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Started with the obvious simulation and coded it up cleanly, then they asked about performance on a long string and I kind of froze.
Model the process as each '1' moving right past adjacent '0's, where the total time equals the maximum over all '1's of the number of '0's to its right that have no '1' between them. Derive a formula by scanning the string and tracking the count of zeros after the last one, updating the answer as the maximum of (zeros + ones) for each '1' encountered. Explain the reasoning clearly and provide a linear-time algorithm.
Pro tip: After presenting the solution, mention that the same logic can be applied to similar problems like counting the number of swaps to group all 1s together, showing pattern recognition and transferable problem-solving skills.
Clarify that each second, every '01' becomes '10' simultaneously, meaning each '1' can swap with a '0' immediately to its right, but only one swap per second per '1'.
Recognize that the total time is determined by the '1' that takes the longest to move past all zeros to its right, which depends on the number of zeros after it and the number of ones before it.
Scan left to right, maintaining a count of zeros seen so far and ones seen so far. For each '1', the time for it to pass all zeros to its right is (zeros seen so far + ones seen so far). Update the maximum time.
Write a linear-time algorithm that computes the maximum, and test with examples like '0011' (0 seconds), '1010' (1 second), '1001' (2 seconds) to verify correctness.
State that the solution runs in O(n) time and O(1) space, and handle edge cases like empty string or all same characters.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.