Get all 1-k tuples in a n-tuple

Question

With n=5 and k=3 the following loop will do it

List l=new ArrayList();
l.add(\"A\");l.add(\"B\");l.add(\"C\");l.add(\"D\");l.add(\"E\         


        

Answer 1

This technique is called Gosper's hack. It only works for n <= 32 because it uses the bits of an int, but you can increase it to 64 if you use a long.

int nextCombo(int x) {
  // moves to the next combination with the same number of 1 bits
  int u = x & (-x);
  int v = u + x;
  return v + (((v ^ x) / u) >> 2);
}

...
for (int x = (1 << k) - 1; (x >>> n) == 0; x = nextCombo(x)) {
  System.out.println(Integer.toBinaryString(x));
}

For n = 5 and k = 3, this prints

111
1011
1101
1110
10011
10101
10110
11001
11010
11100

exactly as you'd expect.