PROBLEM LINK:

Practice
Contest

Author:Bruno Oliveira
Tester:Sergey Kulik
Editorialist:Lalit Kundu

DIFFICULTY:

EASY

PREREQUISITES:

AD-HOC

PROBLEM:

Given a bracket sequence, print the length of largest prefix that is a regular bracket sequence.

EXPLANATION:

A regular bracket sequence is defined as follows:
1. S="" is regular.
2. S="<" + S1 ">" is regular, if S1 is regular.
3. S=S1 concat S2 is regular, is S1 and S2 are regular.

If S is regular bracket sequence, for any i, number of closing brackets in S[0,i] should not exceed number of opening brackets. Also, if number of opening brackets is equal to number of closing brackets in S[0,i], S[0,i] is a regular bracket sequence.

def check(s):    
     t=0,ans=0    
     for i=0 to N-1:    
          if s[i]=='<': t++;   
          else:    
               t--;    
               //Now, if t=0, means, the string s[0,i] is valid.    
               if t==0: ans=max(ans,i+1)   
               else if t<0: break   //string s whole is invalid.    
     print ans

Complexity: O(N).

AUTHOR'S AND TESTER'S SOLUTIONS:

Author's solution
Setter's solution