), where h is the height of the tree. Can be O(n) in worst case of skewed tree.

Trade-offs: The recursive approach is more complex to implement correctly compared to the iterative BFS. While it could potentially save some space if the tree is balanced, the BFS approach is more straightforward and has a guaranteed O(n) space complexity, making it generally preferred.

✨

Key Insights

1Insight 1: A complete binary tree can be validated by performing a level-order traversal (Breadth-First Search).
2Insight 2: The key to identifying incompleteness is detecting a `null` node before all nodes on the last level have been visited. If we encounter a `null` node, any subsequent non-null nodes imply the tree is not complete.
3Insight 3: We can use a queue to efficiently manage the level-order traversal.

📚

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 solution correctly handles this by immediately returning `true`.
Edge case 2: A single-node tree (only root). The solution correctly handles this as the queue will contain only the root, and then become empty, returning `true`.
Edge case 3: A tree with nodes missing only at the last level from the right side. The algorithm correctly identifies this as a complete tree.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Not handling the `null` node correctly. It's essential to correctly identify when a null node is encountered and to set the `found_null` flag appropriately.

✗Common mistake 2: Assuming that a perfectly balanced tree is necessarily complete. A complete tree only requires all levels except the last to be full, and the last level to be filled from left to right. A perfectly balanced tree is always complete, but the reverse is not always true.

✗Common mistake 3: Forgetting to enqueue the children of a node even if one of them is null. You still need to enqueue `null` to detect if a non-null node appears later.

✅

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: Representing heaps. Heaps are typically implemented using complete binary trees to ensure efficient insertion and deletion of elements.

🏦Real-world scenario 2: Data compression. Huffman coding, a popular data compression technique, often uses binary trees that are designed to be complete or near-complete for optimal performance.

💡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: July 29, 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

Try solving this without using extra space first. It's a great exercise for understanding the underlying pattern.

@CodeNinjaJul 13

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

@TechLeadJul 6

❓

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 "Check Completeness of a Binary Tree"?

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 breadth-first search techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

🤖 Need help with this problem?