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Program to print Pascal Triangle in C

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

Program to print Pascal Triangle in C language

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

/* Program to print Pascal Triangle in C language */
#include <stdio.h>
 
long Factorial(int);
 
int main()
{
   int i, Number, j;
 
   printf("\n Please Enter the Number of rows you wish to see in pascal triangle\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;
}

OUTPUT

Program to print Pascal Triangle in C 1

ANALYSIS

Within this pascal triangle in c example, the following 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

long Factorial(int Number)

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

printf("\n Please Enter the Number of rows you wish to see in pascal triangle\n");
scanf("%d", &Number);

Now let us see the Nested for loop

for (i = 0; i < Number; i++)
{
   for (j = 0; j <= (Number - i - 2); j++) // First Inner Loop
   {
  	printf(" ");
   }
   for (j = 0; j <= i; j++) // Second Inner Loop
   {
     	printf("%ld ", Factorial(i) / (Factorial(j) * Factorial(i-j)));
   } 
   printf("\n");
}

Outer Loop – First Iteration

From the above 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 following statement will print Empty space as Output

printf(" ");

Following statement in will increment the Value of j by 1 using the Increment Operator

j++

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

printf(" ");

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

j++

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 statement is to terminate the current line

printf("\n");

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

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(i) / (Factorial(j) * Factorial(i – j) )
It means, 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

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(i) / (Factorial(j) * Factorial(i – j) )
It means, 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. 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(2) / (Factorial(1) * Factorial(1) ) —> Factorial of 2 = 2
= 2 / (1 * 1) = 2

Second Inner Loop – Third Iteration
j = 2, and the condition (2 <= 2) 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(2) / (Factorial(2) * Factorial(0) ) —> Factorial of 2 = 2
= 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

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 for the pascal triangle in c 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.

Please refer C Program to Find Factorial of a Number to understand the steps involved in the first function, i.e., long factorial (int Number)

/* Program to print Pascal Triangle in C using recursion */
#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 in pascal triangle\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;
}

OUTPUT

Program to print Pascal Triangle in C 2