Minimum Cuts to Divide a Circle - Complete Solution Guide

Minimum Cuts to Divide a Circle is LeetCode problem 2481, a Easy level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

A valid cut in a circle can be: A cut that is represented by a straight line that touches two points on the edge of the circle and passes through its center, or A cut that is represented by a straight line that touches one point on the edge of the circle and its center. Some valid and invalid cuts are shown in the figures below. Given the integer n , return the minimum number of cuts needed to divide a circle into n equal slices . Example 1: Input: n = 4 Output: 2 Explanation: The above figure s

Detailed Explanation

The problem asks for the minimum number of cuts needed to divide a circle into `n` equal slices. A valid cut is either a straight line through the center connecting two points on the circle's edge, or a straight line from the center to a single point on the edge. The input is an integer `n` (1 ≤ n ≤ 100) representing the desired number of slices. The output is the minimum number of cuts required.

Solution Approach

The solution uses a straightforward conditional approach. It first handles the base case where `n` is 1 (no cuts needed). Then, it checks if `n` is even or odd. If even, it returns `n/2` as the minimum number of cuts. If odd, it returns `n` as the minimum number of cuts.

Step-by-Step Algorithm

1. Step 1: Check if `n` is equal to 1. If so, return 0 (no cuts needed).
2. Step 2: Check if `n` is even. If so, return `n / 2` (each cut through the center doubles the number of slices).
3. Step 3: If `n` is odd, return `n` (each cut from the center to the circumference creates a new slice).

Key Insights

• Insight 1: If `n` is even, you can make `n/2` cuts through the center, creating `n` equal slices. Each cut creates two new slices.
• Insight 2: If `n` is odd, you cannot create equal slices with cuts only through the center. You need `n` cuts, each from the center to a point on the circumference, creating `n` slices.

Complexity Analysis

Time Complexity: O(1)

Space Complexity: O(1)

Topics

This problem involves: Math, Geometry.

Companies

Asked at: tcs.