Picking a team using recursion

Question

I'm trying to write a program that shows all possible combinations of teams with characters A,B,C... and so on.

Input : (5,3)

5 is the group size and 3 is the team size.

choosing 3 out of {A,B,C,D,E}

Expected output : ABC,ABD,ABE,ACD,ACE,ADE,BCD,BCE,BDE,CDE

Below is the code I've written so far.

public class teamApp 
{
    public static void main(String[] args) {
        int groupSize =5;
        int teamSize = 3;
        char start = 'A';
        String sequence = "";
        showTeam(sequence,start,groupSize,teamSize);
    }

    public static void showTeam(String sequence,char start, int n, int k)
    {
        if(n==0||k==0||k>n) {
            System.out.println(sequence);
            return;
        } else {
            showTeam(sequence+start,start++,n-1,k-1);       
            showTeam(sequence,start++,n-1,k);
        }
    }
}

I tried to use the (n,k) = (n-1,k-1)+(n-1,k) theorem. (where n=groupSize k=teamSize). My current output is

AAA
AAB
AAC
AA
ABB
ABC
AB
ACC
AC
A
BBB
BBC
BB
BCC
BC
B
CCC
CC
C

What am I doing wrong?

Answer 1

First of all, you should change

showTeam(sequence+start,start++,n-1,k-1);
showTeam(sequence,start++,n-1,k);

to

showTeam(sequence+start,(char)(start+1),n-1,k-1);
showTeam(sequence,(char)(start+1),n-1,k);

otherwise, only the second recursive call would get the incremented value of start (since start++ returns the original value of start).

Second of all, when the recursion unwinds, the partial sequences are also printed. To avoid that, add the following condition :

    if (n==0||k==0||k>n) {
        if (k==0) // this condition will make sure that only complete
                  // sequences of k elements will be printed
            System.out.println(sequence);
    } else {
        showTeam(sequence+start,(char)(start+1),n-1,k-1);
        showTeam(sequence,(char)(start+1),n-1,k);
    }

Output :

ABC
ABD
ABE
ACD
ACE
ADE
BCD
BCE
BDE
CDE