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@pertrai1 pertrai1 commented Jan 31, 2026

Summary by CodeRabbit

  • New Features

    • Added "Vertical Order Traversal of a Binary Tree" problem to the LeetCode hard problems collection, bringing the total to 172 problems.
    • Exposed public API for the vertical traversal implementation.
  • Documentation

    • Reorganized and updated documentation for the vertical order traversal problem, including problem statement, examples, and constraints.

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@pertrai1 pertrai1 requested a review from Copilot January 31, 2026 14:28
@pertrai1 pertrai1 added the code challenge this is a coding challenge label Jan 31, 2026
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github-actions bot commented Jan 31, 2026

Claude finished @pertrai1's task in 1m 33s —— View job


Code Review Complete ✓

Summary

This PR successfully moves the "Vertical Order Traversal of a Binary Tree" solution into the proper directory structure and improves code quality. The solution is algorithmically correct and handles all test cases properly.

Correctness ✅

The solution correctly implements vertical order traversal with proper handling of:

  • Nodes at the same column (sorted by row, then by value)
  • The critical edge case where nodes share the same (row, col) position
  • Empty tree handling (implicit in DFS base case)

Mental trace verification for Example 2 [1,2,3,4,5,6,7]:

  • Column -2: [4]
  • Column -1: [2]
  • Column 0: [1,5,6] - nodes 5 and 6 at (2,0) are correctly sorted by value ✓
  • Column 1: [3]
  • Column 2: [7]

Complexity Analysis

Time Complexity: O(n log n) where n is the number of nodes

  • DFS traversal visits each node once: O(n)
  • Sorting columns: O(k log k) where k is number of unique columns (worst case k = n)
  • Sorting nodes within each column: O(m log m) per column, where m is nodes in that column
  • Overall dominated by sorting: O(n log n)

Space Complexity: O(n)

  • HashMap storage: O(n) for storing all nodes
  • Recursion stack: O(h) where h is tree height (worst case O(n) for skewed tree)
  • Output array: O(n)
  • Overall: O(n)

Pattern Recognition: DFS + Hash Map + Multi-level Sorting

Primary Pattern: DFS Traversal with Coordinate Tracking

This problem uses DFS (Depth-First Search) to traverse the tree while tracking 2D coordinates (row, col). The coordinate system transforms the tree structure into a sortable format.

Why This Pattern Works

DFS is ideal here because:

  1. We need to visit ALL nodes (not just find a path or level)
  2. The order of visiting doesn't matter since we sort afterward
  3. Recursive DFS naturally tracks depth (row) through the call stack

Key Insight 💡

The critical insight is treating the tree as a 2D coordinate system where sorting rules define the output order:

  1. Primary sort: Column (left to right) - determines which array
  2. Secondary sort: Row (top to bottom) - handles vertical ordering within columns
  3. Tertiary sort: Value (ascending) - breaks ties for nodes at the same position

The problem is essentially asking you to map tree positions to (row, col) coordinates, then perform a multi-key sort. Most solutions fail by forgetting the tertiary sort condition (nodes at same position must be sorted by value).

Code Quality Review

Strengths

  • ✅ Clear variable names (valueMap, sortedCols, sortedNodes)
  • ✅ Helpful inline comments explaining the map structure
  • ✅ Proper use of TypeScript with explicit types
  • ✅ Exported TreeNode class for testability
  • ✅ Clean separation: DFS logic → column sorting → node sorting

Improvements Made in This PR

Looking at the diff from the original solution:

vertical-order-traversal-of-a-binary-tree.ts:25

- valueMap.get(col).sort(...)
+ valueMap.get(col)!.sort(...)

✅ Added non-null assertion operator (!) - this is correct since we just checked has(col) and set it if missing

vertical-order-traversal-of-a-binary-tree.ts:1-10

+ export class TreeNode {
+   val: number;
+   left: TreeNode | null;
+   right: TreeNode | null;
+   constructor(val?: number, left?: TreeNode | null, right?: TreeNode | null) {
+     this.val = val === undefined ? 0 : val;
+     this.left = left === undefined ? null : left;
+     this.right = right === undefined ? null : right;
+   }
+ }

✅ Exported TreeNode class - enables testing and reusability

vertical-order-traversal-of-a-binary-tree.ts:12

- function verticalTraversal(...)
+ export function verticalTraversal(...)

✅ Added export keyword - makes the function testable

Minor Suggestions

Comment Enhancement (optional)
The sorting comment on line 38 could be more explicit about the tie-breaking:

// sort column entries: row (ascending) -> value (ascending for ties)
const sortedNodes = valueMap.get(col)!.sort((a, b) => a[0] - b[0] || a[1] - b[1]);

Common Mistakes with This Pattern

  1. Forgetting to sort by value when nodes share position - Your solution correctly handles this with || a[1] - b[1]
  2. Using BFS when DFS is simpler - Some solutions use BFS with level tracking, but it's unnecessarily complex
  3. Not handling negative columns - Your solution correctly uses a Map (not array) to handle negative column indices
  4. Inefficient column sorting - Your solution efficiently extracts keys once and sorts them

Alternative Approaches

Approach 1: BFS with Level Tracking (What You Did - Optimal)

  • Pros: Natural coordinate tracking, clean code
  • Cons: None - this is the standard optimal solution
  • Complexity: O(n log n) time, O(n) space

Approach 2: DFS with Tuple Arrays

Store [col, row, val] tuples in a single array, then sort by all three keys:

const nodes: [number, number, number][] = [];
// ... collect nodes
nodes.sort((a, b) => a[0] - b[0] || a[1] - b[1] || a[2] - b[2]);
  • Pros: Single sort operation, potentially clearer
  • Cons: More memory allocation, still O(n log n)

Approach 3: BFS with Queue

Track coordinates using a queue instead of recursion:

  • Pros: Avoids recursion stack (iterative)
  • Cons: More verbose, harder to read, same complexity

Related Problems for Practice

To build pattern recognition with coordinate-based tree traversal:

  1. LeetCode 314 - Binary Tree Vertical Order Traversal (Medium)

    • Similar problem but nodes at same position don't need value sorting
    • Good warmup before this problem
  2. LeetCode 987 - Vertical Order Traversal of a Binary Tree (Hard)

    • This is the SAME problem (just confirming)
  3. LeetCode 102 - Binary Tree Level Order Traversal (Medium)

    • Practices coordinate tracking with row/level grouping
  4. LeetCode 107 - Binary Tree Level Order Traversal II (Medium)

    • Level order but bottom-up (adds sorting dimension)

Learning Summary

Key Concepts Mastered

  • Multi-dimensional sorting: Sorting by multiple keys (col → row → value)
  • Coordinate mapping: Transforming tree structure into sortable coordinates
  • Hash map for grouping: Using Map to group nodes by column
  • DFS with parameter passing: Tracking state (row, col) through recursion

Interview Takeaway

When you see "vertical order" or "group by column", think:

  1. DFS/BFS with coordinate tracking
  2. Hash map to group by column
  3. Multi-level sorting based on problem requirements

The sorting requirements are what make this problem "Hard" - many candidates miss the value-sorting tie-breaker.


Verdict: Excellent solution! The code is clean, correct, and optimal. The PR successfully reorganizes the codebase and improves code quality with proper exports. ✅

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Review was skipped as selected files did not have any reviewable changes.

💤 Files selected but had no reviewable changes (2)
  • .github/backups/code-quality.yml
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📝 Walkthrough

Walkthrough

Problem documentation is reorganized by moving the README to the hard problems directory structure. The root README is updated to reflect the new problem addition, increasing Hard problem count from 14 to 15. The TypeScript implementation exports TreeNode and verticalTraversal function with minor formatting adjustments.

Changes

Cohort / File(s) Summary
Documentation Restructuring
1029-vertical-order-traversal-of-a-binary-tree/README.md, README.md, leetcode/hard/0987-vertical-order-traversal-of-a-binary-tree/README.md
Deletes old README, adds new documentation under hard problems directory, and updates root README to reflect new Hard problem count (14→15) and total problems (171→172). Introduces Tree Problems subsection under Hard Problems.
Public API Exposure
leetcode/hard/0987-vertical-order-traversal-of-a-binary-tree/vertical-order-traversal-of-a-binary-tree.ts
Exports TreeNode class and verticalTraversal function as public entities. Adds non-null assertion for column value map access. Minor formatting adjustments to spacing and undefined checks.

Estimated code review effort

🎯 2 (Simple) | ⏱️ ~10 minutes

Poem

🐰 A problem finds its rightful home,
From scattered paths, now neatly shown,
The tree stands tall, exported bright,
With vertical order shining right! 🌳✨

🚥 Pre-merge checks | ✅ 2 | ❌ 1
❌ Failed checks (1 warning)
Check name Status Explanation Resolution
Docstring Coverage ⚠️ Warning Docstring coverage is 0.00% which is insufficient. The required threshold is 80.00%. Write docstrings for the functions missing them to satisfy the coverage threshold.
✅ Passed checks (2 passed)
Check name Status Explanation
Description Check ✅ Passed Check skipped - CodeRabbit’s high-level summary is enabled.
Title check ✅ Passed The title accurately describes the main change: adding a solution for the Vertical Order Traversal of a Binary Tree problem, which is clearly reflected in the new README documentation, code exports, and main index updates.

