What is the optimal time complexity of solving Sum of First N Natural numbers?

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 Sum of First N Natural numbers?

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 Sum of First N Natural numbers?

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 Sum of First N Natural numbers?

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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Sum of First N Natural numbers

Learn how to solve the 'Sum of First N Natural numbers' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function sum_natural(n) that takes a positive integer n and returns the sum of the first n natural numbers, i.e., 1 + 2 + 3 + ... + n.

Constraints

•1 <= n <= 10^6

Examples

Example 1

Input

n = 5

Output

Explanation

1 + 2 + 3 + 4 + 5 = 15.

Example 2

Input

n = 10

Output

Explanation

1 + 2 + 3 + ... + 10 = 55.

Example 3

Input

n = 1

Output

Explanation

The sum of the first 1 natural number is just 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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