What is the time complexity of Deepest Leaves Sum?

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

What data structures are used to solve Deepest Leaves Sum?

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

What are the key insights for solving Deepest Leaves Sum?

Insight 1: Breadth-First Search (BFS) is a suitable approach because it explores the tree level by level. This makes it easy to determine the deepest level. Insight 2: The sum of the deepest leaves can be efficiently calculated by keeping track of the sum of nodes at each level and updating it as BFS progresses.

Which companies ask LeetCode 1302. Deepest Leaves Sum in interviews?

This problem is frequently asked at Myntra.

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Deepest Leaves Sum - LeetCode 1302 Solution

Q: How to solve Deepest Leaves Sum?

The provided code implements a Breadth-First Search (BFS) algorithm. It uses a queue to traverse the binary tree level by level. At each level, it calculates the sum of the node values. Because BFS guarantees that the last level processed will be the deepest level, the level_sum at the end of the BFS traversal represents the sum of the values of the deepest leaves.

Deepest Leaves Sum - Complete Solution Guide

Deepest Leaves Sum is LeetCode problem 1302, 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 sum of values of its deepest leaves . Example 1: Input: root = [1,2,3,4,5,null,6,7,null,null,null,null,8] Output: 15 Example 2: Input: root = [6,7,8,2,7,1,3,9,null,1,4,null,null,null,5] Output: 19 Constraints: The number of nodes in the tree is in the range [1, 10 4 ] . 1 <= Node.val <= 100

Detailed Explanation

The problem asks us to find the sum of the values of all the nodes that are at the deepest level of a given binary tree. A 'deepest leaf' is a leaf node that has the longest path from the root to that leaf. The input is the root node of the binary tree. The output is the sum of the values of all deepest leaf nodes. The number of nodes in the tree can be up to 10,000, and each node's value is between 1 and 100.

Solution Approach

The provided code implements a Breadth-First Search (BFS) algorithm. It uses a queue to traverse the binary tree level by level. At each level, it calculates the sum of the node values. Because BFS guarantees that the last level processed will be the deepest level, the level_sum at the end of the BFS traversal represents the sum of the values of the deepest leaves.

Step-by-Step Algorithm

Step 1: Initialize a queue and add the root node to it. If the root is null, return 0.
Step 2: Initialize a variable level_sum to store the sum of the deepest level's nodes. Initialize the level_sum to 0.
Step 3: While the queue is not empty, iterate through each level.
Step 4: Inside the outer loop, reset level_sum to 0 for the current level.
Step 5: Determine the size of the current level (number of nodes at the current level) by checking the queue length
Step 6: Iterate from 0 to level_size to process each node at the current level. Pop (or poll) a node from the queue.
Step 7: Add the node's value to the level_sum.
Step 8: Enqueue the node's left child (if it exists).
Step 9: Enqueue the node's right child (if it exists).
Step 10: After the inner loop completes, level_sum contains the sum of the current level's node values. This value will be the deepest level's sum at the end.
Step 11: After the outer loop completes (queue is empty), return level_sum. This value represents the sum of the nodes at the deepest level.

Key Insights

Insight 1: Breadth-First Search (BFS) is a suitable approach because it explores the tree level by level. This makes it easy to determine the deepest level.
Insight 2: The sum of the deepest leaves can be efficiently calculated by keeping track of the sum of nodes at each level and updating it as BFS progresses.
Insight 3: The last level_sum calculated by BFS will be the sum of the deepest leaves, so only the last calculated level_sum has to be remembered.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(w)

Topics

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

Companies

Asked at: Myntra.

Deepest Leaves Sum | LeetCode 1302

Medium

Tree Depth-First Search Breadth-First Search Binary Tree

Time: O(n)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.LinkedList;
import java.util.Queue;

class Solution {
    public int deepestLeavesSum(TreeNode root) {
        if (root == null) {
            return 0;
        }

        Queue<TreeNode> q = new LinkedList<>();
        q.offer(root);
        int level_sum = 0;

        while (!q.isEmpty()) {
            level_sum = 0;
            int level_size = q.size();
            for (int i = 0; i < level_size; i++) {
                TreeNode node = q.poll();
                level_sum += node.val;

                if (node.left != null) {
                    q.offer(node.left);
                }
                if (node.right != null) {
                    q.offer(node.right);
                }
            }
        }
        
        return level_sum;
    }
}

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Problem Info

Description

Problem 1302: Deepest Leaves Sum - Detailed explanation and solution approaches.

