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]

Solution

/**
 * @param {number} x
 * @param {number} n
 * @return {number}
 */
var myPow = function(x, n) {
  if (n === 0) return 1;
  if (n > 0) return pow(x, n);
  if (n < 0) return 1 / pow(x, -n);
};

var pow = function (x, n) {
  if (n === 1) return x;
  var num = pow(x, Math.floor(n / 2));
  if (n % 2 === 0) {
    return num * num;
  } else {
    return x * num * num;
  }
};

Explain:

二分、递归。注意 n 小于 0 的情况。

Complexity:

• Time complexity : O(log(n)).
• Space complexity : O(log(n)).