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.

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

Cartesian product

The Cartesian product of the sets A={−1,−2,−3}A = \{-1,-2,-3\} and B={1,2,3}B = \{1,2,3\} is A×B={(−1,1),(−1,2),(−1,3),(−2,1),(−2,2),(−2,3),(−3,1),(−3,2),(−3,3)}A \times B = \{(-1,1),(-1,2),(-1,3),(-2,1),(-2,2),(-2,3),(-3,1),(-3,2),(-3,3)\}. 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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#include <iostream>
using namespace std;
int main()
{
  for (int e = -1; e >= -3; e--) // Outer loop
  { 
    for (int m = 1; m <= 3; m++) // Inner loop
    { 
      cout << "(" << e << " , " << m << ") " ;
    }
  }
  return 0;
}

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

  • The outer for loop starts from -1 and is decremented to -2 and then -3, 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 starts iterating from 1 and is incremented to 2 and then 3, storing a value to the variable, m, at each iteration.

  • The next statement is cout << "(" << e << " , " << m << ") " ;, which is in the body of the inner loop. The value of e remains -1 for all values of m in the inner loop. Therefore, the program outputs -1 1, -1 2, and -1 3.

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

  • Now, the value of e is -2. The inner loop starts again and outputs -2 1, -2 2, and -2 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 -3. The inner loop restarts and outputs -3 1, -3 2, and -3 3.

Note: We can display the results of the next cout statements on the same line by using "\t" at the end of the text/statement or separately. 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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#include <iostream>
using namespace std;
int main()
{
for (int e = -1; e >= -3; e--) // Outer loop
{ 
    for (int m = 1; m <= 3; m++) // Inner loop
    { 
      cout << e << " " << m << "\t";
    }
  }
  return 0;
}

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 may 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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#include <iostream>
using namespace std;
int main()
{
    //Write your code here 
  return 0; 
}

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

Enter the side length of square: 5

Sample output

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

#include <iostream>
using namespace std;

int main()
{
    // Write your code here
  return 0;    
}
Displaying 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

Enter the height of rectangle: 5
Enter the width of rectangle: 8

Sample output

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

#include <iostream>
using namespace std;

int main()
{
    // Write your code here
  return 0;
}
Displaying 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

Enter the side length of the right triangle: 5

Sample output

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

#include <iostream>
using namespace std;

int main()
{
    //Write your code here
  return 0;   
}
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

Enter the length of the side of the square: 5

Sample output

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

#include <iostream>
using namespace std;

int main()
{
    // Write your code here
  return 0;    
}
Display the hollow square