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

Groovy version based on markt's elegant c# solution above. Dynamically checking open and close (information was repeated in output and args) as well as removing a couple of extraneous logic checks.

3.times{ 
    println bracks(it + 1)
}

def bracks(pairs, output=""){
    def open = output.count('(')
    def close = output.count(')')

    if (close == pairs) {
        print "$output "
    }
    else {
        if (open < pairs) bracks(pairs, "$output(")
        if (close < open) bracks(pairs, "$output)")
    }
    ""
}