Leetcode #2550: Count Collisions of Monkeys on a Polygon

In this guide, we solve Leetcode #2550 Count Collisions of Monkeys on a Polygon in Python and focus on the core idea that makes the solution efficient.

You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.

Problem Statement

There is a regular convex polygon with n vertices. The vertices are labeled from 0 to n - 1 in a clockwise direction, and each vertex has exactly one monkey.

Quick Facts

• Difficulty: Medium
• Premium: No
• Tags: Recursion, Math

Intuition

There is a mathematical invariant or formula that directly leads to the result.

Using math avoids unnecessary loops and reduces complexity.

Approach

Derive the formula or update rule, then compute the answer directly.

Handle edge cases like overflow or zero carefully.

Steps:

• Identify the math relationship.
• Compute the result with a loop or formula.
• Handle edge cases.

Python Solution

Complexity

The time complexity is $O(\log n)$, where $n$ is the number of monkeys. The space complexity is $O(1)$.

Edge Cases and Pitfalls

Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.

Summary

This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.