Re: Bracket Packing (#78)


I’ve refined my solution a little bit. It’s now a bit smarter at
positioning missing opening brackets. The old version would misbehave

[([B])}] -> [([B]){}]

The new version produces…

[([B])}] -> [{([B])}]

After spotting that we had a missing opening bracket, I was trying to
scan backwards to find the last unclosed occurrence of the next expected
bracket. This was getting a bit messy, then I spotted the technique used
by Ross to add the opening position to the stack along with the bracket
type - being a Ruby newbie I didn’t think of pushing a tuple onto the
stack. Slotted that technique in there, and it seems to work a charm.

Some test results below…

[B] -> [B] (valid=true)
[[B] -> [[B]] (valid=false)
[B]] -> [[B]] (valid=false)
[(B)] -> [(B)] (valid=true)
[(B] -> [(B)] (valid=false)
[B)] -> [(B)] (valid=false)
[([B])}] -> [{([B])}] (valid=false)
[{([B])] -> [{([B])}] (valid=false)
[(B)(B)(B)}] -> [{(B)(B)(B)}] (valid=false)
[(B){(B)(B)({B})] -> [(B){(B)(B)({B})}] (valid=false)
[(B)(B)(B)({B}})] -> [(B)(B)(B)({{B}})] (valid=false)
[(B)(B)(B)}({B})] -> [{(B)(B)(B)}({B})] (valid=false)


Hmm, after reading the comments, I realized I missed an important
concept: There can only be individual B(rackets) that must be
individually wrapped. I allow multiple brackets inside an inner wrap.
I guess I should read any clarifications prior to starting out next
time. (I didn’t want to influence my attempt with others’ answers.)

I’d like to discuss the BNF grammar for this with anyone here. I think
that is a great starting
point for any parsing solution.


#!/usr/bin/env ruby


$stack = []
$exit_bad = false

def pop_check(token)
$exit_bad = $stack.empty? || $stack.pop != token

def seq(x)
“#{expr(x)}#{seq(x)}” unless x.empty?

def expr(x)
c = x.shift
if !c.nil?
case c
when ‘[’
$stack.push c
[’[’, expr(x), ‘]’]
when ‘{’
$stack.push c
[’{’, expr(x), ‘}’]
when ‘(’
$stack.push c
[’(’, expr(x), ‘)’]
when ‘]’
pop_check ‘[’
when ‘}’
pop_check ‘{’
when ‘)’
pop_check ‘(’

input = ARGV[0]
abort(“empty input”) if input.nil? || input.empty?

tokens = input.split(’’)
output = seq(tokens)

puts output.to_s
abort if $exit_bad || !$stack.empty?

=begin rdoc

:section: Usage

fixer.rb input_str

Where input_str can be anything. The input_str is output with possible
modifications. Any left ‘[’, ‘{’ or ‘(’ in the input are paired with
matching right token. If the input string does not contain balanced
pairs of
brackets, braces or parens, the correct sequence is inferred and output.
an error occurs, an exit status of 1 is returned. If the input is empty,
an exit status of 1 is output and ‘empty input’ is written to stderr.

:section: About the solution

At first blush, this seems a straightforward paren balancing problem,
with the
twist that there are different kinds of parenthesis. My first attempt
a simple stack based attempt where I pushed the left side tokens and
then popped
the stack when I encountered a right side token. If the right side
its corresponding left side we continued, else if it didn’t match or the
stack was empty I flagged an error and exited. If it reached the end of
input and the stack was not empty it was an error.

The extra credit part of fixing the input was more challenging. I
started out
with a traditional recursive descent parser. I implied the grammer was
like this (forgive my bad BNF style notation:)
seq : expr seq
expr : term
| ‘[’ expr ‘]’
| ‘{’ expr ‘}’
| ‘(’ expr ‘)’
term :

After refactoring, I was left with the simple #seq and #expr with the
statement you see here. It worked for every test case I could throw at
Which left me to wonder how to detect the errors in the input. Finally,
I merged
in the original stack balancer from my first attempt.

The corrected sequence is inferred by left precedence. I.e. Any left
tokens are assumed to be correct, and all right tokens are ignored in
favor of the grammar
above. Ross didn’t state what the correct sequence was for his 2 error
conditions, so I went with this interpretation.