Amazon Interview Question: Implement pow(x, n) – Efficient Exponentiation (Fast Power Algorithm)

Implement the function pow(x, n), which calculates x^n.
Note that you cannot use any built-in functions that directly implement pow.

Examples:

• Input: x = 2, n = 5 → Output: 32
• Input: x = 3.4, n = 3 → Output: 39.04

Key Ideas:

• When n is even: x^n = (x^(n/2))^2
• When n is odd: x^n = x * (x^(n-1))
• Handle negative exponents by returning 1 / pow(x, -n)

This approach tests understanding of recursion, divide and conquer, and edge case handling (e.g. negative powers, floating-point base).

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