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Problem: Minimum Cuts to Divide a Circle

Medium
30 min
Explore how to determine the minimum straight cuts required to split a circle into n equal slices. Understand the geometric constraints and solve problems involving lines passing through the circle's center efficiently.

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

Problem
Ask
Submissions

Problem: Minimum Cuts to Divide a Circle

Medium
30 min
Explore how to determine the minimum straight cuts required to split a circle into n equal slices. Understand the geometric constraints and solve problems involving lines passing through the circle's center efficiently.

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