What is the time complexity of Complete Binary Tree Inserter?

The optimal solution has a time complexity of O(1).

What data structures are used to solve Complete Binary Tree Inserter?

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

What are the key insights for solving Complete Binary Tree Inserter?

Insight 1: We need to efficiently find the parent node where the new node should be inserted to maintain the complete binary tree property. Insight 2: A Breadth-First Search (BFS) during initialization helps us identify the nodes that are missing left or right children. A queue is a suitable data structure for BFS.

Which companies ask LeetCode 919. Complete Binary Tree Inserter in interviews?

This problem is frequently asked at PhonePe.

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Complete Binary Tree Inserter - LeetCode 919 Solution

Complete Binary Tree Inserter - Complete Solution Guide

Complete Binary Tree Inserter is LeetCode problem 919, 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

A complete binary tree is a binary tree in which every level, except possibly the last, is completely filled, and all nodes are as far left as possible. Design an algorithm to insert a new node to a complete binary tree keeping it complete after the insertion. Implement the CBTInserter class: CBTInserter(TreeNode root) Initializes the data structure with the root of the complete binary tree. int insert(int v) Inserts a TreeNode into the tree with value Node.val == val so that the tree remains co

Detailed Explanation

The problem asks us to design a `CBTInserter` class that can insert new nodes into a complete binary tree (CBT) while maintaining its completeness. A CBT is a binary tree where every level, except possibly the last, is completely filled, and all nodes are as far left as possible. The class needs to support three operations: 1. `CBTInserter(TreeNode root)`: Initializes the class with the root of an existing CBT. 2. `int insert(int val)`: Inserts a new node with the given value (`val`) into the CBT, making sure it remains complete. It returns the value of the parent node of the inserted node. 3. `TreeNode get_root()`: Returns the root node of the CBT.

Solution Approach

The solution uses a Breadth-First Search (BFS) during the `CBTInserter` initialization to identify nodes that are either missing a left child or missing both left and right children. These nodes are stored in a deque. The `insert` method then uses the first node in the deque as the parent, inserts the new node as either the left or right child depending on availability, updates the deque, and returns the parent's value. The `get_root` method simply returns the root of the tree.

Step-by-Step Algorithm

Step 1: **Initialization:** Perform a BFS traversal of the tree using a queue. For each node encountered, check if it has a missing left or right child. If it does, add it to the deque of available parents.
Step 2: **Insert:** When inserting a new node with value `val`, retrieve the first node from the deque (this is the parent).
Step 3: **Connect New Node:** Create a new TreeNode with the given value. If the parent node has no left child, add the new node as its left child. Otherwise (parent has a left child but no right child), add the new node as the parent's right child. In this case, remove the parent from the head of deque since it is now full.
Step 4: **Update Deque:** Add the newly inserted node to the end of the deque. This ensures the newly inserted node is considered as a possible parent for future insertions.
Step 5: **Return Parent Value:** Return the value of the parent node.
Step 6: **Get Root:** The get_root function simply returns the root of the tree.

Key Insights

Insight 1: We need to efficiently find the parent node where the new node should be inserted to maintain the complete binary tree property.
Insight 2: A Breadth-First Search (BFS) during initialization helps us identify the nodes that are missing left or right children. A queue is a suitable data structure for BFS.
Insight 3: Using a deque to store the nodes that can still accept children allows for O(1) access to potential parent nodes.

Complexity Analysis

Time Complexity: O(1)

Space Complexity: O(W)

Topics

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

Companies

Asked at: PhonePe.

Complete Binary Tree Inserter | LeetCode 919

Medium

Tree Breadth-First Search Design Binary Tree

Time: O(1)Space: O(W)

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.Deque;
import java.util.LinkedList;

class CBTInserter {

    TreeNode root;
    Deque<TreeNode> deque;

    public CBTInserter(TreeNode root) {
        this.root = root;
        this.deque = new LinkedList<>();
        if (root != null) {
            Deque<TreeNode> q = new LinkedList<>();
            q.offer(root);
            while (!q.isEmpty()) {
                TreeNode node = q.poll();
                if (node.left == null || node.right == null) {
                    this.deque.offer(node);
                }
                if (node.left != null) {
                    q.offer(node.left);
                }
                if (node.right != null) {
                    q.offer(node.right);
                }
            }
        }
    }
    
    public int insert(int val) {
        TreeNode parent = this.deque.peekFirst();
        TreeNode new_node = new TreeNode(val);
        this.deque.offer(new_node);
        
        if (parent.left == null) {
            parent.left = new_node;
        } else {
            parent.right = new_node;
            this.deque.pollFirst();
        }
        
        return parent.val;
    }
    
    public TreeNode get_root() {
        return this.root;
    }
}

/**
 * Your CBTInserter object will be instantiated and called as such:
 * CBTInserter obj = new CBTInserter(root);
 * int param_1 = obj.insert(val);
 * TreeNode param_2 = obj.get_root();
 */

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Problem Info

Description

Problem 919: Complete Binary Tree Inserter - Detailed explanation and solution approaches.

