Arithmetic's Power function (exponentiation)

How to implement Arithmetic's Exponentiation function in Python?

If n is a positive integer and x is any real number, then x^n corresponds to repeated multiplication of x n times.

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x^n = x * x * x * .... * x

x^n is represented as pow(x, n)

pow(x, n) implementation in Python

Brute-Force Implementation

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#!/usr/bin/env python3

# Function to implement power x^y
def power(x, y):

    temp = 1
    if y>0:
        while y>0:
            temp *= x
            y -= 1
    # handle negative y and float x
    else:
        while y<0:
            temp /=x
            y += 1

    return temp

Time Complexity

Time Complexity: O(n)

Optimised Implementation

x^n is represented as pow(x, n)

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#!/usr/bin/env python3

# Function to implement power x^y
def power(x, y):
    if(y == 0):
        return 1
    temp = power(x, int(y/2))

    if (y % 2 == 0):
        return temp * temp
    else:
        # handle negative y and float x
        if(y > 0):
            return x * temp * temp
        else:
            return (temp * temp)/x

Time Complexity

Time Complexity: O(log(n))