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python環(huán)形單鏈表的約瑟夫問(wèn)題詳解

 更新時(shí)間:2018年09月27日 14:18:10   作者:冬日新雨  
這篇文章主要為大家詳細(xì)介紹了python環(huán)形單鏈表的約瑟夫問(wèn)題,具有一定的參考價(jià)值,感興趣的小伙伴們可以參考一下

題目:

一個(gè)環(huán)形單鏈表,從頭結(jié)點(diǎn)開(kāi)始向后,指針每移動(dòng)一個(gè)結(jié)點(diǎn),就計(jì)數(shù)加1,當(dāng)數(shù)到第m個(gè)節(jié)點(diǎn)時(shí),就把該結(jié)點(diǎn)刪除,然后繼續(xù)從下一個(gè)節(jié)點(diǎn)開(kāi)始從1計(jì)數(shù),循環(huán)往復(fù),直到環(huán)形單鏈表中只剩下了一個(gè)結(jié)點(diǎn),返回該結(jié)點(diǎn)。

這個(gè)問(wèn)題就是著名的約瑟夫問(wèn)題。

代碼:

首先給出環(huán)形單鏈表的數(shù)據(jù)結(jié)構(gòu):

class Node(object):
 def __init__(self, value, next=0):
  self.value = value
  self.next = next # 指針

class RingLinkedList(object):
 # 鏈表的數(shù)據(jù)結(jié)構(gòu)
 def __init__(self):
  self.head = 0 # 頭部

 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): # 按列表給出 data
  self.head = Node(data[0])
  p = self.head # 指針指向頭結(jié)點(diǎn)
  for i in data[1:]:
   p.next = Node(i) # 確定指針指向下一個(gè)結(jié)點(diǎn)
   p = p.next # 指針滑動(dòng)向下一個(gè)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): # 打印鏈表中的所有元素
  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): # 將鏈表置空
  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

然后給出約瑟夫算法:

 def josephus_kill_1(head, m):
  '''
  環(huán)形單鏈表,使用 RingLinkedList 數(shù)據(jù)結(jié)構(gòu),約瑟夫問(wèn)題。
  :param head:給定一個(gè)環(huán)形單鏈表的頭結(jié)點(diǎn),和第m個(gè)節(jié)點(diǎn)被殺死
  :return:返回最終剩下的那個(gè)結(jié)點(diǎn)
  本方法比較笨拙,就是按照規(guī)定的路子進(jìn)行尋找,時(shí)間復(fù)雜度為o(m*len(ringlinkedlist))
  '''
  if head == 0:
   print "This is an empty ring linked list."
   return head
  if m < 2:
   print "Wrong m number to play this game."
   return head
  p = head
  while p.next != p:
   for _ in xrange(0, m-1):
    post = p
    p = p.next
   #print post.next.value
   post.next = post.next.next
   p = post.next
  return p

分析:

我采用了最原始的方法來(lái)解決這個(gè)問(wèn)題,時(shí)間復(fù)雜度為o(m*len(ringlinkedlist))。
但是實(shí)際上,如果確定了鏈表的長(zhǎng)度以及要?jiǎng)h除的步長(zhǎng),那么最終剩余的結(jié)點(diǎn)一定是固定的,所以這就是一個(gè)固定的函數(shù),我們只需要根劇M和N確定索引就可以了,這個(gè)函數(shù)涉及到了數(shù)論,具體我就不細(xì)寫(xiě)了。

以上就是本文的全部?jī)?nèi)容,希望對(duì)大家的學(xué)習(xí)有所幫助,也希望大家多多支持腳本之家。

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