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Source : Stanford ACM Programming Contest 2004
Time limit : 1 sec Memory limit : 32 M
Submitted : 188, Accepted : 113
We give the following inductive definition of a “regular brackets” sequence:
• the empty sequence is a regular brackets sequence,
• if s is a regularbrackets sequence,then(s)and[s]are regular brackets sequences, and
• if a and b are regular brackets sequences, then ab is a regular brackets sequence.
• no other sequence is a regular brackets sequence
For 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 of s. That is, you wish to find the largest m such that for indices i1,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 [()].
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. For example:
For each input case, the program should print the length of the longest possible regular brackets subsequence on a single line. For example:
#include <algorithm>using namespace std;