Started with the obvious loop and they let me finish before asking 'can we do better.' Binary exponentiation clicked for me pretty fast but I fumbled the negative n path for a second.
Start by clearly stating the naive O(n) approach, then introduce the optimized binary exponentiation (exponentiation by squaring) method that runs in O(log n). Discuss how to handle negative exponents by taking the reciprocal, and enumerate edge cases such as n=0, x=0, and integer overflow.
Pro tip: Mention that you would use a long long for the exponent to avoid overflow when negating INT_MIN, and that you can optimize further by using bitwise operations or handling even/odd exponents iteratively.
Ask about input ranges (e.g., can x be 0? can n be INT_MIN?), expected time/space complexity, and whether recursion is allowed. This shows you think about edge cases before coding.
Describe a simple loop that multiplies x by itself n times, handling negative n by computing 1/result. Mention its O(n) time complexity and why it's inefficient for large n.
Explain binary exponentiation (exponentiation by squaring): recursively or iteratively compute x^n by halving the exponent, using the fact that x^n = (x^(n/2))^2 for even n, and x * x^(n-1) for odd n. This reduces time to O(log n).
For negative n, compute the positive power and take the reciprocal. Discuss edge cases: n=0 (return 1), x=0 with negative n (undefined/infinity), and integer overflow when negating INT_MIN (use long long).
Compare O(n) vs O(log n) time, O(1) space for iterative vs O(log n) for recursive. Mention potential floating-point precision issues if x is a float, and how to handle large results (e.g., modulo arithmetic).
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