Introduction
A matrix is a two-dimensional array of elements arranged in rows and columns. In coding interviews, matrix-related problems often involve:
- Dynamic Programming: Utilizing matrices to store intermediate results.
- Graph Traversal: Treating the matrix as a grid-based graph for traversal algorithms.
Matrices can represent graphs where each cell is a node with up to four neighbors (top, bottom, left, right), except for edge and corner cells.
Corner Cases to Consider
When working with matrices, be mindful of the following edge cases:
- Empty Matrix: Ensure the matrix is not empty before processing.
- Single Element Matrix: A 1x1 matrix.
- Single Row or Column: Matrices with only one row or one column.
Common Techniques
1. Creating an Empty N x M Matrix
For tasks like traversal or setting up a dynamic programming table, you might need to initialize an empty matrix of the same dimensions. In Python:
# Assuming 'matrix' is a non-empty 2D list
rows = len(matrix)
cols = len(matrix[0])
empty_matrix = [[0 for _ in range(cols)] for _ in range(rows)]
2. Copying a Matrix
To create a duplicate of an existing matrix:
copied_matrix = [row[:] for row in matrix]
3. Transposing a Matrix
Transposing involves swapping rows with columns. This is particularly useful in problems where you need to check both row-wise and column-wise conditions, such as in certain grid-based games.
In Python:
transposed_matrix = list(zip(*matrix))
Note: The zip(*matrix) function pairs elements with the same index from each row, effectively transposing the matrix.