To solve Minimum Absolute Difference in BST, traverse the tree while tracking previous node values to compute differences efficiently. In-order DFS gives a sorted sequence that guarantees minimum difference checks between consecutive nodes. BFS can also be adapted with careful state management, but in-order DFS is typically faster and simpler for most BST layouts.
Problem Statement
Given the root of a Binary Search Tree (BST), determine the minimum absolute difference between values of any two different nodes. You must account for all node pairs and optimize traversal to avoid redundant comparisons.
The BST nodes have integer values, and the tree contains at least two nodes. Implement a solution that efficiently computes the minimum absolute difference while leveraging BST ordering properties and tree traversal patterns.
Examples
Example 1
Input: root = [4,2,6,1,3]
Output: 1
Example details omitted.
Example 2
Input: root = [1,0,48,null,null,12,49]
Output: 1
Example details omitted.
Constraints
- The number of nodes in the tree is in the range [2, 104].
- 0 <= Node.val <= 105
Solution Approach
In-order DFS traversal
Perform an in-order depth-first search (DFS) to visit nodes in ascending order. Track the previous node value and compute the absolute difference with the current node, updating the minimum difference found so far. This approach leverages BST ordering to only compare consecutive values.
Iterative DFS using stack
Use an explicit stack to traverse the BST iteratively in in-order sequence. Maintain previous node value and current minimum difference as state variables. This avoids recursion stack overhead and is practical for large BSTs where recursion depth might be a concern.
BFS with level tracking
While less conventional, a BFS can track all node values and sort them to compute differences. Maintain a list of visited node values and update the minimum absolute difference by comparing each pair. This approach demonstrates state tracking flexibility, though in-order DFS is more efficient.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
Time complexity is O(n) for in-order DFS as each node is visited once. Space complexity is O(h) for recursion stack or iterative stack, where h is tree height. BFS may require O(n) additional space for storing values.
What Interviewers Usually Probe
- Are you tracking previous values correctly during traversal to avoid missing minimum differences?
- Can you implement in-order traversal both recursively and iteratively?
- Do you consider the BST property to reduce comparisons instead of brute-force checking all pairs?
Common Pitfalls or Variants
Common pitfalls
- Comparing all pairs of nodes leads to O(n^2) time complexity instead of leveraging BST ordering.
- Forgetting to initialize previous node value can cause incorrect difference computation on the first node.
- Using BFS without proper sorting or state tracking may miss the minimum absolute difference.
Follow-up variants
- Compute the minimum absolute difference in a Binary Tree without BST ordering, requiring full pairwise comparisons.
- Find the maximum absolute difference between BST nodes, changing comparison logic but using similar traversal techniques.
- Compute the minimum absolute difference for a BST with duplicate values, requiring careful handling of equal consecutive nodes.
How GhostInterview Helps
- Automatically generates traversal sequences highlighting where minimum differences occur, reducing manual debugging.
- Tracks state variables and previous node values for each step to ensure no edge cases are missed during DFS or BFS.
- Provides inline reasoning about BST ordering and difference updates, helping you implement the correct in-order solution efficiently.
Topic Pages
Related GhostInterview Pages
- LeetCode Interview Copilot - Use GhostInterview as a live solver when you want direct help with LeetCode-style coding questions.
- Coding Interview Assistant - See how GhostInterview supports array, string, linked list, graph, and tree interview workflows.
- How GhostInterview Works - Review the screenshot, reasoning, and answer flow before using the solver in a live interview.
FAQ
What is the best approach to find Minimum Absolute Difference in BST?
An in-order DFS traversal is most efficient, as it visits nodes in sorted order and only compares consecutive values to find the minimum difference.
Can BFS be used to solve this problem efficiently?
Yes, BFS can be used if you track all node values and sort them before computing differences, but it is generally less space-efficient than in-order DFS.
How do I handle large BSTs without hitting recursion limits?
Use iterative DFS with a stack to traverse the tree in-order, maintaining previous node and minimum difference state explicitly.
Does this method work if the BST contains duplicate values?
Yes, duplicates are handled naturally in in-order traversal; the minimum absolute difference may be zero if consecutive nodes have equal values.
Why track only previous node value instead of all nodes?
In-order DFS ensures nodes are visited in ascending order, so the minimum difference will always occur between consecutive nodes, avoiding unnecessary comparisons.
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