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Solution: Minimum Cuts to Divide a Circle

Understand how to calculate the minimum number of cuts required to divide a circle into n equal slices. Learn the difference in approach for odd and even values of n, and explore a constant time complexity solution based on geometric properties.

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 ...