Question

General Recursion C++

How many possible bridge hands are there ? This question is a specific case of the general question, “How many combination of X items can I make out of Y items ?” In the case of the bridge hand, X is 4 and Y is 8. The solution is given by the following formula:

Combinations(Y, X) =

Y      if X = 1

1   if X = Y

Combinations(Y-1, X-1) + Combinations(Y-1, X) if Y > X > 1

Task 1: Write a recursive function, Combination(y, x), to implement the definition of the above function.

Task 2: Write a test driver function that calculate the result of Combinations(7, 4), and print out the result on the computer screen.

Answer 1

#include <iostream>
using namespace std;

int Combinations(int Y, int X){
   if(X == 1){
      return Y;
   }
   else if(X == Y){
      return 1;
   }
   else {
      return Combinations(Y-1,X-1)+Combinations(Y-1,X);
   }
}
   
int main()
{
   cout<<Combinations(7,4)<<endl;
   return 0;
}

Output:

35

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