Danh sách liên kết đơn trong cấu trúc dữ liệu

Danh sách liên kết đơn là gì?

Singly Linked List is a linear and unidirectional data structure where data is saved on the nodes, and each node is connected via a link to its next node. Each node contains a data field and a link to the next node. Singly Linked Lists can be traversed in only one direction, whereas a Danh sách được liên kết gấp đôi can be traversed in both directions.

Here is the node structure of a Singly Linked List:

Cấu trúc của một nút trong danh sách liên kết

Why Use a Linked List Over an Array?

Several scenarios favor a Linked List over an Mảng:

• Số phần tử không xác định: When the required element count is not known at compile time, a Linked List allocates memory dynamically as elements get added.
• Truy cập ngẫu nhiên: When random indexed access is not needed, a Linked List is a suitable choice.
• Chèn vào giữa: Inserting in the middle of an array requires shifting elements. A Linked List allows insertion at any position by rewriting only a few pointers.

Operacác chức năng của danh sách liên kết đơn

A Singly Linked List is good for dynamically allocating memory. It supports the standard operations of the linked list, i.e., insertion, deletion, searching, updating, merging two lists, and traversing.

The following operations are discussed in this article:

• Chèn vào đầu
• Chèn ở đuôi
• Chèn sau một nút
• Chèn trước một nút
• Xóa nút đầu
• Xóa nút đuôi
• Tìm kiếm và xóa một nút
• Duyệt qua danh sách liên kết

Here is an example of a linked list with four nodes.

Ví dụ về danh sách liên kết đơn

Insertion at the Head of a Singly Linked List

This is a simple operation. It is generally known as pushing onto a Singly Linked List. A new node is created and placed at the head of the list.

To perform this operation, follow two important conditions:

1. If the list is empty, the newly created node becomes the head node, and its tiếp theo pointer is NULL.
2. If the list is not empty, the new node becomes the head node, and its tiếp theo pointer points to the previous head node.

Here is the pseudo-code for inserting a node at the head of a linked list:

function insertAtHead(head, value):
  newNode = Node(value)
  if head is NULL:
    head = newNode
    return head
  else:
    newNode.next = head
    return newNode

Chèn vào đầu

Insertion at the End of a Singly Linked List

Inserting a node at the end of a linked list is similar to inserting at the head. Traverse to the tail node, then point its tiếp theo pointer to the new node. If the head is NULL, the new node becomes the head.

Bước 1) Traverse until the tiếp theo pointer of the current node becomes NULL.

Bước 2) Tạo một nút mới với giá trị được chỉ định.

Bước 3) Gán nút mới làm nút tiếp theo của nút đuôi.

The pseudo-code for inserting at the tail of a singly list:

function insertAtEnd(head, value):
  newNode = Node(value)
  if head is NULL:
    head = newNode
    return head
  while head.next is not NULL:
    head = head.next
  head.next = newNode
  newNode.next = NULL

Chèn ở đuôi

Insertion After a Node in a Singly Linked List

Inserting after a node has two parts: search for the target node and attach a new node after it. Traverse the list until a match is found, then splice the new node in.

Bước 1) Traverse until the value of the current node equals the search item.

Bước 2) Set the new node’s tiếp theo pointer to the current node’s tiếp theo con trỏ.

Bước 3) Point the current node’s tiếp theo pointer to the new node.

Mã giả:

function insertAfter(head, value, searchItem):
  newNode = Node(value)
  while head.value != searchItem:
    head = head.next
  newNode.next = head.next
  head.next = newNode

Chèn một nút sau một nút trong Danh sách liên kết đơn

Insertion Before a Node in a Singly Linked List

This is similar to insertion after a node. Traverse until the next node matches the search value, then insert the new node before it.

Bước 1) Di chuyển cho đến khi giá trị của nút tiếp theo bằng mục tìm kiếm.

Bước 2) Create a new node and set its tiếp theo pointer to the current node’s tiếp theo.

Bước 3) Point the current node’s tiếp theo to the new node.

function insertBefore(head, value, searchItem):
  newNode = Node(value)
  while head.next.value != searchItem:
    head = head.next
  newNode.next = head.next
  head.next = newNode

Chèn một nút vào trước một nút trong Danh sách liên kết đơn

Delete the Head of the Singly Linked List

The head pointer is provided as the parameter. The head node is removed, and the next node becomes the new head. The memory of the deleted node must be freed to avoid memory leaks.

Bước 1) Assign the next node of the head as the new head.

Bước 2) Free the allocated memory of the previous head node.

