Description
We give the following inductive definition of a “regular brackets” sequence:
the empty sequence is a regular brackets sequence,if s is a regular brackets sequence, then (s) and [s] are regular brackets sequences, andif a and b are regular brackets sequences, then ab is a regular brackets sequence.no other sequence is a regular brackets sequenceFor instance, all of the following character sequences are regular brackets sequences:
(), [], (()), ()[], ()[()]
while the following character sequences are not:
(, ], )(, ([)], ([(]
Given a brackets sequence of characters a1a2 …an, your goal is to find the length of the longest regular brackets sequence that is a subsequence ofs. That is, you wish to find the largest m such that for indicesi1, i2, …, im where 1 ≤i1 < i2 < … < im ≤ n, ai1ai2 …aim is a regular brackets sequence.
Given the initial sequence ([([]])]
, the longest regular brackets subsequence is[([])]
.
Input
The input test file will contain multiple test cases. Each input test case consists of a single line containing only the characters(
,
)
, [
, and ]
; each input test will have length between 1 and 100, inclusive. The end-of-file is marked by a line containing the word “end” and should not be processed.
Output
For each input case, the program should print the length of the longest possible regular brackets subsequence on a single line.
Sample Input
((())) ()()() ([]]) )[)( ([][][) end
Sample Output
6 6 4 0 6
Source
Stanford Local 2004#include