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
rockdude: 2011-12-30 14:27:25

wat if there are odd no of { ,which can never be made stable by replacing with } or the lik... ?

it must be even read input

Last edit: 2011-02-05 16:34:01
Chandra Sekar: 2011-12-30 14:27:25

yes! Sadly, DP solution gets TLE :(

premanandh_j: 2011-12-30 14:27:25

i used a stack with O(N) soln but got WA

Kick: 2011-12-30 14:27:25

Space between 1.<space>answer... Be careful

Nguyen Khac Tung: 2011-12-30 14:27:25

but if you're able to find a correct & fast greedy algo, it's better :D

Ahmed Kamel [ahm.kam_92]: 2011-12-30 14:27:25

Yes, i know that's there is a greedy O(N) solution, but dp should get AC like in the contest.

Ambuj Varshney: 2011-12-30 14:27:25

Think Carefully, a single iteration over each character of the string is sufficient for this question making it in O(N).

Karim: 2011-12-30 14:27:25

I am getting TLE too, i am doing O(N^2) DP solution.

Ahmed Kamel [ahm.kam_92]: 2011-12-30 14:27:25

Does dp solution gets TLE ? O(T*N^2)
T = No. of test cases
N = Length of the string

Last edit: 2009-12-04 22:59:57
[Trichromatic] XilinX: 2011-12-30 14:27:25

Be careful with hidden '\r' at the end of each line...


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