Given a binary string. We need to find the length of longest balanced sub string. A sub string is balanced if it contains equal number of 0 and 1.
Input : input = 110101010 Output : Length of longest balanced sub string = 8 Input : input = 0000 Output : Length of longest balanced sub string = 0
A simple solution is to use two nested loops to generate every substring. And a third loop to count number of 0s and 1s in current substring. Time complexity of this would be O(n3)
An efficient solution is to use hashing.
1) Traverse string and keep track of counts of 1s and 0s as count_1 and count_0 respectively.
2) See if current difference between two counts has appeared before (We use hashing to store all differences and first index where a difference appears). If yes, then substring from previous appearance and current index has same number of 0s and 1s.
Below is the implementation of above approach.
Length of longest balanced sub string = 6
Time Complexity: O(n)
Extended Problem : Largest subarray with equal number of 0s and 1s
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