# Remove duplicates from an unsorted doubly linked list

Given an unsorted doubly linked list containing n nodes. The problem is to remove duplicate nodes from the given list.

Examples: ## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Method 1 (Naive Approach):
This is the simplest way where two loops are used. Outer loop is used to pick the elements one by one and inner loop compares the picked element with rest of the elements.

 `// C++ implementation to remove duplicates from an ` `// unsorted doubly linked list ` `#include ` ` `  `using` `namespace` `std; ` ` `  `// a node of the doubly linked list ` `struct` `Node { ` `    ``int` `data; ` `    ``struct` `Node* next; ` `    ``struct` `Node* prev; ` `}; ` ` `  `// Function to delete a node in a Doubly Linked List. ` `// head_ref --> pointer to head node pointer. ` `// del  -->  pointer to node to be deleted. ` `void` `deleteNode(``struct` `Node** head_ref, ``struct` `Node* del) ` `{ ` `    ``// base case ` `    ``if` `(*head_ref == NULL || del == NULL) ` `        ``return``; ` ` `  `    ``// If node to be deleted is head node ` `    ``if` `(*head_ref == del) ` `        ``*head_ref = del->next; ` ` `  `    ``// Change next only if node to be deleted ` `    ``// is NOT the last node ` `    ``if` `(del->next != NULL) ` `        ``del->next->prev = del->prev; ` ` `  `    ``// Change prev only if node to be deleted ` `    ``// is NOT the first node ` `    ``if` `(del->prev != NULL) ` `        ``del->prev->next = del->next; ` ` `  `    ``// Finally, free the memory occupied by del ` `    ``free``(del); ` `} ` ` `  `// function to remove duplicates from ` `// an unsorted doubly linked list ` `void` `removeDuplicates(``struct` `Node** head_ref) ` `{ ` `    ``// if DLL is empty or if it contains only ` `    ``// a single node ` `    ``if` `((*head_ref) == NULL ||  ` `        ``(*head_ref)->next == NULL) ` `        ``return``; ` ` `  `    ``struct` `Node* ptr1, *ptr2; ` ` `  `    ``// pick elements one by one ` `    ``for` `(ptr1 = *head_ref; ptr1 != NULL; ptr1 = ptr1->next) { ` `        ``ptr2 = ptr1->next; ` ` `  `        ``// Compare the picked element with the ` `        ``// rest of the elements ` `        ``while` `(ptr2 != NULL) { ` ` `  `            ``// if duplicate, then delete it ` `            ``if` `(ptr1->data == ptr2->data) { ` ` `  `                ``// store pointer to the node next to 'ptr2' ` `                ``struct` `Node* next = ptr2->next; ` ` `  `                ``// delete node pointed to by 'ptr2' ` `                ``deleteNode(head_ref, ptr2); ` ` `  `                ``// update 'ptr2' ` `                ``ptr2 = next; ` `            ``} ` ` `  `            ``// else simply move to the next node ` `            ``else` `                ``ptr2 = ptr2->next; ` `        ``} ` `    ``} ` `} ` ` `  `// Function to insert a node at the beginning ` `// of the Doubly Linked List ` `void` `push(``struct` `Node** head_ref, ``int` `new_data) ` `{ ` `    ``// allocate node ` `    ``struct` `Node* new_node =  ` `        ``(``struct` `Node*)``malloc``(``sizeof``(``struct` `Node)); ` ` `  `    ``// put in the data ` `    ``new_node->data = new_data; ` ` `  `    ``// since we are adding at the begining, ` `    ``// prev is always NULL ` `    ``new_node->prev = NULL; ` ` `  `    ``// link the old list off the new node ` `    ``new_node->next = (*head_ref); ` ` `  `    ``// change prev of head node to new node ` `    ``if` `((*head_ref) != NULL) ` `        ``(*head_ref)->prev = new_node; ` ` `  `    ``// move the head to point to the new node ` `    ``(*head_ref) = new_node; ` `} ` ` `  `// Function to print nodes in a given doubly  ` `// linked list ` `void` `printList(``struct` `Node* head) ` `{ ` `    ``// if list is empty ` `    ``if` `(head == NULL) ` `        ``cout << ``"Doubly Linked list empty"``; ` ` `  `    ``while` `(head != NULL) { ` `        ``cout << head->data << ``" "``; ` `        ``head = head->next; ` `    ``} ` `} ` ` `  `// Driver program to test above ` `int` `main() ` `{ ` `    ``struct` `Node* head = NULL; ` ` `  `    ``// Create the doubly linked list: ` `    ``// 8<->4<->4<->6<->4<->8<->4<->10<->12<->12 ` `    ``push(&head, 12); ` `    ``push(&head, 12); ` `    ``push(&head, 10); ` `    ``push(&head, 4); ` `    ``push(&head, 8); ` `    ``push(&head, 4); ` `    ``push(&head, 6); ` `    ``push(&head, 4); ` `    ``push(&head, 4); ` `    ``push(&head, 8); ` ` `  `    ``cout << ``"Original Doubly linked list:n"``; ` `    ``printList(head); ` ` `  `    ``/* remove duplicate nodes */` `    ``removeDuplicates(&head); ` ` `  `    ``cout << ````" Doubly linked list after "``` `            ``"removing duplicates:n"``; ` `    ``printList(head); ` ` `  `    ``return` `0; ` `} `

Output:

```Original Doubly linked list:
8 4 4 6 4 8 4 10 12 12
Doubly linked list after removing duplicates:
8 4 6 10 12
```

Time Complexity: O(n2)
Auxiliary Space: O(1)

Method 2 (Sorting): Following are the steps:

1. Sort the elements of the doubly linked list using Merge Sort. Refer this post.
2. Remove duplicates in linear time using the algorithm to remove duplicates from a sorted doubly linked list.

