To solve the 'Reshape the Matrix' problem, you need to map a 2D matrix into a 1D format and then reshape it into the desired dimensions. If reshaping is impossible, return the original matrix. It tests your ability to handle arrays and matrices efficiently, focusing on row-major ordering and boundary checks.
Problem Statement
You are given an m x n matrix and two integers r and c, which represent the number of rows and columns of the reshaped matrix. Your task is to reshape the matrix into a new matrix of the specified dimensions, while maintaining the original data in the same row-major order.
If it is impossible to reshape the matrix, return the original matrix. The solution requires you to manage the mapping between the original 2D indices and the new reshaped matrix dimensions, ensuring that no data is lost or misplaced.
Examples
Example 1
Input: mat = [[1,2],[3,4]], r = 1, c = 4
Output: [[1,2,3,4]]
Example details omitted.
Example 2
Input: mat = [[1,2],[3,4]], r = 2, c = 4
Output: [[1,2],[3,4]]
Example details omitted.
Constraints
- m == mat.length
- n == mat[i].length
- 1 <= m, n <= 100
- -1000 <= mat[i][j] <= 1000
- 1 <= r, c <= 300
Solution Approach
Flatten the Matrix
Convert the matrix into a 1D array by traversing it row by row. This helps in simplifying the reshaping process, as you can map elements directly from this array to the new reshaped matrix.
Check for Valid Reshape
Before proceeding with reshaping, ensure that the total number of elements in the original matrix matches the product of r and c. If they don’t match, return the original matrix.
Rebuild the Matrix
Using the flattened array, reconstruct the new matrix row by row, ensuring that each row has exactly c elements. This step completes the reshaping process while keeping the data in row-major order.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
The time complexity is O(m * n) for flattening the matrix and rebuilding it, where m is the number of rows and n is the number of columns. The space complexity is O(m * n) for storing the flattened 1D array and the reshaped matrix.
What Interviewers Usually Probe
- The candidate should recognize the importance of handling array indexing correctly when reshaping the matrix.
- Look for the candidate's ability to validate the reshaping dimensions before proceeding.
- Expect the candidate to explain the time and space complexity of their approach.
Common Pitfalls or Variants
Common pitfalls
- Failing to check if the reshape dimensions are valid before attempting to reshape.
- Incorrectly mapping the 1D array back into a 2D matrix, potentially losing elements.
- Not considering edge cases where the reshape operation is impossible.
Follow-up variants
- Given a 2D matrix, reshape it to match any specified dimensions, with varying boundary conditions (e.g., non-matching dimensions).
- Reshape a matrix and also transpose it simultaneously.
- Implement an in-place reshape operation that modifies the original matrix.
How GhostInterview Helps
- GhostInterview helps by guiding the candidate to focus on validating matrix dimensions and preventing unnecessary operations.
- It assists in identifying the correct pattern of flattening and rebuilding the matrix, ensuring efficient memory use.
- GhostInterview also clarifies the process of mapping a 2D matrix to 1D memory and vice versa.
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 key concept behind reshaping a matrix in this problem?
The key concept is converting the matrix from a 2D structure into a 1D array, and then mapping this 1D array back into the new reshaped matrix while maintaining the original row-major order.
How can I handle the case when reshaping is not possible?
If reshaping is not possible (i.e., the total number of elements does not match the product of the desired dimensions), you should return the original matrix.
What is the time complexity of reshaping the matrix?
The time complexity is O(m * n), where m is the number of rows and n is the number of columns in the matrix, due to the need to traverse all elements for reshaping.
Can the matrix be reshaped in-place?
No, reshaping the matrix requires creating a new matrix since the dimensions change. In-place reshaping is not possible for this problem.
What is the role of the primary pattern 'Array plus Matrix' in this problem?
The 'Array plus Matrix' pattern helps in understanding how to flatten a 2D matrix into a 1D array and then rebuild it into a new matrix, ensuring proper data order and efficient memory use.
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