# Which Data Structure Is Used in Josephus Problem?

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Angela Bailey

The Josephus Problem is a mathematical problem that dates back to ancient times. It is named after the Jewish historian Flavius Josephus, who described the problem in his writings. The problem goes as follows:

## The Problem

A group of n people are standing in a circle, and they are numbered from 1 to n. Starting from person 1, a hot potato is passed clockwise around the circle. After a certain number of passes, the person holding the hot potato is eliminated and leaves the circle. The process continues until only one person remains.

The question then arises: Which position should you stand in to be the last person remaining This is where data structures come into play.

## Data Structures for the Josephus Problem

There are several data structures that can be used to solve the Josephus Problem, each with its own advantages and disadvantages.

### 1. Array

An array is a simple and straightforward data structure that can be used to solve this problem. Each element in the array represents a person, and their value indicates their position in the circle.

• Advantages: Easy to implement and understand.
• Disadvantages: Inefficient when it comes to removing elements from the middle of the array.

A linked list is another option for solving the Josephus Problem. Each node in the linked list represents a person, and they are connected by pointers.

• Disadvantages: More complex to implement compared to an array.