50. Pow(x, n)

• Difficulty: Medium

• Topics: Math, Binary Search

• Similar Questions:

  • Sqrt(x)

  • Super Pow

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]

Solutions:

class Solution {
public:
    double myPow(double x, int n) {
        if (n == 0) return 1;
        if (n == 1) return x;
        if (n == -1)    return 1/x;
        double sqrt = myPow(x, n/2); // we should not call two myPow twice! Otherwise time limit exceeds. 
        return sqrt * sqrt * myPow(x, n - n/2 - n/2); 
    }
};