What is the optimal time complexity of solving Power of a Number using Recursion?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Power of a Number using Recursion?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Power of a Number using Recursion?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Power of a Number using Recursion?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Python BasicsMedium

Power of a Number using Recursion

Learn how to solve the 'Power of a Number using Recursion' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Medium

Write a function power(base, exp) that computes base raised to the power exp using recursion. The function should take two integers base and exp as input and return the result as an integer. Assume exp is always non-negative.

Constraints

•0 <= exp <= 20
•-10 <= base <= 10

Examples

Example 1

Input

base = 2, exp = 10

Output

Explanation

2^10 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 = 1024

Example 2

Input

base = 3, exp = 4

Output

Explanation

3^4 = 3 * 3 * 3 * 3 = 81

Example 3

Input

base = 5, exp = 0

Output

Explanation

Any number raised to the power 0 is 1

Need a Hint?

Use simple arithmetic operators (like modulo `%`, division `//`), conditional checks, or loops to inspect number properties.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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