Nested Loops

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 can be the same type or different types of loops. Both loops can be for loops or while loops. The outer loop can 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 $A = \{a,b,c\}$ and $B = \{1,2,3\}$ is $A \times B = \{(a,1),(a,2),(a,3),(b,1),(b,2),(b,3),(c,1),(c,2),(c,3)\}$. 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.

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), 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 , end="\t" as the last parameter of print. The "\t" tab, which includes multiple spaces. We can use " " to show only one space.

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

We can also add parentheses in the output using the statement print("(",e,m,") ",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 can be several ways to write correct solutions in programming.

Ordered pairs

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

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 )

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

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

Rectangle of asterisks

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

Sample input

5
8

Sample output

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

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

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

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

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