Intro

Matrix is a 2-dimensional Array representing a collection of numbers arranged in an order of rows and columns

zero_matrix = [[0 for _ in range(len(matrix[0]))] for _ in range(len(matrix))]

copied_matrix = [row[:] for row in matrix]

Square Matrix has the number of columns = the number of rows

Sorted Matrix has ****elements sorted in increasing/decreasing order

Binary Matrix has ****elements only equal to 0 or 1

Sparse Matrix stores only elements different than 0

Special Matrix has matrix[i][j] = i * j

Upper triangular = upper either diagonal elements

Lower triangular = lower either diagonal elements

Transposing a Matrix achieved by interchanging its rows into columns or columns into rows

transposed_matrix = zip(*matrix)

Relationships in a Matrix

https://cp-algorithms.com/linear_algebra/linear-system-gauss.html

https://cp-algorithms.com/linear_algebra/determinant-gauss.html

https://cp-algorithms.com/linear_algebra/determinant-kraut.html

https://cp-algorithms.com/linear_algebra/rank-matrix.html

Usage

• questions involving Matrices are usually related to Dynamic Programming or Graph Traversal
• can be used to represent graphs where each node is a cell on the matrix and has 4 neighbours (except those cells on the edge and corners)

Comparison

Advantages

Disadvantages

Problems

• [ ] Set Matrix Zeroes
• [ ] Spiral Matrix
• [ ] Rotate Image
• [ ] Valid Sudoku
• [ ] Swapping Diagonals
• [ ] Magic Square

Corner Cases

• empty matrix (check that none of the arrays are 0 length)
• 1 x 1 matrix

Implementation

n is the number of rows

m in the number of columns

Algorithms

Patterns

Code

Row-wise traversal

Column-wise traversal

input : mat = [[1, 2, 3],
               [4, 5, 6],
               [7, 8, 9]]

# accessing element row wise
    for i in range(row):
        for j in range(col):
            ... arr[i][j] ...

output : row-wise: 1 2 3 4 5 6 7 8 9

input : mat = [[1, 2, 3],
               [4, 5, 6],
               [7, 8, 9]]

# accessing element row wise
    for i in range(row):
        for j in range(col):
            ... arr[j][i] ...

output : col-wise: 1 4 7 2 5 8 3 6 9

Clock-wise = Spiral traversal

Resources