What is the optimal time complexity of solving Prime 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 Prime 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 Prime 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 Prime 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

Prime Number using Recursion

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

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Problem Statement

Medium

Write a function is_prime(n) that checks whether the given positive integer n is a prime number using recursion. The function should return True if n is prime and False otherwise. A prime number is a number greater than 1 that has no divisors other than 1 and itself.

Constraints

•1 <= n <= 10000

Examples

Example 1

Input

n = 7

Output

True

Explanation

7 is only divisible by 1 and 7, so it is prime.

Example 2

Input

n = 10

Output

False

Explanation

10 is divisible by 2 and 5, so it is not prime.

Example 3

Input

n = 1

Output

False

Explanation

1 is not considered a prime number by definition.

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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