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: Recursion
square x and cut n in half.
if n is negative, compute 1.0 / pow(x, |n|)
pow(x, n) := pow(x * x, n / 2) * (x if n % 2 else 1)
pow(x, 0) := 1
Example:
pow(x, 5) = pow(x^2, 2) * x
= pow(x^4, 1) * x
= pow(x^8, 0) * x^4 * x
= 1 * x^4 * x = x^5
Time complexity: O(logn)
Space complexity: O(logn)
C++
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// Author: Huahua class Solution { public: double myPow(double x, int n) { return n >= 0 ? myPowImp(x, n) : 1.0 / myPowImp(x, n); } private: double myPowImp(double x, int n) { if (n == 0) return 1; return myPowImp(x * x, n / 2) * (n % 2 ? x : 1); } }; |