# PASCAL'S TRIANGLE

## Background for Pascal's Triangle

Pascal's Triangle is a special triangle formed by the triangular arrangement of numbers. This arrangement is done in such a way that the number in the triangle is the sum of the two numbers directly above it. The first number starts with 1. Refer to this image.GIF Source: Wikipedia |

###
Using __For Loop__ for Pascal's triangle

####
The syntax for __For Loop__ is:

for (intialization;condition;statement update){

statements;

}

####
Flowchart for __For Loop____ __

But single loop is not enough to build a pascal's triangle since there are elements in vertical and horizontal axes. So, we will use nested

__For Loops__i.e

__For Loop__inside

__For Loop__to calculate elements in each row.

## Algorithm for Pascal's Triangle

- Start
- Declare variables i, j, num=1
- Take input (num) for number of rows
- Iterate
*loop1*for 'num' times - Iterate
*loop2*inside*loop1*for (num-1) times - Iterate
*loop3*inside*loop1*after*loop2*for*0-i*times - Inside
*loop3*print*num*if j == 0 or i ==j - Inside
*loop3*else than condition 7 calculate coeffecients according to this formula num=num*(i-j+1)/j - Print numbers after 3 spaces under
*loop2* - Print new line under
*loop1* - End

## Flowchart for Pascal's Triangle

##
SOURCE CODE FOR PASCALS TRIANGLE

#### PROGRAM THAT CONSTRUCTS PASCAL'S TRIANGLE FOR "N" ROWS

```
#include<stdio.h>
#include <stdlib.h>
int main()
{
int i,j,num=1,n,space;
scanf("%d",&n); //takes input for number of rows
system("cls"); //clears screen in windows only
for (i=0;i<n;i++){ //loop for rows
for (space=i;space<n;space++){ //space's loop
printf(" ");
}
for (j=0;j<=i;j++){ //loop for coefficient
if (j == 0 || i == j)//checks for position
num=1;
else
num = num*(i-j+1)/j;
printf(" %d",num); //prints coefficient
}
printf("\n"); //prints new line
} getch(); }
```

## 1 Comments

great job! this explains well about the way c programs are made to program the pascals triangle.Loved it !

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