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Solution: Minimum Cuts to Divide a Circle

Understand how to calculate the minimum cuts required to divide a circle into equal slices based on whether n is odd or even. This lesson explains the geometric approach and provides an efficient O(1) time complexity solution.

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 ...