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Solution: Minimum Cuts to Divide a Circle

Explore the mathematical solution for dividing a circle into n equal slices using the minimum number of cuts. Learn to determine when to use n cuts for odd slices or n divided by 2 cuts for even slices, understanding the logic and geometry behind it. This lesson helps clarify an efficient approach to solving geometry-based coding problems with O(1) complexity.

Statement

Given an integer n, determine the minimum number of cuts required to divide the circle into n equal slices. A valid cut in a circle is defined as one of the following:

  1. A cut is represented by a straight line that passes through the circle’s center and touches two points on its edge.

  2. A cut is represented by a straight line touching one point on the circle’s edge and center.

Examples of some valid and invalid cuts
Examples of some valid and invalid cuts

Constraints:

  • 11 \leq n 100\leq 100

Solution

To cut a circle into nn slices, the process depends on the value of ...