Problem Description
You are given a 0-indexed binary string target of length n. You have another binary string s of length n that is initially set to all zeros. You want to make s equal to target. In one operation, you can pick an index i where 0 <= i < n and flip all bits in the inclusive range [i, n - 1]. Flip means changing '0' to '1' and '1' to '0'. Return the minimum number of operations needed to make s equal to target.
Key Insights
- Each operation can only affect the suffix of the string starting from the chosen index.
- Flipping can change a contiguous block of bits, meaning we need to identify transitions between '0' and '1' in the target string.
- The number of flips required can be determined by counting the transitions from '0' to '1' or '1' to '0' as we traverse the string.
- If the string begins with '1', an initial flip is required to start matching the target.
Space and Time Complexity
Time Complexity: O(n)
Space Complexity: O(1)
Solution
The solution involves iterating through the target string once to count the number of transitions between '0' and '1'. Each transition signifies a necessary flip operation. We start with a counter initialized to zero and increment it whenever we find a change in the bit value. Additionally, if the target starts with '1', we need to account for the initial flip.