50. Pow(x, n)

Problem:

Implement pow(x, n), which calculates x raised to the power n (xn).

Example 1:

Input: 2.00000, 10
Output: 1024.00000

Example 2:

Input: 2.10000, 3
Output: 9.26100

Example 3:

Input: 2.00000, -2
Output: 0.25000
Explanation: 2-2 = 1/22 = 1/4 = 0.25

Note:

• -100.0 < x < 100.0
• n is a 32-bit signed integer, within the range [−231, 231 − 1]

Analysis:

Keep dividing x by half until it reaches 0. If n is odd, say 2^5. res = 2^2 * 2^2 * 2 (x * half  * half). If n is even, say 2^4, res = 2^2 * 2^2 (half * half).

Solution:

class Solution {
    public double myPow(double x, int n) {
        double pow = pow(x, n);
        if (n < 0)
            return 1.0 /pow;
        else 
            return pow;
    }

    private double pow(double x, int n) {
        if (n == 0) return 1;
        double half = pow(x, n/2);
        if (n % 2 == 0) {
            return half * half;
        } else 
        {
            return x * half * half;
        }
    }
}