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Minimum Cuts to Divide a Circle

Difficulty: Easy

Problem Description

Given the integer n, return the minimum number of cuts needed to divide a circle into n equal slices.

Key Insights

  • A valid cut can either pass through the center of the circle or touch the center and one edge point.
  • If n is even, you can achieve n slices with n/2 cuts through the center.
  • If n is odd, you require n cuts, as each slice must be distinct and symmetric.

Space and Time Complexity

Time Complexity: O(1) - The solution involves simple arithmetic operations. Space Complexity: O(1) - No additional space is required.

Solution

To solve the problem, we can use the following approach:

  1. If n is even, the number of cuts required is n/2, as each cut can divide the circle into two equal parts.
  2. If n is odd, we need n cuts, as each slice must be created with a separate cut.

The solution can be implemented using simple conditional logic to determine whether n is even or odd.

Code Solutions

def minCuts(n: int) -> int:
    # Check if n is even
    if n % 2 == 0:
        return n // 2  # n/2 cuts needed
    else:
        return n  # n cuts needed for odd n
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