Pascal Triangle
The Pascal Triangle is a triangle with array of binomial coefficients. In this article we will show you, How to write a Program to print Pascal Triangle in C language with example.
Program to print Pascal Triangle in C language
This C program allows the user to enter the maximum number of rows he/she want to print as 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
ANALYSIS
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 first function
long Factorial(int Number)
Following statements will allow the User to enter the range or maximum Number of rows he/she want to print as 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 and Number is 3 so, 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. Following statement will print Empty space as Output
printf(" ");
Following statement 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 following statement will print Empty space as Output
printf(" ");
First Inner Loop – Third Iteration
The j value will be 2 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. 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
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. Following statement is used 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 be printed as output. Next, 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 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
The j value will be 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
The j value will be 3 and the condition (3 <= 2) is False so it will exit from the for loop. 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 allows the user to enter the number of rows he/she want to print as Pascal triangle. In this example we are going to use the code snippet that we used in our first example but 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 inmvoluved in 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
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