Given a binary string S of length N, the task is to find the minimum number of bit flips required to convert the given string such that it contains only continuous substrings of 0’s and 1’s such that the final string is in the form of 000..000, 111..111, 111…000 or 000…111.
Input: S = 000100101, N = 9
000100101 -> 000000001
Input: S = 01100, N = 5
01100 -> 11100
The minimum number of flips can be calculated efficiently in two linear traversals.
In the first traversal, we will calculate what can be the minimum number of flips required in the worst case, as it can be equal to the number of total 0’s initially.
In the second traversal, at every step, the total number of flip required will be the sum of total 1’s before that point and total 0’s after that point. we will take a minimum of all values calculated at every step.
Hence, to solve the problem, follow the steps below:
- Initialize variables count0 = 0, count1 = 0 and res = 0. where, count0 strores count of 0 and count1 stores count of 1 and res stores the bit flips required.
- Traverse the input string, calculate 0’s and store it in res variable.
- Traverse the input string and subtract the count of 0 if character 0 is found and store the count of character 1 in variable count1 and updates the res as min(res, count0+count1).
Below is the implementation of the above approach.
Time complexity: O(k), where, k is length of binary string.
Space complexity: O(1)
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