Start by iterating diagonals of the matrix, alternating between moving up-right and down-left. Maintain bounds to avoid index errors. This approach leverages the array plus matrix pattern, ensuring each diagonal collects elements in order efficiently.
Problem Statement
Given an m x n matrix mat, return a single array containing all elements in a diagonal zig-zag order. Traverse each diagonal starting from the top-left element and alternate directions between moving up-right and down-left for each successive diagonal.
For example, with mat = [[1,2,3],[4,5,6],[7,8,9]], the traversal order is [1,2,4,7,5,3,6,8,9]. Ensure your solution handles any matrix size within the constraints and correctly switches directions on each diagonal.
Examples
Example 1
Input: mat = [[1,2,3],[4,5,6],[7,8,9]]
Output: [1,2,4,7,5,3,6,8,9]
Example details omitted.
Example 2
Input: mat = [[1,2],[3,4]]
Output: [1,2,3,4]
Example details omitted.
Constraints
- m == mat.length
- n == mat[i].length
- 1 <= m, n <= 104
- 1 <= m * n <= 104
- -105 <= mat[i][j] <= 105
Solution Approach
Iterate Diagonals Using Index Sums
Loop through all possible sums of row and column indices. For each sum, collect elements that satisfy i+j=sum. Reverse the order on alternating diagonals to match the zig-zag pattern.
Use Direction Flag
Maintain a boolean flag to indicate current direction. If moving up-right, traverse elements in reverse order within the current diagonal; if moving down-left, traverse normally. Toggle the flag after completing each diagonal.
Boundary Checks and Result Array
Ensure all indices are valid within matrix bounds to avoid out-of-range errors. Append each element to a pre-allocated result array of size m*n for optimal space usage, adhering to the array plus matrix pattern.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | O(N \cdot M) |
| Space | O(1) |
Time complexity is O(M*N) as each element is visited exactly once. Space complexity is O(1) extra if output array is not counted; using only loop variables and flags.
What Interviewers Usually Probe
- Candidate starts by recognizing the diagonal index sum pattern.
- Candidate correctly alternates traversal direction per diagonal.
- Candidate efficiently handles matrix boundaries without errors.
Common Pitfalls or Variants
Common pitfalls
- Incorrectly reversing elements on diagonals leading to wrong order.
- Off-by-one errors when accessing the last row or column.
- Using extra space unnecessarily instead of in-place collection into the result array.
Follow-up variants
- Traverse diagonals starting from bottom-right instead of top-left.
- Return only the elements of even-numbered diagonals.
- Perform the traversal but output each diagonal as a separate subarray instead of flattening.
How GhostInterview Helps
- Automatically constructs the zig-zag traversal order, highlighting the correct index sums.
- Flags and reversals are managed, preventing common mistakes with alternating directions.
- Optimizes collection of elements into the result array, ensuring constant extra space usage.
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 main pattern behind Diagonal Traverse?
The main pattern is summing row and column indices to identify diagonals and alternating the traversal direction for each diagonal.
Can Diagonal Traverse handle non-square matrices?
Yes, the solution correctly handles any m x n matrix within the given constraints using the same diagonal summing logic.
Why do some diagonals need to be reversed?
Reversing every other diagonal ensures the zig-zag order is maintained, matching the problem's required output sequence.
What is the time complexity of Diagonal Traverse?
Each element is visited once, so the time complexity is O(M*N), where M and N are matrix dimensions.
How does the array plus matrix pattern apply here?
Each diagonal is treated as an array derived from matrix indices; collecting elements efficiently into a single output array follows the pattern precisely.
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