# Union and Intersection of two Linked Lists

Given two Linked Lists, create union and intersection lists that contain union and intersection of the elements present in the given lists. Order of elments in output lists doesn’t matter.

Example:

```Input:
List1: 10->15->4->20
lsit2:  8->4->2->10
Output:
Intersection List: 4->10
Union List: 2->8->20->4->15->10
```

## Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

Method 1 (Simple)
Following are simple algorithms to get union and intersection lists respectively.

Intersection (list1, list2)
Initialize result list as NULL. Traverse list1 and look for its each element in list2, if the element is present in list2, then add the element to result.

Union (list1, list2):
Initialize result list as NULL. Traverse list1 and add all of its elements to the result.
Traverse list2. If an element of list2 is already present in result then do not insert it to result, otherwise insert.

This method assumes that there are no duplicates in the given lists.

Thanks to Shekhu for suggesting this method. Following are C and Java implementations of this method.

## C/C++

 `// C/C++ program to find union and intersection of two unsorted  ` `// linked lists ` `#include ` `#include ` `#include ` `/* Link list node */` `struct` `Node ` `{ ` `    ``int` `data; ` `    ``struct` `Node* next; ` `}; ` ` `  `/* A utility function to insert a node at the beginning of  ` `   ``a linked list*/` `void` `push(``struct` `Node** head_ref, ``int` `new_data); ` ` `  `/* A utility function to check if given data is present in a list */` `bool` `isPresent(``struct` `Node *head, ``int` `data); ` ` `  `/* Function to get union of two linked lists head1 and head2 */` `struct` `Node *getUnion(``struct` `Node *head1, ``struct` `Node *head2) ` `{ ` `    ``struct` `Node *result = NULL; ` `    ``struct` `Node *t1 = head1, *t2 = head2; ` ` `  `    ``// Insert all elements of list1 to the result list ` `    ``while` `(t1 != NULL) ` `    ``{ ` `        ``push(&result, t1->data); ` `        ``t1 = t1->next; ` `    ``} ` ` `  `    ``// Insert those elements of list2 which are not ` `    ``// present in result list ` `    ``while` `(t2 != NULL) ` `    ``{ ` `        ``if` `(!isPresent(result, t2->data)) ` `            ``push(&result, t2->data); ` `        ``t2 = t2->next; ` `    ``} ` ` `  `    ``return` `result; ` `} ` ` `  `/* Function to get intersection of two linked lists ` `  ``head1 and head2 */` `struct` `Node *getIntersection(``struct` `Node *head1,  ` `                              ``struct` `Node *head2) ` `{ ` `    ``struct` `Node *result = NULL; ` `    ``struct` `Node *t1 = head1; ` ` `  `    ``// Traverse list1 and search each element of it in ` `    ``// list2. If the element is present in list 2, then ` `    ``// insert the element to result ` `    ``while` `(t1 != NULL) ` `    ``{ ` `        ``if` `(isPresent(head2, t1->data)) ` `            ``push (&result, t1->data); ` `        ``t1 = t1->next; ` `    ``} ` ` `  `    ``return` `result; ` `} ` ` `  `/* A utility function to insert a node at the begining of a 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; ` ` `  `    ``/* link the old list off the new node */` `    ``new_node->next = (*head_ref); ` ` `  `    ``/* move the head to point to the new node */` `    ``(*head_ref) = new_node; ` `} ` ` `  `/* A utility function to print a linked list*/` `void` `printList (``struct` `Node *node) ` `{ ` `    ``while` `(node != NULL) ` `    ``{ ` `        ``printf` `(``"%d "``, node->data); ` `        ``node = node->next; ` `    ``} ` `} ` ` `  `/* A utility function that returns true if data is  ` `   ``present in linked list else return false */` `bool` `isPresent (``struct` `Node *head, ``int` `data) ` `{ ` `    ``struct` `Node *t = head; ` `    ``while` `(t != NULL) ` `    ``{ ` `        ``if` `(t->data == data) ` `            ``return` `1; ` `        ``t = t->next; ` `    ``} ` `    ``return` `0; ` `} ` ` `  `/* Drier program to test above function*/` `int` `main() ` `{ ` `    ``/* Start with the empty list */` `    ``struct` `Node* head1 = NULL; ` `    ``struct` `Node* head2 = NULL; ` `    ``struct` `Node* intersecn = NULL; ` `    ``struct` `Node* unin = NULL; ` ` `  `    ``/*create a linked lits 10->15->5->20 */` `    ``push (&head1, 20); ` `    ``push (&head1, 4); ` `    ``push (&head1, 15); ` `    ``push (&head1, 10); ` ` `  `    ``/*create a linked lits 8->4->2->10 */` `    ``push (&head2, 10); ` `    ``push (&head2, 2); ` `    ``push (&head2, 4); ` `    ``push (&head2, 8); ` ` `  `    ``intersecn = getIntersection (head1, head2); ` `    ``unin = getUnion (head1, head2); ` ` `  `    ``printf` `(``"\n First list is \n"``); ` `    ``printList (head1); ` ` `  `    ``printf` `(``"\n Second list is \n"``); ` `    ``printList (head2); ` ` `  `    ``printf` `(``"\n Intersection list is \n"``); ` `    ``printList (intersecn); ` ` `  `    ``printf` `(``"\n Union list is \n"``); ` `    ``printList (unin); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program to find union and intersection of two unsorted  ` `// linked lists ` `class` `LinkedList ` `{ ` `    ``Node head;  ``// head of list ` ` `  `    ``/* Linked list Node*/` `    ``class` `Node ` `    ``{ ` `        ``int` `data; ` `        ``Node next; ` `        ``Node(``int` `d) ` `        ``{ ` `            ``data = d; ` `            ``next = ``null``; ` `        ``} ` `    ``} ` ` `  `    ``/* Function to get Union of 2 Linked Lists */` `    ``void` `getUnion(Node head1, Node head2) ` `    ``{ ` `        ``Node t1 = head1, t2 = head2; ` ` `  `        ``//insert all elements of list1 in the result ` `        ``while` `(t1 != ``null``) ` `        ``{ ` `            ``push(t1.data); ` `            ``t1 = t1.next; ` `        ``} ` ` `  `        ``// insert those elements of list2 that are not present ` `        ``while` `(t2 != ``null``) ` `        ``{ ` `            ``if` `(!isPresent(head, t2.data)) ` `                ``push(t2.data); ` `            ``t2 = t2.next; ` `        ``} ` `    ``} ` ` `  `    ``void` `getIntersection(Node head1, Node head2) ` `    ``{ ` `        ``Node result = ``null``; ` `        ``Node t1 = head1; ` ` `  `        ``// Traverse list1 and search each element of it in list2. ` `        ``// If the element is present in list 2, then insert the ` `        ``// element to result ` `        ``while` `(t1 != ``null``) ` `        ``{ ` `            ``if` `(isPresent(head2, t1.data)) ` `                ``push(t1.data); ` `            ``t1 = t1.next; ` `        ``} ` `    ``} ` ` `  `    ``/* Utility function to print list */` `    ``void` `printList() ` `    ``{ ` `        ``Node temp = head; ` `        ``while``(temp != ``null``) ` `        ``{ ` `            ``System.out.print(temp.data+``" "``); ` `            ``temp = temp.next; ` `        ``} ` `        ``System.out.println(); ` `    ``} ` ` `  ` `  `    ``/*  Inserts a node at start of linked list */` `    ``void` `push(``int` `new_data) ` `    ``{ ` `        ``/* 1 & 2: Allocate the Node & ` `                  ``Put in the data*/` `        ``Node new_node = ``new` `Node(new_data); ` ` `  `        ``/* 3. Make next of new Node as head */` `        ``new_node.next = head; ` ` `  `        ``/* 4. Move the head to point to new Node */` `        ``head = new_node; ` `    ``} ` ` `  ` `  `    ``/* A utilty function that returns true if data is present ` `       ``in linked list  else return false */` `    ``boolean` `isPresent (Node head, ``int` `data) ` `    ``{ ` `        ``Node t = head; ` `        ``while` `(t != ``null``) ` `        ``{ ` `            ``if` `(t.data == data) ` `                ``return` `true``; ` `            ``t = t.next; ` `        ``} ` `        ``return` `false``; ` `    ``} ` ` `  ` `  `    ``/* Drier program to test above functions */` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``LinkedList llist1 = ``new` `LinkedList(); ` `        ``LinkedList llist2 = ``new` `LinkedList(); ` `        ``LinkedList unin = ``new` `LinkedList(); ` `        ``LinkedList intersecn = ``new` `LinkedList(); ` ` `  `        ``/*create a linked lits 10->15->5->20 */` `        ``llist1.push(``20``); ` `        ``llist1.push(``4``); ` `        ``llist1.push(``15``); ` `        ``llist1.push(``10``); ` ` `  `        ``/*create a linked lits 8->4->2->10 */` `        ``llist2.push(``10``); ` `        ``llist2.push(``2``); ` `        ``llist2.push(``4``); ` `        ``llist2.push(``8``); ` ` `  `        ``intersecn.getIntersection(llist1.head, llist2.head); ` `        ``unin.getUnion(llist1.head, llist2.head); ` ` `  `        ``System.out.println(``"First List is"``); ` `        ``llist1.printList(); ` ` `  `        ``System.out.println(``"Second List is"``); ` `        ``llist2.printList(); ` ` `  `        ``System.out.println(``"Intersection List is"``); ` `        ``intersecn.printList(); ` ` `  `        ``System.out.println(``"Union List is"``); ` `        ``unin.printList(); ` `    ``} ` `} ``/* This code is contributed by Rajat Mishra */`

