Thread: recursion function / Pascal

I need to write a RECURSIVE function to calculate binomial coefficients.

It has been 9 years since last I took a mathematics course.
I have forgotten the purpose of this formula:

C(n,0) = 1 and C(n,n)=1 fo n >=0
C(n,k)=C(n-1,k)+C(n-1, k-1) for n >k>0

Does anyone know of what this is to yield??
What is C here in the formula(s)??
Does this have to do with coordinates that cross a point on an
(x,y) graph???

Help get me started on this program.

C(n,k) is the number of subsets of size k of the set {1,2,3,...n}
C(n,0)=1 as only one set has 0 elements the empty set
C(n,n)=1 as subset of n elements of a set of n elements must be the whole set
one way to look at this formula is as follows
consider the set S={1,2,...,n}
How many subsets of size k of S are there:C(n,k)
How many subsets of size k of S are there which contain 1:
C(n-1,k-1) (1 is already in , choose the reamining k-1 , from the remaining n-1)
How many subsets of size k of S are there which do not contain 1: C(n-1,k) (choose all k elements from {2,3,4,...n})
Adding up
C(n,k)=C(n-1,k-1)+C(n-1,k)

I have three questions:

1) what is the best method of asking for user input of n and k values ? such as in the form C(1,2)

2) shouldn't the below code have an additional set of parentheses around C(n-1,k) + C(n-1,k-1)
on the line with 'else return' ? so it is returning the value of the addition of the two recursive calls of C ??

3) is this final return line returning a single value???

> What is C here in the formula(s)??
A name for the function - since C is written in terms of C, its a recursive function.

It looks a bit like this

code:--------------------------------------------------------------------------------
int C ( int n, int k ) {
if ( k == 0 || n == k ) return 1;
else return C(n-1,k) + C(n-1,k-1);
}
--------------------------------------------------------------------------------

I have three questions:

1) what is the best method of asking for user input of n and k values ? such as in the form C(1,2)

2) shouldn't the below code have an additional set of parentheses around C(n-1,k) + C(n-1,k-1)
on the line with 'else return' ? so it is returning the value of the addition of the two recursive calls of C ??

3) is this final return line returning a single value???

1) think about what it is you want function to do
2) I think so.
3) put values in for the variables n and k and check and see

Code compiles okay.
But when I run program after I enter my values as asked,
get segFault. Why ???

I think my scanf and printf lines in main() might be the problem.
Please help.

I want the user to input as
(x,y)

and the result to say

The Coefficients of (x,y) is: (return value)

Any ideas??

Code:

#include <stdio.h>
#include <stdlib.h>
#include <math.h>


int c(int row, int index);

main()
{
  int n, k;
  printf("input values of C as (n,k)");
  scanf("%d" "%d",n,k);

  printf("The coefficient of (%d,%d) is : %d",n,k,c(n,k));

  return 0;

}

int c(int row, int index)
{
  if (row == 0 || index == 0)
     return 1;

  else
     return c(row-1,index) + c(row-1,index-1);
}

Your problem is with 'scanf'. Pass it the address of the variables:

scanf( "%d %d", &x, &y );

Quzah.

I fixed the scanf call.

I use input of (7,3)
7th row of pascal's triangle, 3rd element
result should be 35 (i thought this was the 4th element, myself)

getting garbage output, why???

PHP Code:

#include <stdio.h>
#include <stdlib.h>
#include <math.h>


int c(int row, int index);

main()
{
  int n, k;
  printf("input values of C as (n,k)\n");
  scanf("%d" "%d",&n,&k);

  printf("The coefficient of (%d,%d) is : %d\n",n,k,c(n,k));

  return 0;

}

int c(int row, int index)
{
  if (row == 0 || index == 0)
     return 1;

  else
     return c(row-1,index) + c(row-1,index-1);
}