What is the time complexity of Minimum Absolute Difference in BST?

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

What data structures are used to solve Minimum Absolute Difference in BST?

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

What are the key insights for solving Minimum Absolute Difference in BST?

Insight 1: The key property of a BST is that an in-order traversal yields the nodes in sorted order. Insight 2: To find the minimum difference, we only need to compare each node with its immediate predecessor and successor in the in-order traversal.

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Minimum Absolute Difference in BST - LeetCode 530 Solution

Q: How to solve Minimum Absolute Difference in BST?

The solution performs an in-order traversal of the BST. During the traversal, it keeps track of the previous node visited. For each node, it calculates the absolute difference between its value and the value of the previous node. The minimum of these differences is then returned. This approach works because the in-order traversal visits nodes in ascending order, ensuring that we only compare nodes that are close in value.

Minimum Absolute Difference in BST - Complete Solution Guide

Minimum Absolute Difference in BST is LeetCode problem 530, a Easy level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Framing

Minimum Absolute Difference in BST is a Easy LeetCode problem that rewards careful tracing, edge-case handling, and a clear grasp of Tree and Depth-First Search. The best solutions usually explain why the chosen invariant holds before they optimize for time or space.

Quick Example Mindset

A useful way to test Minimum Absolute Difference in BST is to start with a tiny input that exposes the boundary conditions, then run the same logic on a slightly larger case to verify the tree behavior and the depth-first search interaction. That second pass is where off-by-one mistakes and missing updates usually appear.

Problem Statement

Given the root of a Binary Search Tree (BST), return the minimum absolute difference between the values of any two different nodes in the tree . Example 1: Input: root = [4,2,6,1,3] Output: 1 Example 2: Input: root = [1,0,48,null,null,12,49] Output: 1 Constraints: The number of nodes in the tree is in the range [2, 10 4 ] . 0 <= Node.val <= 10 5 Note: This question is the same as 783: https://leetcode.com/problems/minimum-distance-between-bst-nodes/

Detailed Explanation

The problem asks us to find the minimum absolute difference between any two distinct node values in a given Binary Search Tree (BST). The input is the root node of the BST, and the output is the smallest difference between any two node values within that tree. The tree can have between 2 and 10,000 nodes, and each node's value is between 0 and 100,000.

Solution Approach

The solution performs an in-order traversal of the BST. During the traversal, it keeps track of the previous node visited. For each node, it calculates the absolute difference between its value and the value of the previous node. The minimum of these differences is then returned. This approach works because the in-order traversal visits nodes in ascending order, ensuring that we only compare nodes that are close in value.

Step-by-Step Algorithm

Step 1: Initialize `min_diff` to infinity (or a very large number) to store the minimum absolute difference found so far.
Step 2: Initialize `prev` to None (or null) to store the previously visited node during the in-order traversal.
Step 3: Implement an in-order traversal (either recursively or iteratively).
Step 4: During the in-order traversal, for each node, check if `prev` is not None. If `prev` is not None, calculate the absolute difference between the current node's value and `prev`'s value.
Step 5: Update `min_diff` with the minimum of the current `min_diff` and the newly calculated absolute difference.
Step 6: Update `prev` to the current node.
Step 7: Continue the in-order traversal until all nodes have been visited.
Step 8: Return `min_diff`.

Key Insights

Insight 1: The key property of a BST is that an in-order traversal yields the nodes in sorted order.
Insight 2: To find the minimum difference, we only need to compare each node with its immediate predecessor and successor in the in-order traversal.
Insight 3: We can use either an iterative or recursive in-order traversal to solve this problem. The iterative solution uses a stack to simulate the recursion.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(h)

Topics

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

Study Paths

Continue from this problem into the surrounding topic and company clusters to compare how the same pattern appears in other interview settings.

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.

How should I approach easy-level algorithm problems?

Easy problems build foundational skills. Focus on: 1) Understanding the problem completely before coding, 2) Writing clean, readable code, 3) Handling all edge cases (empty input, single element, etc.), 4) Analyzing time and space complexity. Don't skip complexity analysis even for simple solutions.

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.

Minimum Absolute Difference in BST | LeetCode 530

Easy

Tree Depth-First Search Breadth-First Search Binary Search Tree Binary Tree

Study Path

Browse topics

Continue through the pattern hub for deeper coverage and neighboring problem variants.

