数据结构与算法:双向链表

与单向链表相比,双向链表拥有两个指针域,一个指向直接前趋,一个指向直接后继。

双向链表的表示

由图:双向链表

  • 双向链表的结点也由数据域和指针域组成;
  • 结点之间通过指针域相连,Prev指针指向直接前趋,Next指针指向直接后继;
  • 头指针指向首元结点;
  • 首元结点的Prev指针为空指针,尾结点的Next指针为空指针。

基本操作

插入——在链表开头插入一个结点

——在链表尾部插入一个结点

——在链表中某个结点后插入一个结点

删除——删除第一个结点

——删除最后一个结点

——删除指定结点后的一个结点

遍历——顺序遍历

——倒序遍历

插入操作

以下代码展示了如何在双向链表开头插入一个结点:

//insert link at the first location
void insertFirst(int key, int data) {

   //create a link
   struct node *link = (struct node*) malloc(sizeof(struct node));
   link->key = key;
   link->data = data;
	
   if(isEmpty()) {
      //make it the last link
      last = link;
   } else {
      //update first prev link
      head->prev = link;
   }

   //point it to old first link
   link->next = head;
	
   //point first to new first link
   head = link;
}

删除操作

下面的代码展示了如何删除第一个结点:

//delete first item
struct node* deleteFirst() {

   //save reference to first link
   struct node *tempLink = head;
	
   //if only one link
   if(head->next == NULL) {
      last = NULL;
   } else {
      head->next->prev = NULL;
   }
	
   head = head->next;
	
   //return the deleted link
   return tempLink;
}

在链表尾部插入一个结点

代码如下:

//insert link at the last location
void insertLast(int key, int data) {

   //create a link
   struct node *link = (struct node*) malloc(sizeof(struct node));
   link->key = key;
   link->data = data;
	
   if(isEmpty()) {
      //make it the last link
      last = link;
   } else {
      //make link a new last link
      last->next = link;     
      
      //mark old last node as prev of new link
      link->prev = last;
   }

   //point last to new last node
   last = link;
}

C语言实现

各种操作的C语言实现如下:


#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <stdbool.h>

struct node {
   int data;
   int key;
	
   struct node *next;
   struct node *prev;
};

//this link always point to first Link
struct node *head = NULL;

//this link always point to last Link 
struct node *last = NULL;

struct node *current = NULL;

//is list empty
bool isEmpty() {
   return head == NULL;
}

int length() {
   int length = 0;
   struct node *current;
	
   for(current = head; current != NULL; current = current->next){
      length++;
   }
	
   return length;
}

//display the list in from first to last
void displayForward() {

   //start from the beginning
   struct node *ptr = head;
	
   //navigate till the end of the list
   printf("\n[ ");
	
   while(ptr != NULL) {        
      printf("(%d,%d) ",ptr->key,ptr->data);
      ptr = ptr->next;
   }
	
   printf(" ]");
}

//display the list from last to first
void displayBackward() {

   //start from the last
   struct node *ptr = last;
	
   //navigate till the start of the list
   printf("\n[ ");
	
   while(ptr != NULL) {    
	
      //print data
      printf("(%d,%d) ",ptr->key,ptr->data);
		
      //move to next item
      ptr = ptr ->prev;
      printf(" ");
   }
	
   printf(" ]");
}

//insert link at the first location
void insertFirst(int key, int data) {

   //create a link
   struct node *link = (struct node*) malloc(sizeof(struct node));
   link->key = key;
   link->data = data;
	
   if(isEmpty()) {
      //make it the last link
      last = link;
   } else {
      //update first prev link
      head->prev = link;
   }

   //point it to old first link
   link->next = head;
	
   //point first to new first link
   head = link;
}

//insert link at the last location
void insertLast(int key, int data) {

   //create a link
   struct node *link = (struct node*) malloc(sizeof(struct node));
   link->key = key;
   link->data = data;
	
   if(isEmpty()) {
      //make it the last link
      last = link;
   } else {
      //make link a new last link
      last->next = link;     
      
      //mark old last node as prev of new link
      link->prev = last;
   }

   //point last to new last node
   last = link;
}

//delete first item
struct node* deleteFirst() {

   //save reference to first link
   struct node *tempLink = head;
	
   //if only one link
   if(head->next == NULL){
      last = NULL;
   } else {
      head->next->prev = NULL;
   }
	
   head = head->next;
   //return the deleted link
   return tempLink;
}

//delete link at the last location

struct node* deleteLast() {
   //save reference to last link
   struct node *tempLink = last;
	
   //if only one link
   if(head->next == NULL) {
      head = NULL;
   } else {
      last->prev->next = NULL;
   }
	
   last = last->prev;
	
   //return the deleted link
   return tempLink;
}

//delete a link with given key

struct node* delete(int key) {

   //start from the first link
   struct node* current = head;
   struct node* previous = NULL;
	
   //if list is empty
   if(head == NULL) {
      return NULL;
   }

   //navigate through list
   while(current->key != key) {
      //if it is last node
		
      if(current->next == NULL) {
         return NULL;
      } else {
         //store reference to current link
         previous = current;
			
         //move to next link
         current = current->next;             
      }
   }

   //found a match, update the link
   if(current == head) {
      //change first to point to next link
      head = head->next;
   } else {
      //bypass the current link
      current->prev->next = current->next;
   }    

   if(current == last) {
      //change last to point to prev link
      last = current->prev;
   } else {
      current->next->prev = current->prev;
   }
	
   return current;
}

bool insertAfter(int key, int newKey, int data) {
   //start from the first link
   struct node *current = head; 
	
   //if list is empty
   if(head == NULL) {
      return false;
   }

   //navigate through list
   while(current->key != key) {
	
      //if it is last node
      if(current->next == NULL) {
         return false;
      } else {           
         //move to next link
         current = current->next;
      }
   }
	
   //create a link
   struct node *newLink = (struct node*) malloc(sizeof(struct node));
   newLink->key = key;
   newLink->data = data;

   if(current == last) {
      newLink->next = NULL; 
      last = newLink; 
   } else {
      newLink->next = current->next;         
      current->next->prev = newLink;
   }
	
   newLink->prev = current; 
   current->next = newLink; 
   return true; 
}

main() {
   insertFirst(1,10);
   insertFirst(2,20);
   insertFirst(3,30);
   insertFirst(4,1);
   insertFirst(5,40);
   insertFirst(6,56); 

   printf("\nList (First to Last): ");  
   displayForward();
	
   printf("\n");
   printf("\nList (Last to first): "); 
   displayBackward();

   printf("\nList , after deleting first record: ");
   deleteFirst();        
   displayForward();

   printf("\nList , after deleting last record: ");  
   deleteLast();
   displayForward();

   printf("\nList , insert after key(4) : ");  
   insertAfter(4,7, 13);
   displayForward();

   printf("\nList  , after delete key(4) : ");  
   delete(4);
   displayForward();
}

编译运行结果如下:

List (First to Last): [ (6,56) (5,40) (4,1) (3,30) (2,20) (1,10) ] 

List (Last to first): [ (1,10) (2,20) (3,30) (4,1) (5,40) (6,56) ]
List , after deleting first record: [ (5,40) (4,1) (3,30) (2,20) (1,10) ]
List , after deleting last record: [ (5,40) (4,1) (3,30) (2,20) ]
List , insert after key(4) : [ (5,40) (4,1) (4,13) (3,30) (2,20) ]
List , after delete key(4) : [ (5,40) (4,13) (3,30) (2,20) ]