My first instinct was just repeated subtraction and I actually started explaining that before catching myself.
Use bit manipulation and exponential search (doubling) to subtract the largest possible multiples of the divisor from the dividend, achieving O(log n) time. Handle edge cases like overflow (INT_MIN / -1) and signs carefully, and discuss trade-offs between iterative and recursive implementations.
Pro tip: Explicitly mention the overflow case (INT_MIN / -1) and how you'd handle it (e.g., return INT_MAX) before writing code—this shows attention to detail that interviewers at Amazon value. Also, discuss the time complexity: O(log n) where n is the dividend, and space complexity O(1) for iterative or O(log n) for recursive.
Confirm the problem constraints: 32-bit signed integers, no multiplication/division/modulo, handle overflow, and aim for better than linear time. Identify edge cases: divisor zero, dividend zero, INT_MIN, INT_MAX, and sign combinations.
Determine the sign of the result and handle the overflow case (INT_MIN / -1) by returning INT_MAX. Convert both numbers to positive (using long to avoid overflow) for easier processing.
While dividend >= divisor, find the largest multiple of divisor (by doubling) that can be subtracted. Subtract it and add the corresponding power of two to the quotient. Repeat until dividend < divisor.
Apply the previously determined sign to the quotient and return it. Ensure the result fits within 32-bit signed integer range.
Explain that the time complexity is O(log n) because each subtraction reduces the dividend by at least half, and space complexity is O(1) for iterative approach. Discuss potential trade-offs between iterative and recursive implementations.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.