python环形单链表的约瑟夫问题详解

题目：

一个环形单链表，从头结点开始向后，指针每移动一个结点，就计数加1，当数到第m个节点时，就把该结点删除，然后继续从下一个节点开始从1计数，循环往复，直到环形单链表中只剩下了一个结点，返回该结点。

这个问题就是著名的约瑟夫问题。

代码：

首先给出环形单链表的数据结构：

class Node(object): def __init__(self, value, next=0):  self.value = value  self.next = next # 指针class RingLinkedList(object): # 链表的数据结构 def __init__(self):  self.head = 0 # 头部 def __getitem__(self, key):  if self.is_empty():   print 'Linked list is empty.'   return  elif key < 0 or key > self.get_length():   print 'The given key is wrong.'   return  else:   return self.get_elem(key) def __setitem__(self, key, value):  if self.is_empty():   print 'Linked list is empty.'   return  elif key < 0 or key > self.get_length():   print 'The given key is wrong.'   return  else:   return self.set_elem(key, value) def init_list(self, data): # 按列表给出 data  self.head = Node(data[0])  p = self.head # 指针指向头结点  for i in data[1:]:   p.next = Node(i) # 确定指针指向下一个结点   p = p.next # 指针滑动向下一个位置  p.next = self.head def get_length(self):  p, length = self.head, 0  while p != 0:   length += 1   p = p.next   if p == self.head:    break  return length def is_empty(self):  if self.head == 0:   return True  else:   return False def insert_node(self, index, value):  length = self.get_length()  if index < 0 or index > length:   print 'Can not insert node into the linked list.'  elif index == 0:   temp = self.head   self.head = Node(value, temp)   p = self.head   for _ in xrange(0, length):    p = p.next   print "p.value", p.value   p.next = self.head  elif index == length:   elem = self.get_elem(length-1)   elem.next = Node(value)   elem.next.next = self.head  else:   p, post = self.head, self.head   for i in xrange(index):    post = p    p = p.next   temp = p   post.next = Node(value, temp) def delete_node(self, index):  if index < 0 or index > self.get_length()-1:   print "Wrong index number to delete any node."  elif self.is_empty():   print "No node can be deleted."  elif index == 0:   tail = self.get_elem(self.get_length()-1)   temp = self.head   self.head = temp.next   tail.next = self.head  elif index == self.get_length()-1:   p = self.head   for i in xrange(self.get_length()-2):    p = p.next   p.next = self.head  else:   p = self.head   for i in xrange(index-1):    p = p.next   p.next = p.next.next def show_linked_list(self): # 打印链表中的所有元素  if self.is_empty():   print 'This is an empty linked list.'  else:   p, container = self.head, []   for _ in xrange(self.get_length()-1): #    container.append(p.value)    p = p.next   container.append(p.value)   print container def clear_linked_list(self): # 将链表置空  p = self.head  for _ in xrange(0, self.get_length()-1):   post = p   p = p.next   del post  self.head = 0 def get_elem(self, index):  if self.is_empty():   print "The linked list is empty. Can not get element."  elif index < 0 or index > self.get_length()-1:   print "Wrong index number to get any element."  else:   p = self.head   for _ in xrange(index):    p = p.next   return p def set_elem(self, index, value):  if self.is_empty():   print "The linked list is empty. Can not set element."  elif index < 0 or index > self.get_length()-1:   print "Wrong index number to set element."  else:   p = self.head   for _ in xrange(index):    p = p.next   p.value = value def get_index(self, value):  p = self.head  for i in xrange(self.get_length()):   if p.value == value:    return i   else:    p = p.next  return -1