✏️ Tip: You can configure your own custom pre-merge checks in the settings.

✨ Finishing touches
🧪 Generate unit tests (beta)
  • Create PR with unit tests
  • Post copyable unit tests in a comment
  • Commit unit tests in branch leetcode-1312026

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🤖 Gemini Code Review (Model: gemini-2.5-flash)

Here's a review of your LeetCode solution for "Vertical Order Traversal of a Binary Tree":


1. Pattern Identification

This solution primarily uses Tree Traversal (Depth-First Search - DFS) combined with Coordinate Geometry and Custom Sorting. It assigns (row, col) coordinates to each node during traversal and then uses these coordinates to group and sort the nodes.

2. Complexity Verification

  • Time Complexity: O(N log N)

    • Traversal (traverse function): Each node is visited exactly once. For each node, a constant number of operations (map lookup/insertion, array push) are performed. This part is O(N), where N is the number of nodes.
    • Sorting Columns: Array.from(valueMap.keys()).sort(...) takes O(C log C), where C is the number of unique columns. In the worst case (e.g., a skewed tree), C can be up to N. So, this is O(N log N).
    • Sorting Nodes within Columns: For each column j, if there are N_j nodes, sorting takes O(N_j log N_j). The sum of all N_j is N. In the worst case, all N nodes could fall into a single column (e.g., a linked list where col is always 0), leading to O(N log N) for that column. Even if nodes are distributed across columns, the sum sum(N_j log N_j) is bounded by O(N log N).
    • Overall: The dominant factor is the sorting steps, making the total time complexity O(N log N). The stated complexity is accurate.
  • Space Complexity: O(N)

    • valueMap: Stores information for all N nodes. Each node stores [row, val]. This requires O(N) space.
    • Recursion Stack: For DFS, the maximum depth of the recursion stack is equal to the height of the tree, H. In the worst case (a skewed tree), H can be N. This requires O(H) space.
    • Overall: The total space complexity is O(N + H), which simplifies to O(N) since H <= N. The stated complexity is accurate.

3. Key Insight

The key insight is to assign a unique coordinate (row, col) to each node during tree traversal and then use these coordinates for grouping and sorting.

  1. The root is at (0, 0).
  2. A left child of (row, col) is at (row + 1, col - 1).
  3. A right child of (row, col) is at (row + 1, col + 1).

By storing nodes in a Map where keys are col indices and values are lists of [row, node.val], you can easily group all nodes belonging to the same vertical line. The final crucial step is the multi-level sorting: first by column index (left to right), then within each column by row index (top to bottom), and finally by node value (for nodes at the exact same (row, col)).

4. Edge Case Analysis

The solution handles several important edge cases correctly:

  • Empty Tree (root = null): The function correctly returns [] because the if (!root) check at the beginning of traverse prevents any processing, and valueMap remains empty.
  • Single Node Tree (root = [val]): The traverse function will add [0, val] to valueMap.get(0). The sorting logic will correctly produce [[val]].
  • Skewed Trees (e.g., a linked list): The col indices can become negative or very large. The Map handles arbitrary integer keys, and the sorting logic a - b works correctly for negative numbers.
  • Nodes at the Same (row, col): The problem explicitly states to sort these nodes by their values. Your custom sort comparator a[0] - b[0] || a[1] - b[1] correctly implements this tie-breaking rule: it first compares row (a[0] - b[0]), and only if rows are equal (result is 0), it then compares node.val (a[1] - b[1]).

5. Learning Points

  • Similar Problems:
    • Binary Tree Level Order Traversal (BFS): Similar grouping by level, but this problem extends it with horizontal coordinates.
    • Binary Tree Right/Left Side View: Requires tracking nodes by level and often involves a similar traversal approach to identify the first/last node seen at each level.
    • Bottom View / Top View of Binary Tree: These are direct variations where you only keep one node per column based on depth (bottom view) or first seen (top view).
    • Diagonal Traversal of Binary Tree: Another coordinate-based traversal, but using row - col or row + col as an identifier.
  • Common Mistakes with this Pattern:
    • Incorrect Coordinate Calculation: A common error is miscalculating col - 1 or col + 1 for children.
    • Forgetting Tie-Breaking Rules: Overlooking the requirement to sort by node value when nodes share the same (row, col) is a frequent mistake.
    • Inefficient Data Structures: Using an array of arrays and then repeatedly searching for column indices instead of a Map could lead to O(N^2) or worse complexity.
    • Improper Sorting Logic: Incorrectly chaining sort comparators or applying them in the wrong order.
  • Variations of this Problem:
    • Horizontal Order Traversal: Similar logic, but grouping by row and sorting by col.
    • Sum of Nodes in Each Vertical Line: Instead of collecting values, you'd sum them up for each column.
    • Smallest/Largest Value in Each Vertical Line: Keep track of min/max values per column.

6. Code Quality

  • Variable Naming: Names like valueMap, col, row, val, sortedCols, sortedNodes are clear and descriptive, enhancing readability.
  • Code Structure: The use of a helper traverse function keeps the main verticalTraversal function clean and focused on orchestration. The TreeNode class definition is properly exported.
  • Readability: The code is well-structured and easy to follow.
  • TypeScript Best Practices:
    • export class TreeNode and export function verticalTraversal are good for modularity.
    • The ! (non-null assertion operator) in valueMap.get(col)! is used correctly here because sortedCols is derived from valueMap.keys(), guaranteeing that col will exist as a key. However, in general, it's good practice to be explicit with checks (if (valueMap.has(col))) or provide a default if there's any ambiguity. For this specific flow, it's safe.
    • The constructor for TreeNode is well-defined with default values.

7. Alternative Approaches

  1. BFS (Breadth-First Search) Approach:

    • Instead of a recursive DFS, you could use an iterative BFS with a queue. Each element in the queue would be [node, row, col].
    • Dequeue [currNode, r, c], process currNode.val by adding [r, currNode.val] to valueMap.get(c).
    • Enqueue [currNode.left, r + 1, c - 1] and [currNode.right, r + 1, c + 1].
    • Trade-offs: BFS naturally processes nodes level by level (top-to-bottom). However, for nodes at the same (row, col), the order of processing in BFS doesn't guarantee value-based sorting, so the final sorting step (by row then by value) would still be necessary, making its overall time and space complexity similar to DFS (O(N log N) time, O(N) space). BFS might be preferred by some for its iterative nature and explicit queue management.
  2. Collect All and Sort (Single Pass then Sort):

    • Perform a single DFS or BFS traversal to collect all nodes into a flat list, where each entry is [col, row, val].
    • After the traversal, sort this single list of N elements using a custom comparator: (a, b) => a[0] - b[0] || a[1] - b[1] || a[2] - b[2]. This comparator sorts by column, then by row, then by value.
    • Finally, iterate through the sorted list, grouping elements by col to form the final number[][] output.
    • Trade-offs: This approach can be conceptually simpler as it avoids the Map during collection and performs one large sort. The time complexity would still be O(N log N) for the single sort. Space complexity would be O(N) for the list. It might be slightly less efficient in practice compared to the Map-based approach if the number of distinct columns is small, as sorting many small lists is often faster than one very large list.

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🤖 Gemini Code Review (Model: gemini-2.5-flash)

Here's a review of your LeetCode solution for "Vertical Order Traversal of a Binary Tree":


1. Pattern Identification

This solution primarily uses Depth-First Search (DFS) to traverse the binary tree and collect node information. It then employs a HashMap (JavaScript Map) to group nodes by their calculated column index. Finally, it uses sorting to arrange the collected nodes according to the problem's specific multi-level ordering requirements (by column, then by row, then by value).

2. Complexity Verification

  • Time Complexity: O(N log N)

    • The DFS traversal visits each of the N nodes exactly once, taking O(N) time. During traversal, nodes are added to a Map, which involves constant-time operations on average for Map.get() and Map.set().
    • After traversal, Array.from(valueMap.keys()).sort((a, b) => a - b) sorts the column indices. If there are C distinct columns, this takes O(C log C). In the worst case (e.g., a highly skewed tree), C can be O(N), making this O(N log N).
    • The most significant part is sorting the nodes within each column. For each column, if it contains k nodes, sorting takes O(k log k). Summing this over all columns, where the total number of nodes is N, the combined sorting time is bounded by O(N log N).
    • Therefore, the dominant factor is the sorting, leading to an overall time complexity of O(N log N).
  • Space Complexity: O(N)

    • The valueMap stores all N nodes. Each entry in the map stores a list of [row, value] pairs, so it consumes O(N) space.
    • The DFS recursion stack depth can go up to O(H) where H is the height of the tree. In the worst case (a skewed tree), H can be O(N).
    • The sortedCols array stores C column indices, which is at most O(N).
    • The final result array also stores N node values.
    • Combining these, the total space complexity is O(N).

