Book Chapter : Combos

What are variations?

The variations of ABC with length 2 are: AA,AB,AC,BA,BB,BC,CA,CB,CC. In simple english, we are allowed any of the three characters for our first choice, and we are allowed to still take any of the three characters fo the second choice. When computing the variations of length n, the number of variations is equal to the number of choices (here 3) to the power of the length (n). So with ABC and 2, it's three to the power of two, or nine.

Thus each time the algorithm recurses, we use a for loop to try recursing with every single possible additional character. Here's the completed code:

public class MyProgram {
    public static void main(String[] args) {
		variations("ABC","",2); 
    }
	static void variations(String x, String pre, int len) {
		if(len==0) { 
			System.out.println(pre); 
			return; 
		}
		for(int i=0;i<x.length();i++) {
			String p = pre+x.charAt(i);
			variations(x,p,len-1);
		}
	} //note recursive does not remove items
	//outputs AA,AB,AC,BA,BB,BC,CA,CB,CC
}
//If we ran it for XY with length of 3, the execution would look like:
//v("XY","",3)
//  v("XY","X",2)
//    v("XY","XX",1)
//      v("XY","XXX",0) prints "XXX"
//      v("XY","XXY",0) prints "XXY"
//    v("XY","XY",1)
//      v("XY","XYX",0) prints "XYX"
//      v("XY","XYY",0) prints "XYY"
//  v("XY","Y",2)
//    v("XY","YX",1)
//      v("XY","YXX",0) prints "YXX"
//      v("XY","YXY",0) prints "YXY"
//    v("XY","YY",1)
//      v("XY","YYX",0) prints "YYX"
//      v("XY","YYY",0) prints "YYY"

Again, it would require only a small number of changes to modify the function to support arrays or other data structures rather than a String.