Tree Depth-First Search Breadth-First Search Binary Search Tree Binary Tree

Company Signals

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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 {
    Integer prev;
    int minDiff;
    public int getMinimumDifference(TreeNode root) {
        prev = null;
        minDiff = Integer.MAX_VALUE;
        inorder(root);
        return minDiff;
    }
    private void inorder(TreeNode node){
        if(node == null) return;
        inorder(node.left);
        if(prev != null){
            minDiff = Math.min(minDiff, node.val - prev);
        }
        prev = node.val;
        inorder(node.right);
    }
}

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Problem Info

Description

Problem 530: Minimum Absolute Difference in BST - Detailed explanation and solution approaches.

Topics

Tree Depth-First Search Breadth-First Search Binary Search Tree Binary Tree

Stats

Difficulty:Easy

Languages:4

Problem #:530

Problem Explanation

🧭

Next Steps

Use this problem as a starting point, then move into adjacent patterns and company sets to reinforce the same idea in different contexts.

Topic hub

Study neighboring problems by pattern and difficulty.

Company hub

See where this problem appears in interview loops.

Pattern guides

Read deeper walkthroughs of the algorithm family.

💡

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

8 steps

1
Step 1: Initialize `min_diff` to infinity (or a very large number) to store the minimum absolute difference found so far.
2
Step 2: Initialize `prev` to None (or null) to store the previously visited node during the in-order traversal.
3
Step 3: Implement an in-order traversal (either recursively or iteratively).
4
Step 4: During the in-order traversal, for each node, check if `prev` is not None. If `prev` is not None, calculate the absolute difference between the current node's value and `prev`'s value.
5
Step 5: Update `min_diff` with the minimum of the current `min_diff` and the newly calculated absolute difference.
6
Step 6: Update `prev` to the current node.
7
Step 7: Continue the in-order traversal until all nodes have been visited.
8
Step 8: Return `min_diff`.

💡

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 determined by the in-order traversal, which visits each node once. The space complexity is determined by the maximum depth of the recursion stack (recursive solutions) or the maximum size of the stack in the iterative solution. In a balanced tree the recursion/stack depth is logarithmic with respect to the number of nodes, however in a skewed tree the depth is linear with the number of nodes.

📖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

Store in-order traversal in a list

Perform an in-order traversal and store the node values in a list. Then, iterate through the list and calculate the differences between consecutive elements. Find the minimum difference among these differences.

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

Trade-offs: This approach uses more space (O(n)) to store the node values, but it might be easier to understand for some beginners. The main solution is more space-efficient, especially for balanced BSTs.

✨

Key Insights

1Insight 1: The key property of a BST is that an in-order traversal yields the nodes in sorted order.
2Insight 2: To find the minimum difference, we only need to compare each node with its immediate predecessor and successor in the in-order traversal.
3Insight 3: We can use either an iterative or recursive in-order traversal to solve this problem. The iterative solution uses a stack to simulate the recursion.

📚

Key Terms Explained

For Students

Tree

Hierarchical structure with nodes. Like a family tree!

Edge Cases

Edge case 1: Tree with only two nodes. The algorithm correctly calculates the absolute difference between the two nodes and returns it as the minimum difference.
Edge case 2: Skewed tree (e.g., all nodes are only in the left subtree). The algorithm still performs an in-order traversal and calculates the minimum difference correctly, although it results in the worst-case space complexity of O(n).

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Not recognizing the importance of the BST property and not performing an in-order traversal, which results in incorrect results.

✗Common mistake 2: Forgetting to handle the case when `prev` is None during the in-order traversal, which can lead to errors when calculating the difference.

✗Common mistake 3: Not initializing the `min_diff` to infinity or a very large number. This can lead to incorrect results if the actual minimum difference is smaller than the initial value.

✅

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: In database indexing, where you want to find the closest data points to a given value. The BST structure is often used in indexing, and finding the minimum difference is useful for range queries.

🏦Real-world scenario 2: In recommendation systems, where you want to find items with the closest attributes to a user's preference. The BST can store item attributes, and finding the minimum difference helps identify the most relevant items.

💡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

Don't rush. Explain your thought process clearly. Easy problems are often about communication.

⚠️ Watch Out

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

👨‍💻 From Experience

This is one of the first problems I solved when learning Tree. It's a great foundation for more complex problems.

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: November 18, 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

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

@DevExpert92Jul 21

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

@AlgoMasterJul 14

❓

Frequently Asked Questions

How do I choose between recursive and iterative tree traversal?

How should I approach easy-level algorithm problems?

How should I practice algorithm problems effectively?

What is the optimal approach for "Minimum Absolute Difference in BST"?

For this easy-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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