Topics

Tree Depth-First Search Breadth-First Search Binary Tree

Companies

Myntra

Stats

Difficulty:Medium

Languages:4

Companies:1

Problem #:1302

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

11 steps

1
Step 1: Initialize a queue and add the root node to it. If the root is null, return 0.
2
Step 2: Initialize a variable level_sum to store the sum of the deepest level's nodes. Initialize the level_sum to 0.
3
Step 3: While the queue is not empty, iterate through each level.
4
Step 4: Inside the outer loop, reset level_sum to 0 for the current level.
5
Step 5: Determine the size of the current level (number of nodes at the current level) by checking the queue length
6
Step 6: Iterate from 0 to level_size to process each node at the current level. Pop (or poll) a node from the queue.
7
Step 7: Add the node's value to the level_sum.
8
Step 8: Enqueue the node's left child (if it exists).
9
Step 9: Enqueue the node's right child (if it exists).
10
Step 10: After the inner loop completes, level_sum contains the sum of the current level's node values. This value will be the deepest level's sum at the end.
11
Step 11: After the outer loop completes (queue is empty), return level_sum. This value represents the sum of the nodes at the deepest level.

💡

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(w)

📝

Why?

The time complexity is O(n) because we visit each node exactly once. The space complexity is dominated by the queue, which in the worst case, can hold all the nodes at the widest level of the tree. The maximum width of a binary tree can be approximately n/2 in a balanced tree, so the space complexity is O(n) in the worst case, but can be less in skewed trees where the width is much smaller.

📖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

Depth-First Search (DFS)

A recursive DFS approach can be used to find the maximum depth of the tree first. Then, another DFS can be performed to sum the values of the nodes at that maximum depth. You can also achieve this with only one DFS with some additional bookkeeping.

Time: O(n)Space: O(h), where h is the height of the tree. In the worst-case (skewed tree), h can be equal to n, leading to O(n) space complexity. In balanced trees, h is log(n), resulting in O(log(n)) space complexity.

Trade-offs: DFS might be more intuitive for some but has a higher space complexity in the worst case (skewed tree) compared to BFS. BFS space complexity is bound by the tree's width.

✨

Key Insights

1Insight 1: Breadth-First Search (BFS) is a suitable approach because it explores the tree level by level. This makes it easy to determine the deepest level.
2Insight 2: The sum of the deepest leaves can be efficiently calculated by keeping track of the sum of nodes at each level and updating it as BFS progresses.
3Insight 3: The last level_sum calculated by BFS will be the sum of the deepest leaves, so only the last calculated level_sum has to be remembered.

📚

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 code explicitly handles this case by returning 0.
Edge case 2: Tree with only one node (the root). The BFS algorithm will correctly identify the root as the deepest leaf and return its value.
Edge case 3: Skewed tree (all nodes are on one side). The algorithm will still correctly traverse the tree level by level and find the deepest leaf.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Not handling the empty tree case (root is null).

✗Common mistake 2: Incorrectly calculating the level_size during the BFS iteration. It's crucial to get the initial queue size before iterating through the nodes at that level.

✗Common mistake 3: Forgetting to update the `level_sum` before processing each level, leading to an incorrect result.

✗Common mistake 4: Using recursion without considering the stack overflow issues for very deep trees.

✅

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: Determining the deepest level of a organizational chart to analyze leadership impact.

🏦Real-world scenario 2: Finding the deepest level of a file system directory tree. This could be useful for identifying infrequently accessed or deeply nested files.

🎮Real-world scenario 3: In game development, finding the lowest point in a level's terrain represented as a tree structure for optimal resource allocation.

💡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

Medium problems are the bread and butter of technical interviews. Practice explaining your approach before coding.

⚠️ 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 13, 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

I was asked this exact problem at my Google interview. The interviewer wanted me to optimize space complexity.

@InterviewProJul 13

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

@CodeNinjaJul 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 "Deepest Leaves Sum"?

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.

🤖 Need help with this problem?