Spent way too long trying to brute-force count substrings after each attack step.
Clarify the problem constraints and define the irrecoverability condition precisely. Then, use a binary search over time combined with an efficient method to count substrings containing at least one malicious character, such as maintaining intervals of safe characters. Finally, implement and test the solution, ensuring it handles edge cases.
Pro tip: Demonstrate algorithmic maturity by discussing the trade-offs between binary search and linear scan, and mention how to optimize the substring counting using a sliding window or interval merging. This shows you can balance efficiency with correctness, a key trait for Amazon engineers.
Ask questions to confirm the input format, constraints, and the exact definition of 'substrings containing at least one malicious character'. Ensure you understand the order of character replacement and the threshold m.
Given a set of malicious positions at time t, derive a formula to count the number of substrings that contain at least one malicious character. This can be done by total substrings minus substrings consisting only of safe characters.
Since the count is monotonic with time, use binary search over the time steps to find the minimum t where count >= m. For each mid, compute the count efficiently, e.g., by maintaining intervals of safe characters.
Code the binary search and counting function, optimizing the counting using a data structure like a balanced BST or a disjoint-set union to track safe intervals. Analyze time complexity: O(n log n) or better.
Test with edge cases: m=0, m=total substrings, all characters malicious at once, etc. Verify the solution against a brute-force approach for small inputs.
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