3. Key Insight

The core insight for this problem is the combination of:

  1. A relative coordinate system: Recognizing how to assign (row, col) coordinates to each node based on its parent's position and whether it's a left or right child. The problem explicitly defines this: root at (0,0), left child (row+1, col-1), right child (row+1, col+1).
  2. Multi-level sorting: Understanding that merely collecting nodes isn't enough; they need to be grouped by column, then sorted by row within each column, and finally by value if both column and row are identical. A Map<col, List<[row, val]>> is the perfect data structure for this grouping, followed by explicit sorting.

4. Edge Case Analysis

The current solution handles the following edge cases correctly:

  • Empty tree (root = null): The if (!root) check at the beginning returns [], which is correct.
  • Single node tree: root = [X]. The traversal will add [0, X.val] to valueMap[0]. The sorting will correctly produce [[X.val]].
  • Skewed trees (left or right): The coordinate system and map handle nodes spanning a large range of columns correctly.
  • All nodes have the same value: The a[1] - b[1] part of the sort comparator correctly differentiates nodes with the same row and column by their value.
  • Nodes at the same (row, col) but different values: This is explicitly handled by the problem's requirement and the a[1] - b[1] secondary sort.

5. Learning Points

  • Similar problems:
    • Binary Tree Level Order Traversal: A foundational problem for tree traversals, often solved with BFS, but the concept of visiting nodes in a structured order is similar.
    • Binary Tree Vertical Order Traversal (Easier version): LeetCode also has an easier version (e.g., LeetCode 314, premium) where the tie-breaking rule for nodes at the same (row, col) is not by value, but by their appearance in level order (which would slightly favor BFS for collection).
    • Top View / Bottom View of Binary Tree: These problems also involve assigning horizontal distances (column indices) to nodes and then selectively picking nodes based on their vertical position (row) or other criteria.
    • Diagonal Traversal of a Binary Tree: Another variation where nodes are grouped by row - col or row + col to define diagonals.
  • Common mistakes:
    • Incorrectly calculating child coordinates. A common mistake is using col directly instead of col-1 or col+1.
    • Forgetting or misimplementing the multi-level sorting logic. It's crucial to sort by column first, then by row, then by value.
    • Using an inefficient data structure for grouping, or trying to achieve the final sorted output directly during traversal without a post-processing step.
  • Variations:
    • Return nodes in horizontal order (group by row, then sort by column).
    • Return nodes in anti-diagonal order (group by row + col).
    • Change the tie-breaking rule for nodes at the same (row, col) (e.g., by insertion order, or by which subtree they came from).

6. Code Quality

  • TreeNode class definition: The TreeNode class is now correctly exported (export class TreeNode), which is good for modularity and testing.
  • Variable Naming: Names like valueMap, queue (though it's not a queue in this DFS solution, valueMap is the main data structure), node, r, c, sortedCols, sortedNodes are clear and descriptive.
  • Code Structure: The recursive traverse helper function clearly separates the traversal logic from the post-processing and sorting. The main verticalTraversal function orchestrates the setup, traversal, and final result assembly.
  • Readability: The use of Array.from(valueMap.keys()).sort() and the multi-level sort comparator a[0] - b[0] || a[1] - b[1] are standard and easy to understand. The ! (non-null assertion) on valueMap.get(col)! is appropriate in TypeScript as the if (!valueMap.has(col)) ensures the array exists.
  • Exporting verticalTraversal: export function verticalTraversal(...) is good practice for testability.

7. Alternative Approaches

  1. Iterative BFS Approach:

    • Instead of a recursive DFS, an iterative Breadth-First Search (BFS) could be used. You would initialize a queue with [[root, 0, 0]].
    • In each step, dequeue [node, row, col], process it (add to valueMap), and enqueue its children with their respective (row+1, col-1) and (row+1, col+1) coordinates.
    • Trade-offs: BFS naturally processes nodes level by level, which might feel more intuitive for the "top-to-bottom" requirement. However, since the final sorting step explicitly handles the row order, the choice between DFS and BFS for collecting the data doesn't change the overall time or space complexity significantly for this problem. BFS might use slightly more memory for the queue in a wide tree compared to DFS's stack in a deep tree, but both are O(N) in the worst case.
  2. Pre-determining min/max columns:

    • Perform an initial DFS/BFS pass just to determine the minimum and maximum column indices.
    • Then, instead of a Map, you could use an array of arrays (e.g., let resultColumns: Array<Array<[row, val]>> = []) indexed by col - minCol. This might slightly optimize access if the column range is dense, but typically Map is more flexible for sparse column indices.
    • Trade-offs: Adds an extra traversal pass. The Map approach is generally more robust for arbitrary column ranges (positive, negative, sparse). The final sorting of map keys (sortedCols) achieves the same effect as a pre-pass.

Overall, this is a well-implemented and correct solution that demonstrates a solid understanding of tree traversals, data structures, and sorting algorithms. Good work!

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github-actions bot commented Jan 31, 2026

🧮 Solution Analysis

PR: Add Vertical Order Traversal of a Binary Tree solution
Files Changed: leetcode/hard/0987-vertical-order-traversal-of-a-binary-tree/vertical-order-traversal-of-a-binary-tree.ts

📊 Code Quality Results

ESLint Analysis

  • Errors: 0
  • Warnings: 0

🔍 Complexity Analysis

💡 Analysis Tips

  • Time Complexity: Focus on the dominant operation in loops
  • Space Complexity: Consider auxiliary data structures
  • Optimization: Look for opportunities to improve efficiency
  • Edge Cases: Ensure your solution handles empty inputs, null/undefined, edge conditions

📁 Analysis Files Created

Detailed analysis files have been automatically generated and committed to docs/analysis/ for future reference.

🎯 Next Steps

  1. Review any ESLint errors/warnings above
  2. Consider the complexity analysis - is this the optimal approach?
  3. Test with edge cases mentioned in the problem description
  4. Add comments explaining complex logic
  5. Check the docs/analysis/ directory for detailed complexity analysis files

Analysis generated for PR files only

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✅ Test Results

Tests have been executed for this pull request.

📊 Coverage Summary

Metric Coverage
Statements 94.61%
Branches 89.26%
Functions 85.71%
Lines 94.68%

Check the workflow logs for detailed test output.

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Pull request overview

Adds a LeetCode solution + documentation for “Vertical Order Traversal of a Binary Tree” and updates the repository’s top-level index accordingly.

Changes:

  • Adds a formatted problem README under leetcode/hard/... for Vertical Order Traversal.
  • Updates the TypeScript solution module to export TreeNode and verticalTraversal.
  • Updates root README.md counts and adds the problem link under Hard → Tree Problems; removes an extra top-level README.

Reviewed changes

Copilot reviewed 4 out of 4 changed files in this pull request and generated 1 comment.

File Description
leetcode/hard/1029-vertical-order-traversal-of-a-binary-tree/vertical-order-traversal-of-a-binary-tree.ts Exports TreeNode + verticalTraversal and tightens a map access with a non-null assertion.
leetcode/hard/1029-vertical-order-traversal-of-a-binary-tree/README.md Adds the problem statement/examples/constraints for the solution directory.
README.md Increments solved counts and adds the problem link under Hard → Tree Problems.
1029-vertical-order-traversal-of-a-binary-tree/README.md Removes a misplaced/duplicate README outside the leetcode/ structure.
Comments suppressed due to low confidence (1)

leetcode/hard/1029-vertical-order-traversal-of-a-binary-tree/vertical-order-traversal-of-a-binary-tree.ts:39

  • valueMap is effectively storing 2-element tuples [row, value], but using number[][] loses that intent and type safety (e.g., a[0], a[1], n[1]). Consider typing the entries as [row: number, val: number][] (or a small interface) to make the sort/mapping safer and self-documenting.

README.md Outdated

### Tree Problems

- [1029 - Vertical Order Traversal of a Binary Tree](./leetcode/hard/1029-vertical-order-traversal-of-a-binary-tree) ![Hard](https://img.shields.io/badge/Hard-red)
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The LeetCode problem number in this entry/directory appears incorrect. The slug vertical-order-traversal-of-a-binary-tree corresponds to LeetCode #987 (Hard), while 1029 is a different problem; this breaks the repo’s established [number]-[problem-name] naming pattern (e.g., README.md:294-296). Please rename the directory/link text to 0987-vertical-order-traversal-of-a-binary-tree and update this list entry accordingly.

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Actionable comments posted: 1

🤖 Fix all issues with AI agents
In `@README.md`:
- Line 9: Update the LeetCode entry in the README table: change the problem ID
for "Vertical Order Traversal of a Binary Tree" from 1029 to 987 and increment
the LeetCode total count from 172 to 173 so the table row "|
[LeetCode](`#leetcode`)           | Data Structures & Algorithms | 172            
|" reflects the corrected ID and total.
🧹 Nitpick comments (2)
leetcode/hard/1029-vertical-order-traversal-of-a-binary-tree/vertical-order-traversal-of-a-binary-tree.ts (2)

12-16: Add algorithm pattern + complexity + example comments.

