Leetcode #2481: Minimum Cuts to Divide a Circle
In this guide, we solve Leetcode #2481 Minimum Cuts to Divide a Circle 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
A valid cut in a circle can be: A cut that is represented by a straight line that touches two points on the edge of the circle and passes through its center, or A cut that is represented by a straight line that touches one point on the edge of the circle and its center. Some valid and invalid cuts are shown in the figures below.
Quick Facts
- Difficulty: Easy
- Premium: No
- Tags: Geometry, 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.
Example
Input: n = 4
Output: 2
Explanation:
The above figure shows how cutting the circle twice through the middle divides it into 4 equal slices.
Python Solution
class Solution:
def numberOfCuts(self, n: int) -> int:
return n if (n > 1 and n & 1) else n >> 1
Complexity
The time complexity is , and the space complexity is . The space complexity is .
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.