Implementing a Doubly Linked List

Assumes understanding of Big O notation. Examples are in JavaScript. Information references "Cracking the Coding Interview" by Gayle Laakmann McDowell

Understanding Doubly Linked Lists

A doubly linked list is very similar to a singly linked list, except for the node’s structure and the way we add/remove nodes.

Node Structure

A node in a doubly linked list contains a prev pointer, next pointer, and value. The prev pointer points to the previous node and the next pointer points to the next node. By nature, this list goes both ways at each node.

Adding a Node

To insert a new node (newNode) at a specific index:

1. Store the node currently at the insertion index in a temporary variable nextNode.

2. Update the connections for the previous node and the new node:

   • Set the previous node's next pointer to newNode.
   • Set newNode's prev pointer to the previous node.

3. Connect the new node to the next node:

   • Set newNode's next pointer to nextNode.
   • Set nextNode's prev pointer to newNode.

Removing a Node

To remove a node at a specific index:

1. Update the previous node's next pointer:
   • Set it to point to the node after the one being removed.
2. Update the next node's prev pointer:
   • Set it to point to the node before the one being removed.

This effectively "bridges" the gap created by removing the node, maintaining the list's integrity.

Time Complexity Analysis

• Adding/Removing inside the doubly linked list → $O(n)$

• Adding/Removing at the head or tail of doubly linked list → $O(1)$

JavaScript Implementation

Classical OOP

class ListNode {
  constructor(value, prev = null, next = null) {
    this.value = value;
    this.prev = prev;
    this.next = next;
  }
}

class DoublyLinkedList {
  constructor() {
    this.head = null;
    this.tail = null;
    this.size = 0;
  }

  // add a node to the head of the list
  addHead(value) {
    const newNode = new ListNode(value, null, this.head);
    if (this.head) {
      this.head.prev = newNode;
    } else {
      this.tail = newNode; // If list was empty, new node is also the tail
    }
    this.head = newNode;
    this.size++;
  }

  // Add a node to the tail of the list
  addTail(value) {
    const newNode = new ListNode(value, this.tail, null);
    if (this.tail) {
      this.tail.next = newNode;
    } else {
      this.head = newNode; // If list was empty, new node is also the head
    }
    this.tail = newNode;
    this.size++;
  }

  // Remove a node from the head of the list
  removeHead() {
    if (!this.head) return null; // List is empty
    const removedValue = this.head.value;
    this.head = this.head.next;
    if (this.head) {
      this.head.prev = null;
    } else {
      this.tail = null; // List became empty
    }
    this.size--;
    return removedValue;
  }

  // Remove a node from the tail of the list
  removeTail() {
    if (!this.tail) return null; // List is empty
    const removedValue = this.tail.value;
    this.tail = this.tail.prev;
    if (this.tail) {
      this.tail.next = null;
    } else {
      this.head = null; // List became empty
    }
    this.size--;
    return removedValue;
  }

  // Remove a node at a specific index
  removeAt(index) {
    if (index < 0 || index >= this.size) return null;
    let current;
    if (index < this.size / 2) {
      current = this.head;
      for (let i = 0; i < index; i++) {
        current = current.next;
      }
    } else {
      current = this.tail;
      for (let i = this.size - 1; i > index; i--) {
        current = current.prev;
      }
    }
    if (current.prev) current.prev.next = current.next;
    if (current.next) current.next.prev = current.prev;
    if (index === 0) this.head = current.next;
    if (index === this.size - 1) this.tail = current.prev;
    this.size--;
    return current.value;
  }

  // Get the size of the list
  getSize() {
    return this.size;
  }

  // Get the values in the list
  getValues() {
    const values = [];
    let current = this.head;
    while (current) {
      values.push(current.value);
      current = current.next;
    }
    return values;
  }
}

Prototype-based OOP

function ListNode(value, prev = null, next = null) {
  this.value = value;
  this.prev = prev;
  this.next = next;
}

function DoublyLinkedList() {
  this.head = null;
  this.tail = null;
  this.size = 0;
}

// Add a node to the head of the list
DoublyLinkedList.prototype.addHead = function(value) {
  const newNode = new ListNode(value, null, this.head);
  if (this.head) {
    this.head.prev = newNode;
  } else {
    this.tail = newNode;
  }
  this.head = newNode;
  this.size++;
};

// Add a node to the tail of the list
DoublyLinkedList.prototype.addTail = function(value) {
  const newNode = new ListNode(value, this.tail, null);
  if (this.tail) {
    this.tail.next = newNode;
  } else {
    this.head = newNode;
  }
  this.tail = newNode;
  this.size++;
};

// Remove a node from the head of the list
DoublyLinkedList.prototype.removeHead = function() {
  if (!this.head) return null;
  const removedValue = this.head.value;
  this.head = this.head.next;
  if (this.head) {
    this.head.prev = null;
  } else {
    this.tail = null;
  }
  this.size--;
  return removedValue;
};

// Remove a node from the tail of the list
DoublyLinkedList.prototype.removeTail = function() {
  if (!this.tail) return null;
  const removedValue = this.tail.value;
  this.tail = this.tail.prev;
  if (this.tail) {
    this.tail.next = null;
  } else {
    this.head = null;
  }
  this.size--;
  return removedValue;
};

// Remove a node at a specific index
DoublyLinkedList.prototype.removeAt = function(index) {
  if (index < 0 || index >= this.size) return null;
  let current;
  if (index < this.size / 2) {
    current = this.head;
    for (let i = 0; i < index; i++) {
      current = current.next;
    }
  } else {
    current = this.tail;
    for (let i = this.size - 1; i > index; i--) {
      current = current.prev;
    }
  }
  if (current.prev) current.prev.next = current.next;
  if (current.next) current.next.prev = current.prev;
  if (index === 0) this.head = current.next;
  if (index === this.size - 1) this.tail = current.prev;
  this.size--;
  return current.value;
};

// Get the size of the list
DoublyLinkedList.prototype.getSize = function() {
  return this.size;
};

// Get the values in the list
DoublyLinkedList.prototype.getValues = function() {
  const values = [];
  let current = this.head;
  while (current) {
    values.push(current.value);
    current = current.next;
  }
  return values;
};