This solution should include a brief algorithm description, Big‑O time/space with reasoning, and a quick example for clarity and consistency.

✍️ Suggested comment block
+// Algorithm: DFS to collect (row, col, value), then sort columns and entries by row/value.
+// Time: O(N log N) from sorting columns and per-column lists; Space: O(N) for map + recursion.
+// Example: root=[3,9,20,null,null,15,7] → [[9],[3,15],[20],[7]]
 export function verticalTraversal(root: TreeNode | null): number[][] {

As per coding guidelines, leetcode/**/*.{js,ts}: Always document both time and space complexity in Big O notation, document the algorithmic pattern used in solution code comments, and include examples in comments for complex algorithms in solution files.


18-29: Add explicit return type to the helper.

TypeScript guidelines call for explicit return types, including nested functions.

✅ Minimal fix
-  function traverse(node: TreeNode | null, row: number, col: number) {
+  function traverse(node: TreeNode | null, row: number, col: number): void {

As per coding guidelines, **/*.ts: Use explicit type annotations for function parameters and return types.

| Platform | Focus Area | Problems Solved |
| ------------------------------- | ---------------------------- | --------------- |
| [LeetCode](#leetcode) | Data Structures & Algorithms | 171 |
| [LeetCode](#leetcode) | Data Structures & Algorithms | 172 |
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⚠️ Potential issue | 🟡 Minor

🧩 Analysis chain

🏁 Script executed:

#!/bin/bash
# Count problem directories by difficulty
for level in easy medium hard; do
  count=$(find "leetcode/$level" -mindepth 1 -maxdepth 1 -type d 2>/dev/null | wc -l)
  echo "$level: $count"
done
echo "total: $(find leetcode -mindepth 2 -maxdepth 2 -type d 2>/dev/null | wc -l)"

Repository: pertrai1/coding-challenges

Length of output: 109


🌐 Web query:

LeetCode problem number "Vertical Order Traversal of a Binary Tree"

💡 Result:

LeetCode problem number: 987Vertical Order Traversal of a Binary Tree [1][3]


Correct the LeetCode problem ID and update the total count.

The problem ID for "Vertical Order Traversal of a Binary Tree" is 987, not 1029. Additionally, the LeetCode total on line 9 should be 173, not 172, to match the actual number of problems in the directory structure (81 easy + 77 medium + 15 hard).

🤖 Prompt for AI Agents
In `@README.md` at line 9, Update the LeetCode entry in the README table: change
the problem ID for "Vertical Order Traversal of a Binary Tree" from 1029 to 987
and increment the LeetCode total count from 172 to 173 so the table row "|
[LeetCode](`#leetcode`)           | Data Structures & Algorithms | 172            
|" reflects the corrected ID and total.

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github-actions bot commented Jan 31, 2026

Claude finished @pertrai1's task in 1m 50s —— View job


Educational Code Review ✅

Summary

This PR successfully reorganizes the "Vertical Order Traversal of a Binary Tree" solution from the incorrect directory (1029) to the correct one (0987), and the solution itself is algorithmically correct and well-implemented. Excellent work on a challenging Hard problem!


1. Correctness Analysis ✅

Algorithm Verification

The solution correctly implements vertical order traversal with proper handling of all requirements:

✅ Core Logic

  • Assigns (row, col) coordinates correctly: root at (0,0), left child at (row+1, col-1), right at (row+1, col+1)
  • Groups nodes by column using a Map
  • Sorts columns left-to-right (line 34)
  • Sorts nodes within each column by row, then by value (line 38)

✅ Critical Edge Case: Nodes at Same Position
The problem's trickiest requirement is handling nodes at the same (row, col) position. Your solution correctly sorts by value:

// Line 38: First sort by row (a[0] - b[0]), THEN by value (a[1] - b[1])
.sort((a, b) => a[0] - b[0] || a[1] - b[1])

Mental Trace Verification (Example 2)
For root = [1,2,3,4,5,6,7]:

Tree structure:      Coordinates:
      1              (0, 0)
     / \            /      \
    2   3      (1,-1)      (1,1)
   / \ / \      /  \        /  \
  4  5 6  7  (2,-2)(2,0) (2,0)(2,2)
  • Column -2: [4]
  • Column -1: [2]
  • Column 0: [1,5,6] — Nodes 5 and 6 both at (2,0), correctly sorted 5 before 6 by value ✓
  • Column 1: [3]
  • Column 2: [7]

✅ Other Edge Cases

  • Empty tree: Handled by base case (line 19)
  • Single node: Returns [[val]] correctly
  • Negative column indices: Map handles them properly

2. Complexity Analysis

Time Complexity: O(n log n)

Breaking it down:

  1. DFS Traversal (line 31): O(n) — visits each node once
  2. Extract & Sort Column Keys (line 34): O(k log k) where k = number of unique columns
    • Worst case (skewed tree): k ≈ n → O(n log n)
  3. Sort Nodes Within Each Column (line 38):
    • Per column: O(m log m) where m = nodes in that column
    • Across all columns: Σ(m_i log m_i) where Σm_i = n
    • Worst case (all nodes in one column): O(n log n)
    • Best case (evenly distributed): O(n log(n/k)) ≈ O(n log n)

Dominant factor: Sorting operations → O(n log n)

Space Complexity: O(n)

  1. valueMap: Stores all n nodes as [row, val] pairs → O(n)
  2. Recursion Stack: O(h) where h = tree height
    • Balanced tree: O(log n)
    • Skewed tree: O(n)
  3. Output Array: O(n) for storing results

Total: O(n) + O(h) + O(n) = O(n) since h ≤ n


3. Pattern Recognition: DFS + Hash Map + Multi-Key Sorting

Primary Pattern: Tree Traversal with Coordinate Mapping

This problem combines:

  1. DFS (Depth-First Search) — recursive tree traversal
  2. Coordinate System — treating tree as 2D grid with (row, col)
  3. Hash Map Grouping — collecting nodes by column
  4. Multi-Level Sorting — ordering by multiple criteria

Why This Pattern Works

DFS Choice:

  • Need to visit ALL nodes (not early termination like in search problems)
  • Order of visiting doesn't matter since we sort afterward
  • Recursive calls naturally track depth (row)

Coordinate System:

  • Transforms tree structure into sortable 2D coordinates
  • Enables grouping (by column) and ordering (by row, then value)

Multi-Key Sort:
The problem asks for three sorting criteria:

  1. Primary: Column (left to right) — determines output array grouping
  2. Secondary: Row (top to bottom) — vertical ordering within columns
  3. Tertiary: Value (ascending) — tie-breaker for same position

💡 Key Insight

The non-obvious trick: This is fundamentally a sorting problem disguised as a tree traversal problem. The "hard" part isn't the traversal—it's realizing you need to:

  1. Map the tree to (row, col) coordinates
  2. Apply a three-level sort: column → row → value
  3. The tertiary sort (by value) is what catches most people—many solutions fail test cases where nodes share the exact same (row, col) position

Most incorrect solutions either:

  • Forget the value-based tie-breaker entirely
  • Apply the sorts in the wrong order
  • Try to maintain order during traversal (unnecessarily complex)

Your solution nails this by cleanly separating concerns: collect during DFS, sort afterward.


4. Code Quality Review

Strengths ✅

vertical-order-traversal-of-a-binary-tree.ts:13-16

// initialize a map where:
// key = column index
// value = array of [row, node.val]
const valueMap = new Map<number, number[][]>();

✅ Excellent comment explaining the data structure

vertical-order-traversal-of-a-binary-tree.ts:1-10

export class TreeNode {
  val: number;
  left: TreeNode | null;
  right: TreeNode | null;
  constructor(val?: number, left?: TreeNode | null, right?: TreeNode | null) {
    this.val = val === undefined ? 0 : val;
    this.left = left === undefined ? null : left;
    this.right = right === undefined ? null : right;
  }
}

✅ Exported for testability and reusability

vertical-order-traversal-of-a-binary-tree.ts:25

valueMap.get(col)!.push([row, node.val]);

✅ Correct use of non-null assertion — we just checked has(col) on line 22

vertical-order-traversal-of-a-binary-tree.ts:38

const sortedNodes = valueMap.get(col)!.sort((a, b) => a[0] - b[0] || a[1] - b[1]);

✅ Clean chained sort comparator for multi-level sorting

Minor Suggestions

1. Add Algorithm Overview Comment

Consider adding a brief complexity comment at the function start:

// Algorithm: DFS with coordinate tracking + multi-key sorting
// Time: O(n log n) - dominated by sorting operations
// Space: O(n) - Map storage + recursion stack
export function verticalTraversal(root: TreeNode | null): number[][] {

2. Clarify Tertiary Sort in Comment

Line 37's comment could be more explicit:

// sort column entries: row (ascending) -> value (ascending for ties at same position)

3. TypeScript Type Safety (Optional Enhancement)

Your tuple type number[][] works but loses semantic meaning. For even better type safety:

type NodeEntry = [row: number, value: number];
const valueMap = new Map<number, NodeEntry[]>();

This makes a[0] and a[1] self-documenting in the sort.


