Pow(x, n) · Interview Problem

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Leetcode

Medium

Math

Recursion

Divide and Conquer

Google

Pow(x, n)

Compute $x^n$ efficiently for a real base and integer exponent.

Acceptance 80%

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Problem Statement

Problem

Given a real number x and a 32-bit signed integer n, return the value of $x^n$ .

Your solution should handle positive, negative, and zero exponents. Since n may be negative, the result may be a fraction. Use an approach that is efficient enough for large exponent values.

Input Format

A real number x
An integer n

Output Format

Return the computed value of $x^n$ as a real number.

Constraints

n fits in a 32-bit signed integer.
x is a real number.
The answer may be checked with a small floating-point error tolerance.
Avoid naive repeated multiplication for large |n|.

Hints

Consider how to reduce the number of multiplications by reusing the result of smaller powers.
Be careful with negative exponents and with the minimum 32-bit integer value.

Constraints

n is a 32-bit signed integer.
x is a real number.
Floating-point comparisons may allow small error tolerance.
Efficient solutions should run in logarithmic time with respect to |n|.

Examples

Sample cases returned by the problem API.

Example 1

Input

x = 2.00000, n = 10

Output

1024.00000

Explanation

$2^{10} = 1024$ .

Example 2

Input

x = 2.10000, n = 3

Output

9.26100

Explanation

$2.1^3 = 2.1 \times 2.1 \times 2.1 = 9.261$ .

Show 1 more example

Example 3

Input

x = 2.00000, n = -2

Output

0.25000

Explanation

$2^{-2} = 1 / 2^2 = 1/4 = 0.25$ .

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