I would like to efficiently generate a unique list of combinations of numbers based on a starting list of numbers.
example start list = [1,2,3,4,5]
but the algorithm should work for [1,2,3...n]
result =
[1],[2],[3],[4],[5]
[1,2],[1,3],[1,4],[1,5]
[1,2,3],[1,2,4],[1,2,5]
[1,3,4],[1,3,5],[1,4,5]
[2,3],[2,4],[2,5]
[2,3,4],[2,3,5]
[3,4],[3,5]
[3,4,5]
[4,5]
Note. I don't want duplicate combinations, although I could live with them, eg in the above example I don't really need the combination [1,3,2] because it already present as [1,2,3]
Just count 0
to 2^n - 1
and print the numbers according to the binary representation of your count. a 1
means you print that number and a 0
means you don't. Example:
set is {1, 2, 3, 4, 5}
count from 0 to 31:
count = 00000 => print {}
count = 00001 => print {1} (or 5, the order in which you do it really shouldn't matter)
count = 00010 => print {2}
00011 => print {1, 2}
00100 => print {3}
00101 => print {1, 3}
00110 => print {2, 3}
00111 => print {1, 2, 3}
...
11111 => print {1, 2, 3, 4, 5}