5. Common Mistakes with This Pattern

🚨 Pitfalls to Avoid:

  1. Forgetting Value-Based Tie-Breaking

    • Missing || a[1] - b[1] causes wrong output when nodes share (row, col)
    • This is THE most common error for this problem
  2. Wrong Sort Order

    • Sorting by value before row: a[1] - b[1] || a[0] - b[0]
    • Must be row first, then value
  3. Using Array Instead of Map

    • Arrays can't handle negative column indices elegantly
    • Your Map approach is optimal
  4. Trying to Maintain Order During Traversal

    • Some attempt to insert in sorted order during DFS
    • Much more complex than collect-then-sort approach
  5. BFS Complexity

    • Some use BFS thinking it's "more natural" for level-order
    • Adds queue management overhead without improving complexity

6. Alternative Approaches

Approach 1: Your DFS + Map (Optimal) ✅

// Current implementation
  • Time: O(n log n)
  • Space: O(n)
  • Pros: Clean separation of concerns, easy to understand
  • Cons: None—this is the standard optimal solution

Approach 2: BFS with Queue

function verticalTraversal(root: TreeNode | null): number[][] {
  if (!root) return [];
  const queue: [TreeNode, number, number][] = [[root, 0, 0]];
  const map = new Map<number, [number, number][]>();
  
  while (queue.length) {
    const [node, row, col] = queue.shift()!;
    if (!map.has(col)) map.set(col, []);
    map.get(col)!.push([row, node.val]);
    
    if (node.left) queue.push([node.left, row + 1, col - 1]);
    if (node.right) queue.push([node.right, row + 1, col + 1]);
  }
  // ... same sorting logic
}
  • Time: O(n log n) — same complexity
  • Space: O(n) — queue instead of recursion stack
  • Pros: Iterative (no stack overflow risk), processes level-by-level
  • Cons: More verbose, still needs same sorting step, no real advantage

Approach 3: Single Array + One Sort

function verticalTraversal(root: TreeNode | null): number[][] {
  const nodes: [number, number, number][] = []; // [col, row, val]
  
  function dfs(node: TreeNode | null, row: number, col: number) {
    if (!node) return;
    nodes.push([col, row, node.val]);
    dfs(node.left, row + 1, col - 1);
    dfs(node.right, row + 1, col + 1);
  }
  
  dfs(root, 0, 0);
  nodes.sort((a, b) => a[0] - b[0] || a[1] - b[1] || a[2] - b[2]);
  
  // Group by column
  const result: number[][] = [];
  let prevCol = nodes[0]?.[0];
  let currentGroup: number[] = [];
  
  for (const [col, _, val] of nodes) {
    if (col !== prevCol) {
      result.push(currentGroup);
      currentGroup = [];
      prevCol = col;
    }
    currentGroup.push(val);
  }
  if (currentGroup.length) result.push(currentGroup);
  
  return result;
}
  • Time: O(n log n) — single big sort
  • Space: O(n)
  • Pros: One sort operation instead of multiple
  • Cons: More complex grouping logic afterward, arguably less readable

Verdict: Your Map-based approach (Approach 1) is the cleanest and most maintainable.


7. Related Problems for Practice

To build pattern recognition with coordinate-based tree traversals:

Same Pattern, Slight Variations:

  1. LeetCode 314 - Binary Tree Vertical Order Traversal (Medium)

    • Difference: No value sorting for same position—just maintain level-order
    • Why practice: Easier version to warm up before this problem
    • Pattern: DFS/BFS + column grouping (simpler sort)
  2. LeetCode 102 - Binary Tree Level Order Traversal (Medium)

    • Difference: Group by row (level) instead of column
    • Why practice: Fundamental BFS pattern for tree problems
    • Pattern: BFS with level tracking
  3. LeetCode 199 - Binary Tree Right Side View (Medium)

    • Difference: Track only rightmost node at each level
    • Why practice: Similar coordinate tracking, selective collection
    • Pattern: BFS/DFS with level tracking + filtering

Extension Problems:

  1. LeetCode 545 - Boundary of Binary Tree (Medium, Premium)

    • Why practice: Multiple traversal strategies in one problem
    • Pattern: DFS with position awareness
  2. LeetCode 1110 - Delete Nodes And Return Forest (Medium)

    • Why practice: Tree traversal with structural modifications
    • Pattern: DFS with parent-child relationship management

8. Learning Summary

Key Concepts Mastered ✅

  1. Coordinate Mapping in Trees

    • Transforming hierarchical data into 2D coordinates
    • Using (row, col) to enable spatial reasoning about tree nodes
  2. Multi-Level Sorting

    • Chaining sort comparators: a[0] - b[0] || a[1] - b[1]
    • Understanding sort precedence and tie-breaking
  3. Hash Map for Grouping

    • Using Map for efficient column-based grouping
    • Handling arbitrary integer keys (negative columns)
  4. DFS with State Propagation

    • Passing (row, col) parameters through recursion
    • Tracking position without modifying tree nodes

Interview Takeaway 🎯

When you see "vertical order" or "column-based grouping" in a tree problem:

  1. Think: Coordinate system + Hash Map
  2. Assign (row, col) during traversal
  3. Group by the relevant axis (usually column)
  4. Apply multi-level sorting based on problem requirements

What makes this problem "Hard":

  • Not the traversal (that's straightforward DFS)
  • Not the grouping (Map is standard)
  • It's the tertiary sort by value — easy to miss, hard to debug

Many candidates get 90% through this problem and fail on test cases like Example 2 where nodes 5 and 6 share position (2,0). Your solution handles this perfectly!


Final Verdict ✅

Excellent solution! The code is:

  • Correct: Handles all edge cases including the tricky same-position nodes
  • Optimal: O(n log n) time, O(n) space — cannot be improved asymptotically
  • Clean: Well-structured with clear variable names and helpful comments
  • Maintainable: Exported functions, good separation of concerns

The PR also successfully reorganizes the codebase (1029 → 0987) and improves code quality with proper exports.

Strong work on a challenging Hard problem! 🎉


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🤖 Gemini Code Review (Model: gemini-2.5-flash)

Here's a detailed review of the provided LeetCode solution for "Vertical Order Traversal of a Binary Tree."


1. Pattern Identification

This solution primarily uses Tree Traversal (Depth-First Search - DFS) combined with Hash Map (Dictionary) for grouping and Custom Sorting.

The core idea is to traverse the tree, assign coordinates (column and row) to each node, store these nodes grouped by their column index, and then sort them based on the problem's specific rules.

2. Complexity Verification

  • Time Complexity: O(N log N)

    • Stated Complexity (Implicit): The problem doesn't state it, but the solution's operations are analyzed below.
    • Correct Complexity: O(N log N)
    • Why:
      1. DFS Traversal: The traverse function visits each of the N nodes exactly once. For each node, it performs constant time operations (map lookups/insertions). This part is O(N).
      2. Sorting Columns: After the traversal, Array.from(valueMap.keys()).sort() sorts the column indices. In the worst case, there can be N distinct columns (e.g., a skewed tree). This sort takes O(C log C), where C is the number of unique columns. Since C can be up to N, this is O(N log N).
      3. Sorting Nodes within Columns: For each column, the nodes stored in its array are sorted. Let N_k be the number of nodes in column k. The sorting for that column takes O(N_k log N_k). The total time for this step is Sum(O(N_k log N_k)) for all columns k. In the worst case (e.g., all nodes in a single column like a linked list), this becomes O(N log N). In the best case (each node in its own column), it's O(N * 1 log 1) = O(N). Therefore, the dominant factor is O(N log N).

    Combining these, the overall time complexity is dominated by the sorting steps, resulting in O(N log N).

  • Space Complexity: O(N)

    • Stated Complexity (Implicit): Not stated.
    • Correct Complexity: O(N)
    • Why:
      1. valueMap: This map stores all N nodes. Each entry stores a column index as a key and an array of [row, node.val] pairs. In the worst case, all N nodes are stored, leading to O(N) space.
      2. Recursion Stack: The DFS traversal uses the call stack. In the worst case (a skewed tree), the depth of recursion can be N (height of the tree). This requires O(H) space, where H is the height of the tree. Since H can be up to N, this is O(N).

    Combining these, the overall space complexity is O(N).

3. Key Insight

The key insight for this problem is the ability to assign a unique coordinate (column, row) to every node in the binary tree and then use these coordinates to guide the output order.

  1. Coordinate System: The problem explicitly defines how coordinates change for children ((row + 1, col - 1) for left, (row + 1, col + 1) for right). This provides a deterministic way to map every node to a (column, row) pair. Starting root at (0,0) is crucial.
  2. Multi-level Sorting: Realizing that the output requires a specific sorting order:
    • First, by column (ascending).
    • Then, within each column, by row (ascending).
    • Finally, if nodes share the same (column, row) position, sort them by their value (ascending).

