What is the optimal time complexity of solving Sum from 1 to n?

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 from 1 to n?

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 from 1 to n?

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 from 1 to n?

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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Competitive ProgrammingEasy

Sum from 1 to n

Learn how to solve the 'Sum from 1 to n' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function sum_1_to_n(n) that returns the sum of integers from 1 to n.

Constraints

•1 <= n <= 10^5

Examples

Example 1

Input

sum_1_to_n(5)

Output

Explanation

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

Example 2

Input

sum_1_to_n(10)

Output

Explanation

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

Need a Hint?

Define subproblem states, establish the recurrence relation, and use memoization (top-down) or tabulation (bottom-up).

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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