To solve the problem, calculate the number of distinct values along each diagonal of a matrix. For each matrix cell, compare the diagonal values using set logic to count distinct values. The output matrix will reflect the differences between distinct diagonal values for each cell.
Problem Statement
You are given a 2D matrix of size m x n. For each cell in the matrix, you need to calculate the difference between the number of distinct values on its diagonal compared to the main diagonal. A diagonal is defined as a line of cells starting from any cell in the topmost row or the leftmost column, extending bottom-right until the end of the matrix.
Return a new matrix of the same size, where each cell contains the calculated difference of distinct diagonal values for that position. You must focus on efficient array scanning and hash lookups to solve the problem.
Examples
Example 1
Input: grid = [[1,2,3],[3,1,5],[3,2,1]]
Output: Output: [[1,1,0],[1,0,1],[0,1,1]]
To calculate the answer cells:
Example 2
Input: grid = [[1]]
Output: Output: [[0]]
Example details omitted.
Constraints
- m == grid.length
- n == grid[i].length
- 1 <= m, n, grid[i][j] <= 50
Solution Approach
Array Scanning
Iterate over the matrix and for each element, scan its diagonal starting from that element. This ensures you capture all relevant diagonal values for each cell.
Hash Set for Distinct Values
Use a hash set to keep track of the distinct values encountered on the diagonal. This enables efficient counting and ensures uniqueness.
Efficient Calculation
For each cell, calculate the number of distinct diagonal values by comparing the hash set size and store the result in the output matrix.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
The time complexity depends on the approach chosen for scanning the diagonals. If each diagonal is scanned independently, the time complexity is O(m * n). The space complexity is also O(m * n) because of the additional storage required for the hash set and the output matrix.
What Interviewers Usually Probe
- Ability to optimize matrix traversal with hash sets for distinct values.
- Understanding of how to use efficient data structures like hash sets in matrix-related problems.
- Experience with solving problems involving matrix diagonals and distinct value counting.
Common Pitfalls or Variants
Common pitfalls
- Overcomplicating the problem by failing to recognize the need for efficient scanning.
- Misunderstanding the concept of diagonals, leading to incorrect traversal logic.
- Failing to handle edge cases such as single-row or single-column matrices.
Follow-up variants
- Modify the problem to handle larger matrices efficiently.
- Consider cases where the diagonals can be in different directions.
- Optimize the approach for matrices with larger values or constraints.
How GhostInterview Helps
- GhostInterview provides step-by-step guidance to approach the problem, from matrix scanning to leveraging hash sets.
- It helps identify common pitfalls in diagonal-based matrix problems and suggests optimizations.
- GhostInterview can suggest code snippets to implement array scanning and hash set usage effectively.
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
How do I calculate the difference of distinct values on diagonals?
You can calculate the difference by scanning each cell's diagonal, storing values in a hash set to count distinct elements, and comparing the results.
What pattern does the 'Difference of Number of Distinct Values on Diagonals' problem follow?
The problem follows the array scanning plus hash lookup pattern, where you traverse the matrix and use hash sets to count distinct values efficiently.
How do I optimize this problem?
Optimize by using hash sets to track distinct values on each diagonal and by minimizing redundant scans of the matrix.
What if the matrix is very large?
For larger matrices, optimize the diagonal scanning logic and consider using more advanced data structures to handle larger input sizes efficiently.
Are there any edge cases for this problem?
Yes, edge cases include matrices with only one row or column, which should be handled with care to avoid incorrect diagonal scanning.
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