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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.

Checkpoint

List-of-lists

Concepts in Practice

Lists

For each of the questions below, consider the following matrix:


mat A= 7 4 5 3 9 6 1 2 8 mat A= 7 4 5 3 9 6 1 2 8
1.
What would be the correct way to represent matA in Python?
  1. [[7, 4, 5], [3, 9, 6], [1, 2, 8]]
  2. [7, 4, 5
    3, 9, 6
    1, 2, 8]
  3. [[7, 3, 1], [4, 9, 2], [1, 2, 8]
2.
What would be the correct index for the number 6 in the above list?
  1. [5]
  2. [2][1]
  3. [1][2]
3.
What would be the result of the following code:
  print(matA[0])
  1. Error
  2. 7
  3. [7, 4, 5]

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 9.4

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.

1
"""Iterating a list-of-lists."""
2
3
# Create a list of numbers
4
list1 = [[1, 2, 3],
5
        [1, 4, 9],
6
        [1, 8, 27]]
7
8
# Iterating the list-of-lists
9
for row in list1:
10
  for num in row:
11
    print(num, end=" ")
12
  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]]
4.
Which code prints each number in my_list starting from 7, then 4, and so on ending with -5?
  1. for row in my_list:
      for elem in row:
        print(elem)
    
  2. for elem in my_list:
        print(elem)
    
5.
The range() function can also be used to iterate a list-of-lists. Which code prints each number in my_list starting from 7, then 4, and so on, ending with -5, using counting for loops?
  1. for column_index in range(0, len(my_list[0])):
      for row_index in range (0, len(my_list)):
        print(my_list[row_index][column_index])
    
  2. for row_index in range(0, len(my_list)):
      for column_index in range (0, len(my_list)):
        print(my_list[row_index][column_index])
      print()
    
  3. for row_index in range(0, len(my_list)):
      for column_index in range (0, len(my_list[0])):
        print(my_list[row_index][column_index])
    

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= 13 4 5 2 9 7 7 3 19 mat Z= 2 1 5 3 7 9 1 13 19 mat W= 13 4 5 2 9 7 7 3 19 mat Z= 2 1 5 3 7 9 1 13 19
result= 33 106 196 30 30 62 4 275 423 result= 33 106 196 30 30 62 4 275 423

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[1][2]= 2 -9 7 * 5 9 19 result[1][2]= 2 -9 7 * 5 9 19


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