Time Complexity: O(nLogn)
Auxiliary Space: O(1)

Note that this method doesn’t preserve the original order of elements.

Method 3 Efficient Approach(Hashing):
We traverse the doubly linked list from head to end. For every newly encountered element, we check whether it is in the hash table: if yes, we remove it; otherwise we put it in the hash table. Hash table is implemented using unordered_set in C++.

 `// C++ implementation to remove duplicates from an ` `// unsorted doubly linked list ` `#include ` ` `  `using` `namespace` `std; ` ` `  `// a node of the doubly linked list ` `struct` `Node { ` `    ``int` `data; ` `    ``struct` `Node* next; ` `    ``struct` `Node* prev; ` `}; ` ` `  `// Function to delete a node in a Doubly Linked List. ` `// head_ref --> pointer to head node pointer. ` `// del  -->  pointer to node to be deleted. ` `void` `deleteNode(``struct` `Node** head_ref, ``struct` `Node* del) ` `{ ` `    ``// base case ` `    ``if` `(*head_ref == NULL || del == NULL) ` `        ``return``; ` ` `  `    ``// If node to be deleted is head node ` `    ``if` `(*head_ref == del) ` `        ``*head_ref = del->next; ` ` `  `    ``// Change next only if node to be deleted  ` `    ``// is NOT the last node ` `    ``if` `(del->next != NULL) ` `        ``del->next->prev = del->prev; ` ` `  `    ``// Change prev only if node to be deleted  ` `    ``// is NOT the first node ` `    ``if` `(del->prev != NULL) ` `        ``del->prev->next = del->next; ` ` `  `    ``// Finally, free the memory occupied by del ` `    ``free``(del); ` `} ` ` `  `// function to remove duplicates from ` `// an unsorted doubly linked list ` `void` `removeDuplicates(``struct` `Node** head_ref) ` `{ ` `    ``// if doubly linked list is empty ` `    ``if` `((*head_ref) == NULL) ` `        ``return``; ` ` `  `    ``// unordered_set 'us' implemented as hash table ` `    ``unordered_set<``int``> us; ` ` `  `    ``struct` `Node* current = *head_ref, *next; ` ` `  `    ``// traverse up to the end of the list ` `    ``while` `(current != NULL) { ` ` `  `        ``// if current data is seen before ` `        ``if` `(us.find(current->data) != us.end()) { ` ` `  `            ``// store pointer to the node next to  ` `            ``// 'current' node ` `            ``next = current->next; ` ` `  `            ``// delete the node pointed to by 'current' ` `            ``deleteNode(head_ref, current); ` ` `  `            ``// update 'current' ` `            ``current = next; ` `        ``} ` ` `  `        ``else` `{ ` ` `  `            ``// insert the current data in 'us' ` `            ``us.insert(current->data); ` ` `  `            ``// move to the next node ` `            ``current = current->next; ` `        ``} ` `    ``} ` `} ` ` `  `// Function to insert a node at the beginning ` `// of the Doubly Linked List ` `void` `push(``struct` `Node** head_ref, ``int` `new_data) ` `{ ` `    ``// allocate node ` `    ``struct` `Node* new_node =  ` `         ``(``struct` `Node*)``malloc``(``sizeof``(``struct` `Node)); ` ` `  `    ``// put in the data ` `    ``new_node->data = new_data; ` ` `  `    ``// since we are adding at the beginning, ` `    ``// prev is always NULL ` `    ``new_node->prev = NULL; ` ` `  `    ``// link the old list off the new node ` `    ``new_node->next = (*head_ref); ` ` `  `    ``// change prev of head node to new node ` `    ``if` `((*head_ref) != NULL) ` `        ``(*head_ref)->prev = new_node; ` ` `  `    ``// move the head to point to the new node ` `    ``(*head_ref) = new_node; ` `} ` ` `  `// Function to print nodes in a given doubly  ` `// linked list ` `void` `printList(``struct` `Node* head) ` `{ ` `    ``// if list is empty ` `    ``if` `(head == NULL) ` `        ``cout << ``"Doubly Linked list empty"``; ` ` `  `    ``while` `(head != NULL) { ` `        ``cout << head->data << ``" "``; ` `        ``head = head->next; ` `    ``} ` `} ` ` `  `// Driver program to test above ` `int` `main() ` `{ ` `    ``struct` `Node* head = NULL; ` ` `  `    ``// Create the doubly linked list: ` `    ``// 8<->4<->4<->6<->4<->8<->4<->10<->12<->12 ` `    ``push(&head, 12); ` `    ``push(&head, 12); ` `    ``push(&head, 10); ` `    ``push(&head, 4); ` `    ``push(&head, 8); ` `    ``push(&head, 4); ` `    ``push(&head, 6); ` `    ``push(&head, 4); ` `    ``push(&head, 4); ` `    ``push(&head, 8); ` ` `  `    ``cout << ``"Original Doubly linked list:n"``; ` `    ``printList(head); ` ` `  `    ``/* remove duplicate nodes */` `    ``removeDuplicates(&head); ` ` `  `    ``cout << ````" Doubly linked list after "``` `             ``"removing duplicates:n"``; ` `    ``printList(head); ` ` `  `    ``return` `0; ` `} `

Output:

```Original Doubly linked list:
8 4 4 6 4 8 4 10 12 12
Doubly linked list after removing duplicates:
8 4 6 10 12
```

Time Complexity: O(n)
Auxiliary Space: O(n)