Program to print Pascal Triangle in C

How to write a program to print Pascal Triangle in C language with example?. The C Pascal is a triangle with an array of binomial coefficients.

Program to print Pascal Triangle in C language

This pascal triangle in C program allows the user to enter the maximum number of rows he/she want to print. We are going to print the C pascal triangle of integers until it reaches the user-specified rows.

#include <stdio.h>
 
long Factorial(int);
 
int main()
{
   int i, Number, j;
 
   printf("\n Please Enter the Number of rows you wish to see \n");
   scanf("%d", &Number);
 
   for (i = 0; i < Number; i++)
   {
      for (j = 0; j <= (Number - i - 2); j++)
      {
      	printf(" ");
	  }
 
      for (j = 0; j <= i; j++)
      {
      	printf("%ld ", Factorial(i) / (Factorial(j) * Factorial(i-j)));
	  } 
 
      printf("\n");
   }
 
   return 0;
}
 
long Factorial(int Number)
{
   int i;
   long Fact = 1;
 
   for (i = 1; i <= Number; i++)
         Fact = Fact * i;
 
   return Fact;
}
Program to print Pascal Triangle in C 1

Within this pascal triangle in c example, the long Factorial(int Number) function declaration will find the factorial of the given number. Please refer C Program to Find Factorial of a Number to understand the steps involved in the first function

The following C Programming printf and scanf statements will allow the User to enter the range or maximum Number of rows he/she want to print as a pascal triangle.

Now let us see the Nested for loop in the iteration wise.

Outer Loop – First Iteration

From the above Pascal triangle in c screenshot, you can observe that the value of i is 0, the Number is 3, and the condition (i < 3) is True. So, it will enter into second for loop

First Inner Loop – First Iteration
The j value is 0 and the condition (j <= (3 – 0 – 2) is True. So, it will start executing the statements inside the loop. The printf(” “) statement will print Empty space as Output

The following j++ statement in will increment the Value of j by 1 using the Increment Operator

Pascal Triangle in C program First Inner Loop – Second Iteration

The j value will be 1, and the condition (1 <= (3 – 0 – 2)) is True so that the following statement will print Empty space as Output

First Inner Loop – Third Iteration

The j value will be two, and the condition (2 <= (3 – 0 – 2)) is False. So, it will exit from the for loop.

Next, it will enter into second For Loop

for (j = 0; j <= i; j++) // Second Inner Loop
   {
     	printf("%ld ", Factorial(i) / (Factorial(j) * Factorial(i-j)));
   }

Second Inner Loop – First Iteration
We haven’t finished the first iteration of the Outer for loop so, i value is still 0.

The j value is 0 and the condition (j <= 0) is True. So, it will start executing the statements inside the loop. The following statement will find the factorials of i and j and prints the output

printf("%ld ", Factorial(i) / (Factorial(j) * Factorial(i-j)));

factorial(i) / (Factorial(j) * Factorial(i – j) )
It means, factorial(0) / (Factorial(0) * Factorial(0) ) —> Factorial of 0 = 1
= 1 / (1 * 1) = 1

The j++ statement will increment the value of j by 1 using the Increment Operator

Second Inner Loop – Second Iteration

The j value will be 1, and the condition (1 <= 0) is False. So, it will exit from the for loop. The following printf(“\n”) statement is to terminate the current line

Final Output after the First Iteration = [Empty Space] [Empty Space] 1

Pascal triangle in C program Outer Loop – Second Iteration
The value of i will be ,1 and the condition (1 < 3) is True. So, it will enter into second for loop

First Inner Loop – First Iteration

The value of j is 0 and the condition (0 <= 0) is True. So, empty space will print as output. Next, the j value will also be incremented by 1.

First Inner Loop – Second Iteration

The value of j is 1, and the condition (1 <= 0) is False. So, it will exit from the for loop. Now, it will enter into second For Loop

Second Inner Loop – First Iteration
We haven’t finished the second iteration of the Outer for loop so, i value is still 1.

The j value is 0 and the condition (0 <= 1) is True. So, it will start finding the factorials of i and j and prints the output

factorial(i) / (Factorial(j) * Factorial(i – j) )
It means, factorial(1) / (Factorial(0) * Factorial(1) ) —> Factorial of 0 = 1
= 1 / (1 * 1) = 1

Second Inner Loop – Second Iteration
The j value will be 1 and the condition (1 <= 1) is True So, it will start finding the factorials of i and j and prints the output

factorial(1) / (Factorial(1) * Factorial(0) ) —> Factorial of 0 = 1
= 1 / (1 * 1) = 1

Second Inner Loop – Third Iteration

The j value will be 2, and the condition (2 <= 1) is False so that it will exit from the for loop. Final Output after the Second Iteration = [Empty Space] 1 1

Pascal triangle in C Outer Loop – Third Iteration
The value of i will be 2, and the condition (2 < 3) is True. So it will enter into second For Loop

Second Inner Loop – First Iteration
We haven’t finished the third iteration of the Outer for loop so, i value is still 2.

The j value is 0 and the condition (0 <= 2) is True. So, it will start finding the factorials of i and j and prints the output

factorial(2) / (Factorial(0) * Factorial(2) ) —> Factorial of 0 = 1
= 2 / (1 * 2) = 1

Second Inner Loop – Second Iteration
The j value will be 1, and the condition (1 <= 2) is True.

factorial(2) / (Factorial(1) * Factorial(1) ) —> Factorial of 2 = 2
= 2 / (1 * 1) = 2

Second Inner Loop of the pascal triangle in c – Third Iteration
j = 2, and the condition (2 <= 2) is True.

factorial(2) / (Factorial(2) * Factorial(0) )
= 2 / (2 * 1) = 1

Second Inner Loop – Fourth Iteration
j = 3, and the condition (3 <= 2) is False. So, it will exit from the for loop. The final Output after the Third Iteration = 1 2 1

Outer Loop – Fourth Iteration of the pascal triangle in c

The value of i will be 3, and the condition (3 < 3) is False. So it will exit from the for loop.

Final Output is:

[Empty Space] [Empty Space] 1
= [Empty Space] 1 1
1 2 1

C Program to print Pascal Triangle in C using recursion

This program allows the user to enter the number of rows he/she want to print as a Pascal triangle. In this example, we are going to use the code snippet that we used in our first example. However, this time we are using the recursive function to find factorial.

#include <stdio.h>
long Factorial(int Number)
{
  if (Number == 0 || Number == 1)  
    return 1;
  else
    return Number * Factorial (Number -1);
}

int main()
{
   int i, Number, j, Fact;
   printf("\n Please Enter Number of rows you want to see \n");
   scanf("%d", &Number);
   for (i = 0; i < Number; i++)
   {
      for (j = 0; j <= (Number - i - 2); j++)
      {
      	printf(" ");
      }
      for (j = 0; j <= i; j++)
      {
      	Fact = Factorial(i) / (Factorial(j) * Factorial(i-j));
	printf("%ld ", Fact);
      } 
      printf("\n");
   }
   return 0;
}
 Please Enter Number of rows you want to see
9
        1 
       1 1 
      1 2 1 
     1 3 3 1 
    1 4 6 4 1 
   1 5 10 10 5 1 
  1 6 15 20 15 6 1 
 1 7 21 35 35 21 7 1 
1 8 28 56 70 56 28 8 1 

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