This multi-level sorting requirement means you can't just do a simple traversal and print. You need to collect all nodes with their coordinates and then apply a custom sort function. The use of a Map<number, Array<[number, number]>> (column -> list of [row, value]) is an elegant way to group by column first before applying the secondary sorting criteria.

4. Edge Case Analysis

The current solution appears robust and correctly handles the specified edge cases:

  • Empty Tree (root = null): The initial if (!root) check handles this, returning an empty array [].
  • Single Node Tree (root = [val]): traverse is called once for (root, 0, 0). valueMap will contain 0: [[0, root.val]]. sortedCols will be [0]. The result will be [[root.val]], which is correct.
  • Skewed Tree (e.g., all left children): The coordinates will correctly adjust (e.g., (0,0), (1,-1), (2,-2), ...). The sorting logic will handle this correctly.
  • All Nodes in One Column: This happens with a "zigzag" tree where left child has col-1 and right child has col+1, but if a series of left-right-left-right children could end up in the same column. The sorting a[0] - b[0] || a[1] - b[1] correctly handles sorting by row and then value.
  • Multiple Nodes at Same (col, row): The problem explicitly states this and requires sorting by value. The a[0] - b[0] || a[1] - b[1] comparator handles this directly: if a[0] - b[0] is 0 (same row), it then compares a[1] - b[1] (values).

Constraints Handling:

  • N up to 1000 nodes: O(N log N) and O(N) complexities are well within limits for N=1000.
  • 0 <= Node.val <= 1000: Node values are non-negative, which doesn't introduce any special sorting concerns.

5. Learning Points

  • Similar Problems using this Pattern:

    • Binary Tree Level Order Traversal (LeetCode 102): A simpler version, essentially vertical traversal where col is always 0. Often solved with BFS.
    • Binary Tree Right Side View (LeetCode 199): Uses BFS/DFS to track nodes at each level.
    • Diagonal Traversal of a Binary Tree (similar concept): Instead of col - 1 and col + 1, children might share row - col or row + col values. The coordinate system changes, but the approach of grouping and sorting remains similar.
    • Bottom View/Top View of a Binary Tree: These problems also involve assigning horizontal distances (column indices) and then selecting specific nodes based on depth.
  • Common Mistakes with this Pattern:

    1. Incorrect Coordinate Calculation: Miscalculating col or row for children.
    2. Incomplete Sorting Logic: Forgetting one of the three sorting criteria (column, then row, then value), especially the tie-breaking by value.
    3. Using BFS vs. DFS: Both can work, but DFS naturally explores deeper nodes first. If using BFS, you'd process level by level, and the row coordinate would be equivalent to the level. The key is to correctly collect all nodes with their coordinates before sorting.
    4. Efficiency with Data Structures: Using inefficient data structures for valueMap (e.g., an array of arrays that needs constant shifting) could degrade performance. A Map (or HashMap in other languages) is good here.
    5. Not Handling Empty Tree: A common oversight for tree problems.
  • Variations of this Problem:

    • Horizontal Order Traversal: Not a standard term, but if the problem asked to group by row instead of column.
    • Anti-Diagonal Traversal: Similar to diagonal, but with a different coordinate transformation (e.g., row + col or row - col remaining constant).
    • Printing only Top/Bottom/Left/Right-most nodes in vertical traversal: This would add a filtering step after collecting all nodes and their coordinates.

6. Code Quality

The code quality is generally good:

  • Variable Naming: valueMap, sortedCols, sortedNodes, root, node, col, row are all clear and descriptive. a and b in sort comparators are standard.
  • Code Structure: The use of a nested helper function traverse is excellent for encapsulating the recursive logic and accessing valueMap and minCol/maxCol from the outer scope.
  • Readability: The code is easy to follow. The comments in the valueMap initialization clearly explain its purpose.
  • TypeScript Best Practices:
    • export class TreeNode and export function verticalTraversal are good for modularity and testing.
    • The non-null assertion ! on valueMap.get(col)! is appropriate because sortedCols are derived directly from the map's keys, guaranteeing col exists as a key.
    • Type annotations are correctly used.
  • Minor Improvement: The minCol and maxCol variables are not strictly necessary as valueMap.keys() provides all columns, and Array.from(...).sort() will handle the range. You could remove minCol and maxCol and the associated Math.min/Math.max updates without changing correctness or complexity. It doesn't hurt, but it's slightly redundant.
// Optional improvement: minCol and maxCol are not strictly needed.
// The range of columns is implicitly handled by iterating over valueMap.keys() after traversal.

// function verticalTraversal(root: TreeNode | null): number[][] {
//   const valueMap = new Map<number, Array<[number, number]>>(); // key = column index, value = array of [row, node.val]

//   const traverse = (node: TreeNode | null, row: number, col: number) => {
//     if (!node) {
//       return;
//     }

//     if (!valueMap.has(col)) {
//       valueMap.set(col, []);
//     }
//     valueMap.get(col)!.push([row, node.val]);

//     traverse(node.left, row + 1, col - 1);
//     traverse(node.right, row + 1, col + 1);
//   };

//   traverse(root, 0, 0);

//   const sortedCols = Array.from(valueMap.keys()).sort((a, b) => a - b);

//   return sortedCols.map((col) => {
//     const sortedNodes = valueMap.get(col)!.sort((a, b) => a[0] - b[0] || a[1] - b[1]);
//     return sortedNodes.map((n) => n[1]);
//   });
// }

7. Alternative Approaches

  1. Breadth-First Search (BFS):

    • Approach: Instead of a recursive DFS, use an iterative BFS with a queue. Each element in the queue would be [node, row, col]. When dequeuing, process the node, add its children with updated row and col to the queue.
    • Trade-offs:
      • Pro: BFS naturally processes nodes level by level (increasing row), which might simplify the initial grouping slightly, but you'd still need to sort by column and then by value for nodes at the same (row, col).
      • Con: The core logic of collecting all nodes and then sorting them by column, row, and value remains. The overall time and space complexity would be very similar (O(N log N) time, O(N) space for map and queue). The specific order of nodes pushed into the valueMap might differ from DFS, but the final sorting handles it.
  2. Using a TreeMap (or SortedMap):

    • Approach: If the language provided a TreeMap (like Java's TreeMap) which automatically keeps keys sorted, you could use TreeMap<number, Array<[number, number]>> where the key is the column index. This would eliminate the Array.from(valueMap.keys()).sort() step, as the map's keys would always be retrieved in sorted order.
    • Trade-offs:
      • Pro: Simplifies the final column sorting step.
      • Con: JavaScript's Map does not guarantee key order by value; it maintains insertion order. Therefore, this approach isn't directly applicable in standard JavaScript/TypeScript without implementing a custom sorted map or using a library. Even with a TreeMap, you'd still need to sort the [row, value] arrays within each column, so the overall O(N log N) complexity wouldn't change drastically unless the number of columns C was very large compared to N.

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Claude finished @pertrai1's task in 1m 50s —— View job


Educational Code Review ✅

Summary

This PR successfully reorganizes the "Vertical Order Traversal of a Binary Tree" solution into the correct directory structure (problem #0987), and the implementation is algorithmically correct and well-crafted. Excellent work on this challenging Hard problem!


1. Correctness Analysis ✅

Algorithm Verification

The solution correctly implements all requirements:

✅ Coordinate System

  • Root starts at (0, 0)
  • Left child: (row + 1, col - 1)
  • Right child: (row + 1, col + 1)

✅ Grouping & Sorting

  • Nodes grouped by column using Map (line 16) ✓
  • Columns sorted left-to-right (line 34) ✓
  • Within each column: sorted by row, then by value (line 38) ✓

✅ Critical Edge Case: Same Position Nodes

The trickiest requirement is handling nodes at identical (row, col) positions. Line 38 handles this perfectly:

.sort((a, b) => a[0] - b[0] || a[1] - b[1])
//              ^^^^^^^^^^^^^^^^  ^^^^^^^^
//              Sort by row first  Then by value

Mental Trace (Example 2)

For root = [1,2,3,4,5,6,7]:

Tree Structure:          Coordinates:
       1                    (0, 0)
      / \                  /      \
     2   3            (1,-1)      (1,1)
    / \ / \            /  \        /  \
   4  5 6  7       (2,-2)(2,0) (2,0)(2,2)

Expected output: [[4],[2],[1,5,6],[3],[7]]

Trace:

  • Column -2: Node 4 → [4]
  • Column -1: Node 2 → [2]
  • Column 0: Nodes 1, 5, 6
    • Node 1 at (0, 0)
    • Nodes 5 and 6 both at (2, 0) — sorted by value: 5 before 6 ✓
    • Result: [1, 5, 6]
  • Column 1: Node 3 → [3]
  • Column 2: Node 7 → [7]

✅ Other Edge Cases

  • Empty tree: Base case at line 19 returns correctly
  • Single node: Returns [[val]]
  • Negative columns: Map handles arbitrary integer keys
  • All nodes in one column: Sorting handles correctly

2. Complexity Analysis

Time Complexity: O(n log n)

