9.4 Nested lists

Learning objectives

By the end of this section you should be able to

Demonstrate the use of a list-of-lists to structure data.
Demonstrate individual element addressing using multi-dimensional indexing.
Use nested loops to iterate a list-of-lists.

List-of-lists

Lists can be made of any type of element. A list element can also be a list. Ex: [2, [3, 5], 17] is a valid list with the list [3, 5] being the element at index 1.

When a list is an element inside a larger list, it is called a nested list. Nested lists are useful for expressing multidimensional data. When each of the elements of a larger list is a smaller list, the larger list is called a list-of-lists.

Ex: A table can be stored as a two-dimensional list-of-lists, where each row of data is a list in the list-of-lists.

Using nested loops to iterate nested lists

A nested loop structure can be used to iterate a list-of-lists. For a two-dimensional list-of-lists, an outer for loop can be used for rows, and an inner for loop can be used for columns.

Example 1 Iterating a list-of-lists

The code below demonstrates how to iterate a list-of-lists.

The outer loop on line 9 goes element by element for the larger list. Each element in the larger list is a list. The inner loop on line 10 iterates through each element in each nested list.

"""Iterating a list-of-lists."""

# Create a list of numbers
list1 = [[1, 2, 3],
        [1, 4, 9],
        [1, 8, 27]]

# Iterating the list-of-lists
for row in list1:
  for num in row:
    print(num, end=" ")
  print()

The above code's output is:


    1 2 3
    1 4 9
    1 8 27

Concepts in Practice

Iterating a list-of-lists

For each question below, consider the following list:

my_list = [[7, 4, 5, 12],
          [24, 3, 9, 16],
          [12, 8, 91, -5]]

Try It

Matrix multiplication

Write a program that calculates the matrix multiplication product of the matrices matW and matZ below and prints the result. The expected result is shown.

$mat W = [\begin{matrix} 13 & 4 & 5 \\ 2 & - 9 & 7 \\ 7 & 3 & 19 \end{matrix}] mat Z = [\begin{matrix} 2 & 1 & 5 \\ 3 & 7 & 9 \\ - 1 & 13 & 19 \end{matrix}]$

$result = [\begin{matrix} 33 & 106 & 196 \\ - 30 & 30 & 62 \\ 4 & 275 & 423 \end{matrix}]$

In the result matrix, each element is calculated according to the position of the element. The result at position [i][j] is calculated using row i from the first matrix, W, and column j from the second matrix, Z.

Ex:

result[1][2] = (row 1 in W) times (column 2 in Z)

$result open bracket 1 close bracket open bracket 2 close bracket equals open bracket 2, -9, 7 close bracket * open bracket 5; 9; 19 close bracket$

$result [1] [2] = 2 * 5 + (-9) * 9 + 7 * 19 = 10 - 81 + 133 = 62$

# Create two lists for the matrices W and Z
matW = [[13,4,5],
    [2,-9,7],
    [7,3,19]]

matZ = [[2,1,5],
    [3,7,9],
    [-1,13,19]]

Adapted from Introduction to Python Programming by OpenStax (openstax.org), licensed under CC BY-NC-SA 4.0. Changes were made. License: CC-BY-NC-SA-4.0.