What is the optimal time complexity of solving Finding Prime Factors of a number?

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 Finding Prime Factors of a number?

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 Finding Prime Factors of a number?

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 Finding Prime Factors of a number?

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 BasicsEasy

Finding Prime Factors of a number

Learn how to solve the 'Finding Prime Factors of a number' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function prime_factors(n) that takes a positive integer n (n >= 2) and returns a list of its prime factors in ascending order. If a prime factor appears multiple times, include it multiple times in the list.

Constraints

•2 <= n <= 10^6

Examples

Example 1

Input

n = 12

Output

[2, 2, 3]

Explanation

12 = 2 × 2 × 3. The prime factors are 2, 2, and 3.

Example 2

Input

n = 7

Output

[7]

Explanation

7 is itself a prime number.

Example 3

Input

n = 60

Output

[2, 2, 3, 5]

Explanation

60 = 2 × 2 × 3 × 5.

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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