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 visa-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

hide comments
amit1_sharma: 2020-10-02 10:45:29

How for input "{{{}" answer is 1 while it should be 2?

adarshgaur: 2020-08-05 10:59:02

With dp it will be solved in O(N^2) but using stack(or similar concept) it can be implemented in O(N)

akash_arelli7: 2020-07-23 06:47:35

If you know how to implement stack. Just go with it. Don't waste your time.

jeets: 2020-07-16 09:03:14

What if No. of braces are odd?
Such a string can't be made stable ...

kumar_anubhav: 2020-06-27 10:07:22

AC in one go!!
think what if there is no opening bracket :)
good problem

robosapien: 2020-06-03 01:20:52

Dont forget about the output format.. :/

broken_forever: 2020-05-24 08:17:14

Try to use DP not stack...it provide better insight of DP
..actually stack isn't necessary to solve ,generic dp logic can solve this

Last edit: 2020-05-24 08:18:50
majd211: 2020-05-23 07:48:42

Beware of output format!! It gave me 2 wrong answers.

Ayush Mahajan: 2020-05-15 15:04:49

Simple greedy will work.

pharoaheye: 2020-05-15 10:22:39

very easy problem , just watch carefully on output format


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