Bước 3) Trả lại nút đầu mới.

function deleteHead(head):
  temp = head
  head = head.next
  free(temp)
  return head

Xóa phần đầu của danh sách liên kết

Delete the Tail of the Singly Linked List

Deleting the tail node is similar to deleting the head node. The difference is that traversal to the end of the list is required. In a Singly Linked List, the node whose tiếp theo pointer is NULL is the tail node.

Bước 1) Traverse until just before the tail node. Save the current node.

Bước 2) Free the memory of the next node (the tail).

Bước 3) Set the next node of the current node to NULL.

function deleteTail(head):
  while head.next.next is not NULL:
    head = head.next
  free(head.next)
  head.next = NULL

Xóa phần đuôi của Danh sách liên kết đơn

Search and Delete a Node from a Singly Linked List

This function performs two tasks: search and delete. Traverse until the end of the list. If a matching node is found, remove it and relink the previous node’s tiếp theo con trỏ.

Bước 1) Traverse until the end of the list. Check whether the current node equals the search node.

Bước 2) If a match is found, store a pointer to the current node.

Bước 3) tiếp theo of the previous node becomes the next node of the current node.

Bước 4) Delete the current node and free its memory.

function searchAndDelete(head, searchItem):
  while head.next.next is not NULL and head.next.value != searchItem:
    head = head.next
  temp = head.next
  head.next = head.next.next
  free(temp)

Tìm kiếm và xóa một nút khỏi Danh sách liên kết đơn

Traverse a Singly Linked List

A Singly Linked List only supports traversal from head to tail. There is no pointer to the previous node, so reverse traversal is not possible. Each node is visited in turn, printing its value until NULL is reached.

Bước 1) Traverse each node until NULL is reached.

Bước 2) In giá trị của nút hiện tại.

function traverse(head):
  while head is not NULL:
    print head.value
    head = head.next

Ví dụ về danh sách liên kết đơn trong C++

#include<iostream>
using namespace std;
struct Node{
  int data;
  struct Node *next;
};
void insertAtHead(Node* &head, int value){
  Node* newNode = new Node();
  newNode->data = value;
  newNode->next = NULL;
  if(head != NULL){
    newNode->next = head;
  }
  head = newNode;
  cout<<"Added "<<newNode->data<<" at the front"<<endl;
}
void insertEnd(Node* &head, int value){
  if(head == NULL){
    insertAtHead(head, value);
    return;
  }
  Node* newNode = new Node();
  newNode->data = value;
  newNode->next = NULL;
  Node *temp = head;
  while(temp->next != NULL){
    temp = temp->next;
  }
  temp->next = newNode;
  cout<<"Added "<<newNode->data<<" at the end"<<endl;
}
void searchAndDelete(Node **headPtr, int searchItem){
  Node *temp = NULL;
  if((*headPtr)->data == searchItem){
    temp = *headPtr;
    *headPtr = (*headPtr)->next;
    free(temp);
  } else {
    Node *currentNode = *headPtr;
    while(currentNode->next != NULL){
      if(currentNode->next->data == searchItem){
        temp = currentNode->next;
        currentNode->next = currentNode->next->next;
        free(temp);
        break;
      } else {
        currentNode = currentNode->next;
      }
    }
  }
  cout<<"Deleted Node\t"<<searchItem<<endl;
}
void insertAfter(Node* &headPtr, int searchItem, int value){
  Node* newNode = new Node();
  newNode->data = value;
  newNode->next = NULL;
  Node *head = headPtr;
  while(head->next != NULL && head->data != searchItem){
    head = head->next;
  }
  newNode->next = head->next;
  head->next = newNode;
  cout<<"Inserted "<<value<<" after node\t"<<searchItem<<endl;
}
void insertBefore(Node* &headPtr, int searchItem, int value){
  Node* newNode = new Node();
  newNode->data = value;
  newNode->next = NULL;
  Node *head = headPtr;
  while(head->next != NULL && head->next->data != searchItem){
    head = head->next;
  }
  newNode->next = head->next;
  head->next = newNode;
  cout<<"Inserted "<<value<<" before node\t"<<searchItem<<endl;
}
void traverse(Node *headPointer){
  Node* tempNode = headPointer;
  cout<<"Traversal from head:\t";
  while(tempNode != NULL){
    cout<<tempNode->data;
    if(tempNode->next)
      cout<<" --> ";
    tempNode = tempNode->next;
  }
  cout<<endl;
}
int main(){
  Node *head = NULL;
  insertAtHead(head, 5);
  insertAtHead(head, 6);
  insertAtHead(head, 7);
  insertEnd(head, 9);
  traverse(head);
  searchAndDelete(&head, 6);
  traverse(head);
  insertAfter(head, 7, 10);
  insertBefore(head, 9, 11);
  traverse(head);
}

