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Solution: Minimum Cuts to Divide a Circle

Understand how to determine the least number of cuts required to split a circle into n equal slices based on whether n is even or odd. Explore the simple algorithm that uses center-passing lines to solve the problem efficiently with constant time 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 ...