Breakdown:

  1. DFS Traversal (line 31): O(n)

    • Visits each node exactly once
    • Constant-time operations per node (Map operations)
  2. Sort Column Keys (line 34): O(k log k) where k = unique columns

    • Worst case (skewed tree): k ≈ n → O(n log n)
    • Best case (balanced): k ≈ log n → O(log n · log log n)
  3. Sort Nodes Within Columns (line 38): O(n log n) total

    • For column with m nodes: O(m log m)
    • Sum across all columns: Σ(m_i log m_i) where Σm_i = n
    • Worst case (all nodes in one column): O(n log n)

Dominant Operation: Sorting → O(n log n)

Space Complexity: O(n)

  1. valueMap: Stores all n nodes as [row, val] pairs → O(n)
  2. Recursion Stack: O(h) where h = tree height
    • Balanced tree: O(log n)
    • Skewed tree: O(n)
  3. Output Array: O(n)

Total: O(n) + O(h) + O(n) = O(n) (since h ≤ n)


3. Pattern Recognition

Primary Pattern: DFS + Hash Map + Multi-Key Sorting

This problem combines three fundamental techniques:

  1. Tree Traversal (DFS) — Recursive exploration
  2. Coordinate Mapping — Transform tree into 2D grid
  3. Multi-Level Sorting — Order by multiple criteria

Why This Pattern Works

DFS Choice:

  • Must visit ALL nodes (not a search problem with early termination)
  • Visit order doesn't matter since we sort afterward
  • Recursion naturally tracks depth (row coordinate)

Hash Map Grouping:

  • Efficiently groups nodes by column in O(1) per insertion
  • Handles arbitrary column indices (including negative)

Multi-Key Sort:
The problem requires three levels of ordering:

  1. Primary: Column (left → right) — determines output array structure
  2. Secondary: Row (top → bottom) — vertical ordering within columns
  3. Tertiary: Value (ascending) — tie-breaker for same position

💡 Key Insight

The non-obvious realization: This is fundamentally a sorting problem disguised as a tree problem.

The "Hard" difficulty comes from:

  1. Recognizing you need a coordinate system to make tree nodes sortable
  2. Understanding the three-level sort hierarchy
  3. The tertiary sort by value — this is what catches most candidates

Many incorrect solutions:

  • ❌ Forget the value-based tie-breaker entirely
  • ❌ Apply sorts in wrong order (value before row)
  • ❌ Try to maintain order during traversal (unnecessarily complex)

Your solution excels by cleanly separating concerns: collect during DFS, sort afterward.


4. Code Quality Review

Strengths ✅

1. Clear Data Structure Documentation (vertical-order-traversal-of-a-binary-tree.ts:13-16)

// initialize a map where:
// key = column index
// value = array of [row, node.val]

✅ Excellent comment explaining the Map structure

2. Exported API (vertical-order-traversal-of-a-binary-tree.ts:1-10)

export class TreeNode { ... }

✅ Makes TreeNode testable and reusable

3. Clean Sort Chaining (vertical-order-traversal-of-a-binary-tree.ts:38)

.sort((a, b) => a[0] - b[0] || a[1] - b[1])

✅ Concise multi-level comparator

4. Safe Non-Null Assertions (vertical-order-traversal-of-a-binary-tree.ts:25, 38)

valueMap.get(col)!.push([row, node.val]);

✅ Correct use of ! — we just verified existence with has(col) on line 22

Suggestions for Enhancement

1. Add Complexity Documentation

Consider adding algorithm overview at function start:

// Algorithm: DFS with coordinate tracking + multi-key sorting
// Time: O(n log n) - dominated by sorting operations  
// Space: O(n) - Map storage + recursion stack
export function verticalTraversal(root: TreeNode | null): number[][] {

2. Enhance Sort Comment

Line 37's comment could be more explicit about the tie-breaking:

// sort column entries: row (ascending) → value (ascending for same position)
const sortedNodes = valueMap.get(col)!.sort((a, b) => a[0] - b[0] || a[1] - b[1]);

3. TypeScript Type Safety (Optional)

For even better type safety, consider named tuple types:

type NodeEntry = [row: number, value: number];
const valueMap = new Map<number, NodeEntry[]>();

This makes a[0] and a[1] self-documenting in the sort comparator.


5. Common Mistakes with This Pattern

🚨 Pitfalls to Avoid:

  1. Missing Value Sort ⚠️

    • Forgetting || a[1] - b[1] causes wrong output when nodes share (row, col)
    • This is THE most common error on this problem
  2. Wrong Sort Order ⚠️

    • Sorting by value before row: a[1] - b[1] || a[0] - b[0]
    • Must be row first, then value
  3. Array Instead of Map ⚠️

    • Arrays can't elegantly handle negative column indices
    • Your Map approach is optimal
  4. Maintaining Order During Traversal ⚠️

    • Some try to insert in sorted order during DFS
    • Much more complex than collect-then-sort
  5. Unnecessary BFS ⚠️

    • Some use BFS thinking it's "more natural"
    • Adds queue overhead without improving complexity

6. Alternative Approaches

Approach 1: Your DFS + Map (Optimal) ✅

Current Implementation

  • Time: O(n log n)
  • Space: O(n)
  • Pros: Clean separation of concerns, intuitive, standard solution
  • Cons: None — this is optimal

Approach 2: BFS with Queue

function verticalTraversal(root: TreeNode | null): number[][] {
  if (!root) return [];
  const queue: [TreeNode, number, number][] = [[root, 0, 0]];
  const map = new Map<number, [number, number][]>();
  
  while (queue.length) {
    const [node, row, col] = queue.shift()!;
    if (!map.has(col)) map.set(col, []);
    map.get(col)!.push([row, node.val]);
    
    if (node.left) queue.push([node.left, row + 1, col - 1]);
    if (node.right) queue.push([node.right, row + 1, col + 1]);
  }
  // ... same sorting logic
}
  • Time: O(n log n) — same complexity
  • Space: O(n) — queue instead of recursion stack
  • Pros: Iterative (no stack overflow), processes level-by-level
  • Cons: More verbose, still requires same sorting, no real advantage

Approach 3: Single Array + Global Sort

function verticalTraversal(root: TreeNode | null): number[][] {
  const nodes: [number, number, number][] = []; // [col, row, val]
  
  function dfs(node: TreeNode | null, row: number, col: number) {
    if (!node) return;
    nodes.push([col, row, node.val]);
    dfs(node.left, row + 1, col - 1);
    dfs(node.right, row + 1, col + 1);
  }
  
  dfs(root, 0, 0);
  nodes.sort((a, b) => a[0] - b[0] || a[1] - b[1] || a[2] - b[2]);
  
  // Group by column into final result
  const result: number[][] = [];
  let prevCol = nodes[0]?.[0];
  let currentGroup: number[] = [];
  
  for (const [col, _, val] of nodes) {
    if (col !== prevCol) {
      result.push(currentGroup);
      currentGroup = [];
      prevCol = col;
    }
    currentGroup.push(val);
  }
  if (currentGroup.length) result.push(currentGroup);
  
  return result;
}
  • Time: O(n log n) — single big sort
  • Space: O(n)
  • Pros: One sort operation instead of multiple
  • Cons: More complex grouping logic, less readable

Verdict: Your Map-based approach (Approach 1) is the cleanest and most maintainable.


7. Related Problems for Practice

Same Pattern, Easier Variations:

1. LeetCode 314 - Binary Tree Vertical Order Traversal (Medium)

  • Difference: No value sorting for same position — just level-order
  • Why practice: Simpler version to warm up
  • Pattern: DFS/BFS + column grouping

2. LeetCode 102 - Binary Tree Level Order Traversal (Medium)

  • Difference: Group by row (level) instead of column
  • Why practice: Fundamental BFS pattern
  • Pattern: BFS with level tracking

3. LeetCode 199 - Binary Tree Right Side View (Medium)

  • Difference: Track only rightmost node per level
  • Why practice: Selective collection with coordinates
  • Pattern: BFS/DFS + filtering

Extension Problems:

4. LeetCode 545 - Boundary of Binary Tree (Medium)

  • Why practice: Multiple traversal strategies combined
  • Pattern: DFS with position awareness

5. LeetCode 1110 - Delete Nodes And Return Forest (Medium)

  • Why practice: Tree traversal with structural changes
  • Pattern: DFS with parent-child management

8. Learning Summary

Key Concepts Mastered ✅

  1. Coordinate Mapping in Trees

    • Transform hierarchical structure into 2D coordinates
    • Enable spatial reasoning about tree nodes
  2. Multi-Level Sorting

    • Chain sort comparators: a - b || c - d
    • Understand precedence and tie-breaking
  3. Hash Map for Grouping

    • Efficient column-based grouping
    • Handle arbitrary integer keys (negative columns)
  4. DFS with State Propagation

    • Pass coordinates through recursion
    • Track position without modifying nodes

Interview Takeaway 🎯

When you see "vertical order" or "column grouping" in tree problems:

  1. Think: Coordinate system + Hash Map
  2. Assign (row, col) during traversal
  3. Group by relevant axis (usually column)
  4. Apply multi-level sorting per requirements

What makes this problem "Hard":

  • ✅ Not the traversal (straightforward DFS)
  • ✅ Not the grouping (standard Map usage)
  • It's the tertiary sort by value — easy to miss, hard to debug

Many candidates get 90% through and fail on Example 2 where nodes 5 and 6 share position (2, 0). Your solution handles this perfectly!


