50. Pow(x, n)

1. Description

Implement pow(x, n), which calculates x raised to the power n (i.e. $x^n$).

2. Example

Example 1

Input: x = 2.00000, n = 10
Output: 1024.00000

Example 2

Input: x = 2.10000, n = 3
Output: 9.26100

Example 3

Input: x = 2.00000, n = -2
Output: 0.25000
Explanation: $2{-2}$ = 1/$2^2$ = 1/4 = 0.25

3. Constraints

• -100.0 < x < 100.0
• -$2^{31}$ <= n <= $2^{31}$-1
• n is an integer.
• Either x is not zero or n > 0.
• -$10^4$ <= $x^n$ <= $10^4$

4. Solutions

Math

Time complexity : O(logn)
Space complexity : O(1)

class Solution {
public:
    double myPow(double x, int n) {
        double base = n > 0 ? x : 1 / x;
        long long exp = llabs((long long)n);

        double result = 1;
        while (exp > 0) {
            if (exp & 1) {
                result *= base;
            }

            base *= base;
            exp >>= 1;
        }

        return result;
    }
};