What is the optimal time complexity of solving Find the prime numbers between 1 to 100?

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 Find the prime numbers between 1 to 100?

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 Find the prime numbers between 1 to 100?

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 Find the prime numbers between 1 to 100?

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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Find the prime numbers between 1 to 100

Learn how to solve the 'Find the prime numbers between 1 to 100' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function primes_up_to_100() that takes no arguments and returns a list of all prime numbers between 1 and 100 (inclusive of 100 if it were prime).

A prime number is a number greater than 1 that has no divisors other than 1 and itself. The first few primes are 2, 3, 5, 7, 11, ...

Constraints

•The range is fixed: 1 to 100
•Return a list sorted in ascending order

Examples

Example 1

Input

primes_up_to_100()

Output

[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]

Explanation

There are 25 prime numbers between 1 and 100. Each number in the list is only divisible by 1 and itself.

Example 2

Input

len(primes_up_to_100())

Output

Explanation

The total count of primes between 1 and 100 is 25.

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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