What is the optimal time complexity of solving Maximum number of handshakes?

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 Maximum number of handshakes?

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 Maximum number of handshakes?

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 Maximum number of handshakes?

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 BasicsHard

Maximum number of handshakes

Learn how to solve the 'Maximum number of handshakes' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Hard

Write a function max_handshakes(n) that takes a positive integer n representing the number of people in a room and returns the maximum number of handshakes that can happen if every person shakes hands with every other person exactly once.

The formula is: max_handshakes = n * (n - 1) / 2. This is because each pair of people shakes hands once.

Constraints

•1 <= n <= 10^4

Examples

Example 1

Input

max_handshakes(5)

Output

Explanation

5 people: 5 × 4 / 2 = 10 handshakes. Each of the 5 people shakes hands with 4 others, divided by 2 since each handshake is counted twice.

Example 2

Input

max_handshakes(2)

Output

Explanation

2 people can only have 1 handshake between them.

Example 3

Input

max_handshakes(10)

Output

Explanation

10 × 9 / 2 = 45 handshakes.

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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