Final Verdict ✅

Outstanding solution! The code is:

  • Correct: Handles all edge cases including same-position nodes
  • Optimal: O(n log n) time, O(n) space — asymptotically best possible
  • Clean: Well-structured, clear names, helpful comments
  • Maintainable: Exported functions, good separation of concerns

The PR also successfully reorganizes the codebase and improves code quality with proper exports.

Strong work on this challenging Hard problem! 🎉


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🤖 Gemini Code Review (Model: gemini-2.5-flash)

Here's a review of your LeetCode solution for "Vertical Order Traversal of a Binary Tree."


1. Pattern Identification

This solution primarily uses Tree Traversal, specifically a Depth-First Search (DFS), combined with Hashing/Mapping to store and group nodes by their column index. Finally, Sorting is applied to arrange the results according to the problem's specific ordering rules.

2. Complexity Verification

  • Time Complexity: O(N log N)

    • Traversal (DFS): Visiting each node once takes O(N) time, where N is the number of nodes in the tree.
    • Storing in valueMap: Each node is inserted into the map. Map operations (get, set, push) are typically O(1) on average.
    • Sorting Columns: Array.from(valueMap.keys()) takes O(C) where C is the number of unique columns. Sorting these keys takes O(C log C).
    • Sorting Nodes within Columns: This is the dominant factor. For each column, we sort a list of nodes. If there are C columns and N_i nodes in column i, the total sorting time is sum(N_i log N_i) for all i from 1 to C. In the worst case (e.g., a degenerate tree where all nodes are in one column), this could be O(N log N). Even in a balanced tree, the total number of elements across all lists is N, so the overall sorting time is O(N log N).
    • Overall: O(N log N) is accurate due to the sorting of nodes within columns.
  • Space Complexity: O(N)

    • valueMap: Stores information for all N nodes. Each entry stores [row, node.val]. In the worst case, all N nodes are distinct and occupy space proportional to N.
    • Recursion Stack: For DFS, in the worst case (a skewed tree), the recursion depth can be O(N).
    • Overall: O(N) is accurate.

3. Key Insight

The key insight for this problem is the assignment of a unique coordinate (row, col) to each node and then systematically grouping and sorting them based on these coordinates.

  1. Coordinate System: The problem defines how children's coordinates relate to their parent's:

    • Root is at (0, 0).
    • Left child of (row, col) is at (row + 1, col - 1).
    • Right child of (row, col) is at (row + 1, col + 1).
      This allows a straightforward way to determine the (row, col) for every node via traversal.
  2. Multi-level Sorting: There are specific rules for ordering:

    • Primary Sort: By column index (left to right).
    • Secondary Sort: Within each column, by row index (top to bottom).
    • Tertiary Sort (Tie-breaker): If nodes are at the exact same (row, col), sort them by their value (ascending).

The solution correctly captures these insights by using a map to group by column, then sorting the column keys, and finally sorting the lists within each column using a custom comparator (a, b) => a[0] - b[0] || a[1] - b[1] which prioritizes row, then value.

4. Edge Case Analysis

The current solution handles common edge cases correctly:

  • Empty Tree (root = null): The if (!root) check at the beginning of traverse and the main function ensures valueMap remains empty, leading to an empty result array [], which is correct.
  • Single Node Tree (root = [val]): traverse will be called once for (val, 0, 0). valueMap will contain {-0: [[0, val]]}. sortedCols will be [0]. The result will be [[val]], which is correct.
  • Skewed Trees (e.g., all left or all right children): The coordinate system and sorting logic naturally extend to these cases, correctly assigning column and row indices and sorting. This will result in a wide range of column indices.
  • Nodes with Same (row, col) but Different Values: The a[0] - b[0] || a[1] - b[1] comparator correctly handles this by sorting first by row (a[0] - b[0]) and then by value (a[1] - b[1]) if rows are equal. This is crucial for problems like Example 2 and 3.

5. Learning Points

  • Similar Problems:

    • Binary Tree Vertical Order Traversal (LeetCode 314 - Medium): A simpler version where you don't need to sort by value if nodes are at the same (row, col). Often solved with BFS to naturally achieve top-to-bottom order.
    • Binary Tree Diagonal Traversal (LeetCode 1429 - Medium): Uses a similar coordinate system but sums row + col for one diagonal or row - col for another.
    • Level Order Traversal (BFS): Fundamental tree traversal that orders nodes by level/row.
    • Top View / Bottom View of Binary Tree: These problems also involve projecting nodes onto a horizontal line (columns) and selecting specific nodes based on visibility.
  • Common Mistakes with this Pattern:

    • Incorrect Coordinate Calculation: Miscalculating col or row for children.
    • Mishandling Tie-breaking Rules: Forgetting to sort by value when (row, col) are identical, or sorting in the wrong order (e.g., descending instead of ascending).
    • Not Sorting Columns: Forgetting to iterate through the columns in increasing order, leading to an incorrect final output order.
    • Choosing the Wrong Traversal: While DFS works, BFS can sometimes simplify the logic for "top-to-bottom" ordering within a column because it naturally processes nodes level by level. With DFS, you must store row information to sort correctly.
  • Variations of this Problem:

    • Return nodes grouped by row instead of column.
    • Return only the "top view" or "bottom view" of the tree.
    • Change the coordinate system for children (e.g., left child (row+1, col), right child (row+1, col+1)).
    • Return only a specific range of columns.

6. Code Quality

  • TreeNode Definition: Moving the TreeNode class definition out of the comment block and making it exportable is a good improvement, aligning with module best practices.
  • Variable Naming: valueMap, sortedCols, sortedNodes, col, row, node are all clear and descriptive.
  • Type Safety: Using valueMap.get(col)! correctly asserts that the value will not be undefined after checking valueMap.has(col).
  • Readability: The code is well-structured and easy to follow. The traverse helper function encapsulates the DFS logic cleanly.
  • Consistency: Using Array.from(valueMap.keys()).sort(...) is a standard way to get sorted keys from a Map in JavaScript.
  • Export: Exporting verticalTraversal is good for testing and modularity.

7. Alternative Approaches

  1. Breadth-First Search (BFS):

    • Approach: Instead of DFS, use a BFS traversal. You would use a queue to store [node, row, col]. When processing a node, add its children to the queue with their respective (row, col) coordinates. Store nodes in the valueMap just as in the DFS approach.
    • Trade-offs:
      • Pros: BFS naturally processes nodes level by level (row by row). This means that for a given column, nodes from higher rows will be encountered before nodes from lower rows. This can simplify the sorting within columns: if you store [value, row] in the list for each column, you only need to sort by value for elements that happen to be at the exact same (row, col) (which BFS doesn't strictly guarantee order for within a level if multiple are at same (col,row)), or you can just push [value] and sort by value, knowing the BFS order already handles row. However, to truly replicate the "top-to-bottom, then value" rule, you still need to store [row, value] and apply the same sorting logic as in the DFS solution.
      • Cons: Might use more memory for the queue in certain tree shapes compared to the DFS recursion stack. The overall complexity remains O(N log N) for time and O(N) for space.
  2. Custom Data Structure for Columns (e.g., TreeMap in Java):

    • Approach: In languages like Java, a TreeMap<Integer, List<Pair<Integer, Integer>>> could be used. The TreeMap automatically keeps keys (column indices) sorted. Each List would store [row, value] pairs.
    • Trade-offs:
      • Pros: Eliminates the explicit Array.from(valueMap.keys()).sort((a, b) => a - b) step, as the map itself maintains sorted keys.
      • Cons: JavaScript's native Map does not guarantee sorted iteration order for keys (it maintains insertion order). Therefore, this approach isn't directly applicable in JavaScript without implementing a custom sorted map or using a library, which would add overhead. The core logic of sorting the inner lists by row then value would still be required.

The chosen DFS approach is perfectly valid and efficient for this problem in JavaScript, correctly addressing all requirements.

@pertrai1 pertrai1 merged commit 683f66b into main Jan 31, 2026
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@pertrai1 pertrai1 deleted the leetcode-1312026 branch January 31, 2026 15:54
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📅 Spaced Repetition Reviews Scheduled!

Great job solving #0987 - Vertical Order Traversal Of A Binary Tree! 🎉

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🧠 Why Spaced Repetition?

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Check docs/reviews/review-schedule.json to see your review schedule.

github-actions bot pushed a commit that referenced this pull request Jan 31, 2026
…A Binary Tree

  Problem: #0987 - Vertical Order Traversal Of A Binary Tree
  PR: #220
  First review scheduled (subsequent reviews auto-scheduled on completion)

  [skip ci]
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