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 [−2^31, 2^31− 1]

Problem Summary

Implement pow(x, n), that is, calculate the function x raised to the nth power.

Solution Ideas

• The requirement is to calculate Pow(x, n)
• This problem uses a recursive approach, continuously dividing n by 2. Pay attention to whether n is positive or negative, and whether n is odd or even.

Code

package leetcode

// Time complexity O(log n), space complexity O(1)
func myPow(x float64, n int) float64 {
	if n == 0 {
		return 1
	}
	if n == 1 {
		return x
	}
	if n < 0 {
		n = -n
		x = 1 / x
	}
	tmp := myPow(x, n/2)
	if n%2 == 0 {
		return tmp * tmp
	}
	return tmp * tmp * x
}