Given a binary string of 0s and 1s. The task is to find the maximum difference between the number of 0s and number of 1s in any sub-string of the given binary string. That is maximize ( number of 0s – number of 1s ) for any sub-string in the given binary string.
Input : S = "11000010001" Output : 6 From index 2 to index 9, there are 7 0s and 1 1s, so number of 0s - number of 1s is 6. Input : S = "1111" Output : -1
We have discussed Dynamic Programing approach in below post :
Maximum difference of zeros and ones in binary string | Set 1.
In the post we seen an efficient method that work in O(n) time and in O(1) extra space. Idea behind that if we convert all zeros into 1 and all ones into -1.now our problem reduces to find out the maximum sum sub_array Using Kadane’s Algorithm.
Input : S = "11000010001" After converting '0' into 1 and '1' into -1 our S Look Like S = -1 -1 1 1 1 1 -1 1 1 1 -1 Now we have to find out Maximum Sum sub_array that is : 6 is that case Output : 6
Below is the implementation of above idea.
Time Complexity : O(n)
Space complexity : O(1)
- Maximum difference of zeros and ones in binary string
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- Maximum absolute difference between sum of two contiguous sub-arrays
- Maximum length subsequence with difference between adjacent elements as either 0 or 1
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