Solving the Josephus problem with circular lists
Ioan Vlad Luca
March 29, 2019
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Introduction
• The goal of the project is to implement the Josephus problem using circular
lists. Josephus problem with circular lists consist in: given some numbers put
them in a circular list. After that given a starting point delete every 3rd element
from the list until only one element remains.
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Content of the project
• The project contains 3 important files:
• main.cpp: containing the Josephus problem;
• Circular list.h: containing the functions necessary for the list
• Heap.h: containing the functions for a node
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Functions choices
• The node class contains trivial functions for accessing and changing the value
or the connection of the node like:
• getInfo()
• getNextNode()
• setValue()
• etc...
• The list class contains functions for viewing,deleting, changing and searching
an element:
• searchNodeWithInfo(int value)
• addBeforeHead(int value)
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• delete node(node *n) deletes node with address n
• SkipNodesAferNode(node* start = NULL, int i = 0) jumps i nodes after
node start and returns the address
• printList() prints the list
• getLength()
• The main.cpp contains the algorithm for Josephus problem and does the
reading for the array.
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Design choices
My choices of design (the functions used) come from the requires of the Josephus problem. We need first to search for the starting point in the list, for
that the function searchNodeWithInfo is used. After that we need to jump
2 nodes, so i used: SkipNodesAferNode and delete it: delete node. The
getLength() function is used for knowing when to stop.
The pseudocode for tho Josephus problem using my choices of functions will
look like:
Josephus problem:
begin
start = searchNodeWithInfo(value)
sword = SkipNodesAferNode(start,2)
while (getLength() > 1) :
deletenode(sword)
sword = SkipNodesAferNode(sword,3)
end
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Tests and encountered issues
• The program works on any given input of integers numbers, with any length
smaller than 231 (int limit in Codeblocks).
• One important issue is the time it take to run. Because I printed the list at
every state, the algorithm takes a significant time to run. To avoid this issue
the cout statements can be deleted or commented and only the final element
can be printed.
Another possible problem encountered is when 2 or more nodes have the same
value. If this value is given as the starting point the first value in the list will
be selected, so it’s best to have different content for the nodes.
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