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Clarify the tax bracket structure (marginal vs. flat) and edge cases, then design an algorithm that iterates through brackets, applying the rate only to income within each bracket. Implement the solution with clean code, test with examples, and discuss complexity and potential optimizations.
Pro tip: Mention that you would confirm whether the brackets are marginal (progressive) and handle edge cases like zero income, income exceeding the highest bracket, and negative income. Also, discuss how to structure the code for maintainability, such as using a list of tuples or a class.
Ask questions to confirm the tax bracket structure (marginal rates), input format, and expected output. Discuss edge cases: zero income, negative income, income above the highest bracket, and empty brackets.
Choose an iterative approach: sort brackets by lower bound, then for each bracket, compute the taxable amount within that bracket and multiply by the rate. Accumulate the total tax.
Write clean, modular code with clear variable names. Use a loop over brackets, tracking remaining income. Handle edge cases explicitly.
Walk through test cases: income in first bracket, middle bracket, top bracket, and above top bracket. Verify calculations manually.
State time complexity O(n) where n is number of brackets, and space O(1). Mention potential optimizations like binary search for large n, but note that O(n) is optimal for a single query.
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