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Multidimensional Lists (Matrices)

Introduction

In Python, a 2D array (matrix) is simply a list of lists.

You will use 2D lists heavily in Graph problems (adjacency matrices), Dynamic Programming (2D memoization tables), and Grid traversal problems (like Islands or Mazes).

The Danger of [[0] * C] * R

The most common bug in Python coding interviews is initializing a 2D matrix incorrectly.

❌ Incorrect Initialization: 

R, C = 3, 3
matrix = [[0] * C] * R
If you print matrix, it looks correct: [[0, 0, 0], [0, 0, 0], [0, 0, 0]]

But if you modify one element: 

matrix[0][0] = 1
print(matrix)
Output: [[1, 0, 0], [1, 0, 0], [1, 0, 0]]

Why? The outer multiplication * R copied the reference to the inner list \(R\) times. There is only one inner list in memory, and every row points to it.

The Correct Way: List Comprehensions

To properly initialize a matrix, you must create a new inner list on every iteration. Use a list comprehension.

✅ Correct Initialization: 

R, C = 3, 3
matrix = [[0] * C for _ in range(R)]

Now, modifying one cell works correctly: 

matrix[0][0] = 1
print(matrix)
Output: [[1, 0, 0], [0, 0, 0], [0, 0, 0]]

Memorize This Pattern

# Create an R x C matrix filled with default_value
matrix = [[default_value] * C for _ in range(R)]

Iterating Over a Matrix

1. By Index

Use this when you need the coordinates \((r, c)\) for logic.

for r in range(len(matrix)):
    for c in range(len(matrix[0])):
        val = matrix[r][c]

2. By Value

Use this when you only need to read the values.

for row in matrix:
    for val in row:
        print(val)

3. Both (Using enumerate)

for r, row in enumerate(matrix):
    for c, val in enumerate(row):
        print(f"Cell ({r},{c}) is {val}")

Accessing Columns

To extract a specific column from a matrix, use a list comprehension. (Unlike NumPy, standard Python lists don't support matrix[:, c]).

matrix = [
    [1, 2, 3],
    [4, 5, 6],
    [7, 8, 9]
]

# Extract column index 1
col = [row[1] for row in matrix]
print(col) # [2, 5, 8]

Time and Space Complexity

  • Time Complexity: \(O(R \times C)\) to initialize the matrix.
  • Space Complexity: \(O(R \times C)\) to store the matrix.

Summary

  • Never initialize a 2D list using [[0] * C] * R.
  • Always use [[0] * C for _ in range(R)].
  • Know how to iterate through a matrix using nested loops and enumerate.