Nested Loops

Learn and practice using a loop inside another loop.

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Nested loop

When we use a loop inside another loop, we call them nested loops. The first loop is called the outer loop, and the second loop is called the inner loop. Nested loops may be the same type or different types of loops. Both loops may be for loops or while loops. The outer loop may be a for loop and the inner loop a while loop, or vice versa.

Let’s use the Cartesian product of two sets as an illustration of nested loops.

Cartesian product

The Cartesian product of the sets A={a,b,c}A = \{a,b,c\} and B={1,2,3}B = \{1,2,3\} is A×B={(a,1),(a,2),(a,3),(b,1),(b,2),(b,3),(c,1),(c,2),(c,3)}A \times B = \{(a,1),(a,2),(a,3),(b,1),(b,2),(b,3),(c,1),(c,2),(c,3)\}. This can be achieved in programming with the help of two nested for loops. The outer loop iterates through the elements of the first set, and the inner loop iterates through the elements of the second set against each element of the first set.

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for e in ['a', 'b', 'c'] # Outer loop
  for m in [1, 2, 3] # Inner loop
    print("(#{e}, #{m})\n")
  end
end

There are a few new things in the code above that we need to understand.

  • The outer for loop iterates the values, [‘a’,‘b’,‘c’], one by one, storing a value to the variable e at each iteration of this loop.

  • The next statement is also a for loop, which is in the body of the outer loop.

  • This inner for loop iterates the values, [1,2,3], one by one, storing a value to the variable, m, at each iteration.

  • The next statement is print("(#{e}, #{m})\n"), which is in the body of the inner loop. The value of e remains a for all values of m in the inner loop. Therefore, the program outputs (a, 1), (a, 2), and (a, 3).

  • Then, the inner loop terminates, and the control goes to the next iteration of the outer loop.

  • Now, the value of e is b. The inner loop starts again and outputs (b, 1), (b, 2), and (b, 3).

  • Then, the inner loop terminates again, and the control goes to the next iteration of the outer loop.

  • Now, the value of e is c. The inner loop restarts and outputs (c, 1), (c, 2), and (c, 3).

These steps are also shown in the following execution sheet:

Note: We can display the results of the next print() statements on the same line by using "\t" at the end of print(). The "\t" tab includes multiple spaces. We may use " " to show only one space.

The following code demonstrates the functionality of showing the output on a single line:

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for e in ['a', 'b', 'c'] # Outer loop
  for m in [1, 2, 3] # Inner loop
    print("#{e} #{m}\t")
  end
end

Practice nested loops

The following are a few example programs that can help you practice writing nested loops. By clicking the “Show Solution” button, you’ll find a program that solves the respective problem. You can copy and paste the given solution into the code widget to make sure the output of your solution matches the given solution. There may be several ways to write correct solutions in programming.

Ordered pairs

Write a program that shows the ordered pairs (x,y)(x,y) so that 1<=x<=51 <= x <= 5 and 1<=y<=51 <= y <= 5.

Sample output

( 1 , 1 )	( 1 , 2 )	( 1 , 3 )	( 1 , 4 )	( 1 , 5 )	
( 2 , 1 )	( 2 , 2 )	( 2 , 3 )	( 2 , 4 )	( 2 , 5 )	
( 3 , 1 )	( 3 , 2 )	( 3 , 3 )	( 3 , 4 )	( 3 , 5 )	
( 4 , 1 )	( 4 , 2 )	( 4 , 3 )	( 4 , 4 )	( 4 , 5 )	
( 5 , 1 )	( 5 , 2 )	( 5 , 3 )	( 5 , 4 )	( 5 , 5 )
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# Write your code below

Square of asterisks

Write a program that shows a square shape built with asterisks. The number of asterisks on the side of the square is input by the user.

Sample input

5

Sample output

*****
*****
*****
*****
*****

# Write your code here
Display the square of asterisks

Rectangle of asterisks

Write a program that shows a rectangular shape built with asterisks. The height and width of the rectangle are input by the user.

Sample input

5
8

Sample output

********
********
********
********
********

# Write your code here
Display the rectangle of asterisks

Right triangle

Write a program that shows a right triangle built with asterisks. The side length of the right triangle is input by the user.

Sample input

5

Sample output

*
**
***
****
*****

# Write your code here
Display the right triangle

Hollow square

Write a program that displays a hollow square built with asterisks. The length of each side of the hollow square shape is input by the user.

Sample input

5

Sample output

*****
*   *
*   *
*   *
*****

# Write your code here
Display the hollow square of asterisks