Raw Input

..(.(..(..)..)..)..(..(..)..(..)..)..(..)..

Desired Output

..\(.(..(..)..)..\)..\(..(..)..(..)..\)..\(..\)..

Description

To assign a level number to every parenthesis, we keep a counter whose initial value is zero.

This process scans the line from left to right:

Whenever a `(' is meet, we increase the counter by one, and the resulting number is used as its level number.
Whenever a `)' is meet, the value of the counter is used as its level number, then we decrease the counter by one.

For the example above, the level number is shown under every parenthesis:

..(.(..(..)..)..)..(..(..)..(..)..)..(..)..
  1 2  3  3  2  1  1  2  2  2  2  1  1  1

Script and Comments

Script₁

[ 1] s/\(.*$/\n&\n/
[ 2] /\n/!b
[ 3] :loop
[ 4] /\n\(/s/$/#/
[ 5] /\n#$/s/\n/\\\n/
[ 6] /\n\)/s/#$//
[ 7] s/\n(.[^\n()]*)/\1\n/
[ 8] /\n\n/!b loop
[ 9] s/\n//g

Comments

When scanning a line, two newline characters are used:
- the character next to the first newline is the parenthesis to be examined in this iteration.
- the `#' characters following the second newline are used to keep the value of the counter.
Step [1] is used to insert a newline before the first `(' and at the end of line
If a line does not have any `(', Step [2] will print it and start a new cycle.
Step [3] adds a `#' to the counter if the parenthesis is a `('
If the parenthesis is outermost, Step [4] escapes it by inserting a `\'.
Step [5] removes a `#' from the counter if the parenthesis is a `)'.
Step [6] moves the first newline character to the next parenthesis.
If there exist parentheses not examined, jumps to Step [3]; otherwise removes all newline characters.