Jumped straight to binary search which was the right call.
Start by clarifying the problem constraints (e.g., input size, expected time complexity) and then propose a binary search solution over the range [0, x]. Explain how to avoid overflow by using division or long integers, and discuss the trade-offs between binary search and Newton's method.
Pro tip: Mention that you can use bit manipulation (e.g., bitwise shifts) to optimize the binary search, and always test edge cases like x=0 and x=1. This shows attention to detail and performance.
Ask about input range, expected time/space complexity, and whether the function will be called frequently. This helps tailor the solution.
Explain that you will binary search for the largest n such that n*n <= x, using low=0 and high=x. Emphasize avoiding overflow by using mid <= x/mid instead of mid*mid <= x.
Mention Newton's method for faster convergence but note its complexity and potential floating-point issues. Compare with binary search's simplicity and O(log x) time.
Demonstrate with x=0, x=1, x=8, and a large number like 2^31-1. Show how the algorithm handles them correctly.
State time complexity O(log x) and space O(1). Mention possible optimizations like using bitwise operations or precomputed tables for small ranges.
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