I have a List of elements (1, 2, 3), and I need to get the superset (powerset) of that list (without repeating elements). So basically I need to create a List of Lists that looks like:
{1}
{2}
{3}
{1, 2}
{1, 3}
{2, 3}
{1, 2, 3}
What is the best (simplicity > efficiency in this case, the list won't be huge) way to implement this? Preferably in Java, but a solution in any language would be useful.
Use bitmasks:
int allMasks = (1 << N);
for (int i = 1; i < allMasks; i++)
{
for (int j = 0; j < N; j++)
if ((i & (1 << j)) > 0) //The j-th element is used
System.out.print((j + 1) + " ");
System.out.println();
}
Here are all bitmasks:
1 = 001 = {1}
2 = 010 = {2}
3 = 011 = {1, 2}
4 = 100 = {3}
5 = 101 = {1, 3}
6 = 110 = {2, 3}
7 = 111 = {1, 2, 3}
You know in binary the first bit is the rightmost.