ANARC09A - Seinfeld

I’m out of stories. For years I’ve been writing stories, some rather silly, just to make simple problems look difficult and complex problems look easy. But, alas, not for this one.

You’re given a non empty string made in its entirety from opening and closing braces. Your task is to find the minimum number of “operations” needed to make the string stable. The definition for being stable is as follows:

  1. An empty string is stable.
  2. If S is stable, then {S} is also stable.
  3. If S and T are both stable, then ST (the concatenation of the two) is also stable.

All of these strings are stable: {}, {}{}, and {{}{}}; But none of these: }{, {{}{, nor {}{.
The only operation allowed on the string is to replace an opening brace with a closing brace, or vice-versa.

Input

Your program will be tested on one or more data sets. Each data set is described on a single line. The line is a non-empty string of opening and closing braces and nothing else. No string has more than 2000 braces. All sequences are of even length.

The last line of the input is made of one or more ’-’ (minus signs.)

Output

For each test case, print the following line:

k. N

Where k is the test case number (starting at one,) and N is the minimum number of operations needed to convert the given string into a balanced one.

Example

Input:
}{
{}{}{}
{{{}
---

Output: 1. 2
2. 0
3. 1

Added by:Mohammad Kotb
Date:2009-11-28
Time limit:3.236s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64 BASH JS-RHINO
Resource:http://www.icpc-anarc.org

hide comments
2013-07-03 17:29:55 BLANKRK
simplex... :D green light in fst attempt
jus stack o(N)....
2013-05-25 12:37:11 rahul kumar singh
solution id is 9344000.i am getting correct ans for all the test cases but still getting wa..plz let me know

Last edit: 2013-05-25 12:37:33
2013-03-28 10:54:15 Ujjwal Arora
very simple O(n) solution
avoid dp or any complex algo
2013-01-10 17:18:06 recurcode!!
plz check my solution id 8465812....dnt knw d reason for wa
2013-01-02 09:39:43 a b
}}{{}{ ans will be 2 (1st and last to be changed)
2012-12-24 20:05:05 gourav
no DP... simple adhoc... O(n).. simple code... :-D
2012-12-14 07:17:42 Paul Draper
Look for the (very simple) linear time solution. No DP necessary.
2012-09-25 12:31:01 nik
Aggrrrhh! Extra characters on each line. Use strip in python or both checks for "{" and "}".

<EDITED: No swearing. If you can't write two sentences with proper English, than don't write at all!!>

Last edit: 2012-12-14 07:23:36
2012-08-13 04:16:47 mostafa hany
O(n) without stack :D
2012-08-02 23:39:15 Simón Murillo Gómez
Easy one with stack
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