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
hamjosh1: 2016-09-17 16:55:24

Be careful of the output format caused me 2 wa :'(

davidgalehouse: 2016-09-14 04:52:56

This problem is hard for people who don't read the comments, because you try to use DP... I could only think of an O(n^3) DP solution but I figure you need O(n^2) so I gave up and read the comments. But I used it to verify my greedy solution. And I don't think the greedy solution is as simple as everyone says, plus is anyone proving optimality? Can someone teach me the DP solution and prove optimality for the greedy? Thank YOU!!!

ajeyo: 2016-09-08 16:24:39

No DP! No Stacks! the tag should be rather changed to Ad-Hoc!!

cubalgo: 2016-08-22 17:10:53

WA's due to getline .

jasbir_220b2: 2016-08-13 18:41:01

O(n) without stack .... no need of DP ..happy coding :-)

cnexans: 2016-07-30 21:45:38

Easy question nonetheless you might get WA because of getline or gets. Hint: you do it everytime you program. No need for stacks.

nandhan: 2016-07-20 20:16:16

how the output is 1 for this case "{{{}" ??

adi_1996: 2016-07-05 12:53:02

O(n) without stack !1 :)

blackjack123: 2016-07-04 23:16:44

that was odd right...

sonali9696: 2016-06-30 22:59:19

What about cases like {}{ --> how to make such braces stable by just substitution?
Edit- such test cases are not included

Last edit: 2016-06-30 23:05:26

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