Finding all combinations of well-formed brackets

Question

This came up while talking to a friend and I thought I\'d ask here since it\'s an interesting problem and would like to see other people\'s solutions.

The task is to

Answer 1

ruby version:

def foo output, open, close, pairs
  if open == pairs and close == pairs
      p output
  else
    foo(output + '(', open+1, close, pairs) if open < pairs
    foo(output + ')', open, close+1, pairs) if close < open
  end
end
foo('', 0, 0, 3)