C Program to find out ncr factor by using a user defined function for factorial. FORMULA : ncr = n! / ((n-r)! * r!)
Objective
Write a C program to calculate the nCr (Combinations) factor using a factorial function.
Algorithm / Approach
- Read values for
nandr. - The mathematical formula for nCr is:
n! / ((n-r)! * r!). - Instead of writing three separate loops to calculate three factorials, call the
fact()function three times:fact(n) / (fact(n-r) * fact(r)). - Print the result.
main.c
#include<stdio.h>
int fact(int);
int main(){
int n,r, res;
printf("Enter n: ");
scanf("%d",&n);
printf("Enter r: ");
scanf("%d",&r);
res = fact(n)/(fact(n-r)*fact(r));
printf("Result nCr Is: %d",res);
}
int fact(int x){
int i, f=1;
for(i=1; i<=x; i++){
f = f*i;
}
return f;
}Expected Output
Enter n: 5 Enter r: 3 Result nCr Is : 10
Explanation of the Program
- This program perfectly illustrates the power of code reusability.
- If we didn't have a function, we would have had to write three separate loops in
main()to calculate the three different factorials, making the code messy and repetitive.
Complexity
Time Complexity
O(n) - Calling factorial multiple times, bounded by n.
Space Complexity
O(1)
