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Leetcode 2481. Minimum Cuts to Divide a Circle

Problem Statement

Given a circle, you need to determine the minimum number of cuts required to divide it into exactly n equal parts.

Clarifying Questions

1. Input Constraints:
   • What is the range of n?
   • Are there any special values for n we need to consider (e.g., n = 1)?

Clarifications:

• The value of n will be a positive integer.
• For n = 1, no cuts are needed since the circle is already in one piece.

Code

class Solution {
public:
    int minimumCuts(int n) {
        if (n == 1) return 0;
        return n;
    }
};

Strategy

1. Understanding the Problem:
   • If n is 1, no cuts are required.
   • For any n > 1, we simply need n radial cuts to divide the circle into n parts.
2. Implementation Details:
   • For n = 1, the answer is 0.
   • For any other n, the minimum number of radial cuts needed to divide a circle into n equal parts is straightforwardly n.
3. Example Analysis:
   • n = 1: No cuts required.
   • n = 2: One radial cut divides the circle into 2 equal parts.
   • n = 3: Two radial cuts originating from the center divide the circle into 3 equal parts.

Time Complexity

• The time complexity of this function is O(1), since it involves a simple conditional check and constant time operations.

This solution provides the minimum number of cuts directly for any given n, adhering to the principles of simplicity and efficiency.

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