Đầu ra

Added 5 at the front
Added 6 at the front
Added 7 at the front
Added 9 at the end
Traversal from head:    7 --> 6 --> 5 --> 9
Deleted Node    6
Traversal from head:    7 --> 5 --> 9
Inserted 10 after node  7
Inserted 11 before node 9
Traversal from head:    7 --> 10 --> 5 --> 11 --> 9

Ví dụ về danh sách liên kết đơn trong Python

class Node:
  def __init__(self, data=None, next=None):
    self.data = data
    self.next = next
class SinglyLinkedList:
  def __init__(self):
    self.head = None
  def insertAtHead(self, value):
    newNode = Node(data=value)
    if self.head is not None:
      newNode.next = self.head
    self.head = newNode
    print(f'Added {newNode.data} at the front.')
  def insertAtEnd(self, value):
    if self.head is None:
      self.insertAtHead(value)
      return
    newNode = Node(value)
    temp = self.head
    while temp.next is not None:
      temp = temp.next
    temp.next = newNode
    print(f'Added {newNode.data} at the end.')
  def searchAndDelete(self, searchItem):
    if self.head is None:
      return
    if self.head.data == searchItem:
      self.head = self.head.next
      print(f'Deleted node\t{searchItem}')
      return
    currentNode = self.head
    while currentNode.next is not None:
      if currentNode.next.data == searchItem:
        currentNode.next = currentNode.next.next
        print(f'Deleted node\t{searchItem}')
        return
      currentNode = currentNode.next
  def insertAfter(self, searchItem, value):
    newNode = Node(data=value)
    temp = self.head
    while temp.next is not None and temp.data != searchItem:
      temp = temp.next
    newNode.next = temp.next
    temp.next = newNode
    print(f'Inserted {value} after node\t{searchItem}')
  def insertBefore(self, searchItem, value):
    newNode = Node(data=value)
    temp = self.head
    while temp.next is not None and temp.next.data != searchItem:
      temp = temp.next
    newNode.next = temp.next
    temp.next = newNode
    print(f'Inserted {value} before node\t{searchItem}')
  def traverse(self):
    temp = self.head
    print("Traversing from head:\t", end="")
    while temp:
      print("{}\t".format(temp.data), end="")
      temp = temp.next
    print()
singlyLinkedList = SinglyLinkedList()
singlyLinkedList.insertAtHead(5)
singlyLinkedList.insertAtHead(6)
singlyLinkedList.insertAtHead(7)
singlyLinkedList.insertAtEnd(9)
singlyLinkedList.traverse()
singlyLinkedList.searchAndDelete(6)
singlyLinkedList.traverse()
singlyLinkedList.insertAfter(7, 10)
singlyLinkedList.insertBefore(9, 11)
singlyLinkedList.traverse()

Đầu ra

Added 5 at the front.
Added 6 at the front.
Added 7 at the front.
Added 9 at the end.
Traversing from head:   7       6       5       9
Deleted node    6
Traversing from head:   7       5       9
Inserted 10 after node  7
Inserted 11 before node 9
Traversing from head:   7       10      5       11      9

Độ phức tạp của danh sách liên kết đơn

There are two kinds of complexity: time complexity and space complexity. The worst and average case time complexity are the same for a Singly Linked List.

Best-case time complexity:

• Insertion at the head can be done in O(1). No traversal inside the list is required.
• Search and delete can be done in O(1) if the target element is at the head node.

Average-case time complexity:

• Insertion inside a linked list takes O(n), where n is the total number of elements.
• Search and delete can take O(n) too, because the target element can reside anywhere up to the tail node.

Space complexity of Singly Linked List

A Singly Linked List dynamically allocates memory. To store n elements, it allocates n memory units. So the space complexity is O(n).

Applications of Singly Linked List

Singly Linked Lists appear in many places where forward-only traversal and dynamic memory are useful:

• Stacks and queues: Underlying storage for LIFO stacks and FIFO queues built from nodes.
• Hash table chaining: Collisions are resolved by chaining entries into a Singly Linked List per bucket.
• Adjacency lists: Sparse graphs use a Singly Linked List of neighbors for each vertex.
• Bảng ký hiệu: Compilers and interpreters chain identifiers into a Singly Linked List per scope.
• Memory allocators: Free-list allocators track free blocks as a Singly Linked List.

Câu Hỏi Thường Gặp