Topics

Tree Breadth-First Search Design Binary Tree

Companies

PhonePe

Stats

Difficulty:Medium

Languages:4

Companies:1

Problem #:919

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

6 steps

1
Step 1: **Initialization:** Perform a BFS traversal of the tree using a queue. For each node encountered, check if it has a missing left or right child. If it does, add it to the deque of available parents.
2
Step 2: **Insert:** When inserting a new node with value `val`, retrieve the first node from the deque (this is the parent).
3
Step 3: **Connect New Node:** Create a new TreeNode with the given value. If the parent node has no left child, add the new node as its left child. Otherwise (parent has a left child but no right child), add the new node as the parent's right child. In this case, remove the parent from the head of deque since it is now full.
4
Step 4: **Update Deque:** Add the newly inserted node to the end of the deque. This ensures the newly inserted node is considered as a possible parent for future insertions.
5
Step 5: **Return Parent Value:** Return the value of the parent node.
6
Step 6: **Get Root:** The get_root function simply returns the root of the tree.

💡

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(1)

⚡ Constant time - Super fast! Same speed regardless of input size.

💾

Space Complexity

O(W)

📝

Why?

The `insert` and `get_root` operations involve constant-time operations like deque access and node creation/assignment. The constructor's BFS visits each node once, hence O(N), but only stores nodes that may require children, so the deque size is O(W) where W is the maximum width 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

Level Order Traversal with Node Counting

Instead of storing parent candidates in a queue, we could calculate the number of nodes currently in the tree and derive where the next node should be placed based on its index in a hypothetical complete binary tree represented as an array. This eliminates the need for the deque, but requires calculating the correct position by using log2 arithmetic.

Time: O(log N) for insert (due to calculating the levels)Space: O(1)

Trade-offs: This approach avoids the deque and maintains a constant space complexity. However, it involves more complex calculations during insertion to determine the parent and the appropriate side (left or right), resulting in logarithmic time complexity for the insert operation. The main solution is more efficient O(1) for insert. This approach may be faster if only a small number of inserts are performed relative to the size of the initial tree.

✨

Key Insights

1Insight 1: We need to efficiently find the parent node where the new node should be inserted to maintain the complete binary tree property.
2Insight 2: A Breadth-First Search (BFS) during initialization helps us identify the nodes that are missing left or right children. A queue is a suitable data structure for BFS.
3Insight 3: Using a deque to store the nodes that can still accept children allows for O(1) access to potential parent nodes.

📚

Key Terms Explained

For Students

Tree

Hierarchical structure with nodes. Like a family tree!

Edge Cases

Edge case 1: Empty Tree - If the initial tree is empty (root is null), the constructor creates an empty deque, and inserting will proceed correctly.
Edge case 2: Single Node Tree - If the tree only has a root node, the root node will be added to the deque during initialization. The insert method will correctly add the new node as the left child.
Edge case 3: Full Tree - If the tree is a complete binary tree, then all leaves will get added to the queue and new nodes will be added accordingly.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Not handling the case where the parent node already has a left child but no right child. This can lead to an incomplete binary tree.

✗Common mistake 2: Forgetting to add the newly inserted node to the deque after inserting it as a child. This will lead to incorrect parent selection in future insertions.

✗Common mistake 3: Incorrectly calculating the size of the initial queue/deque used in the constructor resulting in memory issues.

✅

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: Building a priority queue represented as a heap (which is a CBT). When new elements are added to the priority queue, maintaining the heap property requires inserting the element into the CBT structure.

🏦Real-world scenario 2: Distributing tasks among workers in a balanced manner. If each node in the tree represents a worker, inserting a new node can represent assigning a task to a less loaded worker, ensuring fair task distribution.

💡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: June 20, 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 13

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

@DevExpert92Jul 6

The key insight here is recognizing the pattern. Once you see it, the solution becomes straightforward.

@AlgoMasterJun 29

❓

Frequently Asked Questions

What is the difference between DFS and BFS for trees?

DFS (using recursion or stack) explores depth-first, useful for path-finding and backtracking problems. BFS (using queue) explores level-by-level, ideal for finding shortest paths or processing nodes by depth. Choose based on whether level information matters.

How much time should I spend on a medium problem in interviews?

In a 45-minute interview, aim for: 5-10 minutes understanding and clarifying, 5-10 minutes discussing approach, 20-25 minutes coding, and 5-10 minutes testing. If stuck after 15 minutes of thinking, verbalize your thought process and ask for hints.

What is the importance of time and space complexity analysis?

Complexity analysis is crucial because: 1) Interviewers always ask about it, 2) It helps you choose between approaches, 3) It demonstrates CS fundamentals. Always state both time and space complexity, and be prepared to explain how you derived them.

What is the optimal approach for "Complete Binary Tree Inserter"?

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.

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