Josephu问题的解决方案

1. 问题描述：

    设编号为1，2，…，n的n个人围坐一圈，约定编号为k（1 <=k <=n）的人从1开始报数，数到m的那个人出列，它的下一位又从1开始报数，数到m的那个人又出列，依次类推，直到所有人出列为止，由此产生一个出队编号的序列。

 

2. 分析: 该问题可以使用多种数据结构, 但是比较简单和自然的做法是利用一个具有n个链接点且不带头接点的循环链表.

 

3. 实现:

  1) 建立循环链表:

 

    public class CirculaLinkedNode<T>
    {
        public T Data { set; get; }
        public CirculaLinkedNode<T> Next { set; get; }
    }

    public class CirculaLinkedList<T>
    {
        public CirculaLinkedNode<T> Head { set; get; }

        public CirculaLinkedList(CirculaLinkedNode<T> head)
        {
            this.Head = head;
        }

        public CirculaLinkedList(T[] data)
        {
            if (data == null || data.Length < 1)
            {
                throw new ArgumentNullException("data");
            }

            CirculaLinkedNode<T> head = new CirculaLinkedNode<T>
            {
                Data = data[0],
                Next = null
            };
            CirculaLinkedNode<T> currentNode = head, node = null;
            for (int i = 1; i < data.Length; i++)
            {
                node = new CirculaLinkedNode<T>
                {
                    Data = data[i],
                    Next = null
                };
                currentNode.Next = node;

                currentNode = node;
            }
            currentNode.Next = head;

            this.Head = head;
        }

        public void Remove(CirculaLinkedNode<T> node)
        {
            if (this.Head == null)
            {
                return;
            }

            if (this.Head.Equals(node))
            {
                if (Head.Next.Equals(Head))
                {
                    Head = null;
                }
                else
                {
                    var n = Head.Next;
                    while (!n.Next.Equals(Head))
                    {
                        n = n.Next;
                    }
                    n.Next = Head.Next;
                    Head = Head.Next;
                }
            }
            else
            {
                var n = Head;
                while (!n.Next.Equals(Head))
                {
                    if (n.Next.Equals(node))
                    {
                        n.Next = n.Next.Next;
                        break;
                    }

                    n = n.Next;
                }
            }            
        }

        public CirculaLinkedNode<T> GetNodeByValue(T value)
        {
            var node = this.Head;
            while (!node.Next.Equals(Head))
            {
                if (node.Data.Equals(value))
                {
                    return node;
                }

                node = node.Next;
            }

            return null;
        }
    }

 

   2) 实现Josephu解决方案:

 

        /// <summary>
        /// Josephy Problem
        /// </summary>
        /// <param name="n">N people</param>
        /// <param name="m"></param>
        /// <param name="k"></param>
        public static void Josephu(int n, int m, int k)
        {
            if (n < 1)
            {
                throw new ArgumentOutOfRangeException("n");
            }
            if (m < 1)
            {
                throw new ArgumentOutOfRangeException("m");
            }
            if (k < 1 || k > n)
            {
                throw new ArgumentOutOfRangeException("k");
            }

            int[] personArray = new int[n];
            for (int i = 0; i < n; i++)
            {
                personArray[i] = i + 1;
            }

            CirculaLinkedList<int> cList = new CirculaLinkedList<int>(personArray);
            var firstNode = cList.GetNodeByValue(k);
            var node = firstNode;
            while (cList != null && cList.Head != null)
            {
                for (int i = 1; i < m; i++)
                {
                    node = node.Next;
                }
                Console.Write("---> {0}", node.Data);
                firstNode = node.Next;
                cList.Remove(node);
                node = firstNode;
            }
            Console.WriteLine("");
        }

    3) 测试:

 

CirculaLinkedListAction.Josephu(8, 4, 3);

 

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