C++ Program to Compute Combinations using Recurrence Relation for nCr

This is a C++ program to compute combinations using recurrence relation for nCr.

1. This algorithm prints a total number of combination possible for given n and r value.
2. The time complexity of this algorithm is O(r).

1. This algorithm takes the input of n and r value.
2. Print the result using recurrence relation.
3. Exit.

C++ Program to compute combinations using recurrence relation for nCr.
This program is successfully run on Dev-C++ using TDM-GCC 4.9.2 MinGW compiler on a Windows system.

#include<iostream>
 
using namespace std;
 
// A function to calculate combination using recurrence relation.
float CalcCombination(float n, float r)
{
	int i, res;
	if(r > 0)
		return (n/r)*CalcCombination(n-1,r-1);
	else 
		return 1;
}
 
int main()
{
	float n, r;
	int result;
	cout<<"A program to find combination from nCr format";
	cout<<"\n\n\tEnter the value of n: ";
	cin>>n;
	cout<<"\tEnter the value of r: ";
	cin>>r;
 
	// Get result using recurrence relation.
	result = CalcCombination(n,r);
	cout<<"\nThe number of possible combinations is: "<<result;
}

1. Take the input of n and r in floating type.
2. Using CalcCombination(), calculate (n/r)*CalcCombination(n-1,r-1) recursively.
3. Return to main and print the result in an integer type.
4. Exit.

Case 1:
A program to find combination from nCr format using ( n! / (r! * (n-r)!))
 
        Enter the value of n: 5
        Enter the value of r: 3
 
The number of possible combinations is: 10
 
Case 2:
A program to find combination from nCr format using ( n! / (r! * (n-r)!))
 
        Enter the value of n: 13
        Enter the value of r: 4
 
The number of possible combinations is: 221

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