The First Program :

                                                              PASCAL TRIANGLE

The Pascal Triangle is one of the important and difficult programs to understand for a C beginner and if you are an Indian student pursuing Engineering you would feel the real struggle as it is made  complicated using UNNECESSARY formula and multiple variables.

A Pascal Triangle looks like this:
                                                    
                                                                     1
                                                               1          1
                                                          1         2          1
                                                     1        3          3         1
                                              1          4         6          4         1
                                         1         5        10        10        5           1

A Pascal Triangle gives the coefficients of the terms formed when two different variables are added or subtracted over a power.

Example:

(x+y)^0 =                                1         ------                          ( default case )
(x+y)^1 =                          1.x + 1.y
(x+y)^2 =                 1.x^2 + 2. xy + 1.y^2
(x+y)^3 =         1.x^3 + 3.x^2y + 3.xy^2 + 1.y^3
(x+y)^4 = 1.x^4 + 4.x^3y + 6.x^2.y^2 + 4.xy^3 + 1.y^4


Basically , the coefficients of 1st and last terms for any power will be 1 .
To get the remaining terms' coefficients :

We add the y and y+1 terms' coefficient values of 'x' to get the y+1 value of 'x+1' i.e

• 2nd and 3rd coefficient values of power 4 are 4 and 6 respectively.
• Now 3rd term's coefficient of  power 5 is 10 which is 4+6.

One thing that is important to remember is that power 'x' has x+1 terms and power 'x+1' has 'x+2' and that is how the 1s present at the start and end will be handy to compute the coefficients of the next powers.


PROGRAM :

#include<stdio.h>
void main()
{
            int i,j,k,l,n;
            printf("Enter the power whose coefficients are required:");
            scanf("%d",&n);
            int a[n],b[n],temp[n];
            a[0]=temp[0]=1;                                            // for the first 1 value in all powers
            a[1]=1;                                                           // only for the first case
            printf("1\n");                                                  // for the default case
            for(j=2;j<n+1;  )
            {
                       for(i=0;i<j;i++)
                       {
                                 printf("%d\t",a[i]);                   //printing of coefficient values
                        }
                        printf("\n");
                        j=j+1;
                       for(k=0;k<j;k++)
                       {
                                  if(k==j-1)
                                  {
                                            temp[k]=1;                    // for the last 1 value in all powers
                                  }
                                  else
                                  temp[k+1]=a[k+1]+a[k];       //result of addition of coefficients into temp array
                        }                                                      //so that no loss of data happens
                        for(l=0;l<j;l++)
                        {
                                  a[l]=temp[i];                         //updated values into array.
                        }
             }
}

Input:
3

Output:
 1
 1         1
 1         2          1
 1         3          3         1


Input:
1

Output:
1
1         1





* The above written code is an original one.

* Corrections and suggestions are appreciated.