Output:

``` First list is
10 15 4 20
Second list is
8 4 2 10
Intersection list is
4 10
Union list is
2 8 20 4 15 10
```

Time Complexity: O(mn) for both union and intersection operations. Here m is the number of elements in first list and n is the number of elements in second list.

Method 2 (Use Merge Sort)
In this method, algorithms for Union and Intersection are very similar. First we sort the given lists, then we traverse the sorted lists to get union and intersection.
Following are the steps to be followed to get union and intersection lists.

1) Sort the first Linked List using merge sort. This step takes O(mLogm) time. Refer this post for details of this step.
2) Sort the second Linked List using merge sort. This step takes O(nLogn) time. Refer this post for details of this step.
3) Linearly scan both sorted lists to get the union and intersection. This step takes O(m + n) time. This step can be implemented using the same algorithm as sorted arrays algorithm discussed here.

Time complexity of this method is O(mLogm + nLogn) which is better than method 1’s time complexity.

Method 3 (Use Hashing)
Union (list1, list2)
Initialize the result list as NULL and create an empty hash table. Traverse both lists one by one, for each element being visited, look the element in hash table. If the element is not present, then insert the element to result list. If the element is present, then ignore it.

Intersection (list1, list2)
Initialize the result list as NULL and create an empty hash table. Traverse list1. For each element being visited in list1, insert the element in hash table. Traverse list2, for each element being visited in list2, look the element in hash table. If the element is present, then insert the element to result list. If the element is not present, then ignore it.

Both of the above methods assume that there are no duplicates.

 `// Java code for Union and Intersection of two ` `// Linked Lists ` `import` `java.util.HashMap; ` `import` `java.util.HashSet; ` ` `  `class` `LinkedList { ` `    ``Node head; ``// head of list ` `     `  `    ``/* Linked list Node*/` `    ``class` `Node ` `    ``{ ` `        ``int` `data; ` `        ``Node next; ` `        ``Node(``int` `d) ` `        ``{ ` `            ``data = d; ` `            ``next = ``null``; ` `        ``} ` `    ``} ` `         `  `    ``/* Utility function to print list */` `    ``void` `printList() ` `    ``{ ` `        ``Node temp = head; ` `        ``while``(temp != ``null``) ` `        ``{ ` `            ``System.out.print(temp.data+``" "``); ` `            ``temp = temp.next; ` `        ``} ` `        ``System.out.println(); ` `    ``} ` `     `  `    ``/* Inserts a node at start of linked list */` `    ``void` `push(``int` `new_data) ` `    ``{ ` `        ``/* 1 & 2: Allocate the Node & ` `        ``Put in the data*/` `        ``Node new_node = ``new` `Node(new_data); ` `     `  `        ``/* 3. Make next of new Node as head */` `        ``new_node.next = head; ` `     `  `        ``/* 4. Move the head to point to new Node */` `        ``head = new_node; ` `    ``} ` `     `  `    ``public` `void` `append(``int` `new_data) ` `    ``{ ` `        ``if``(``this``.head == ``null``) ` `        ``{ ` `            ``Node n = ``new` `Node(new_data); ` `            ``this``.head = n; ` `            ``return``; ` `        ``} ` `        ``Node n1 = ``this``.head; ` `        ``Node n2 = ``new` `Node(new_data); ` `        ``while``(n1.next != ``null``) ` `        ``{ ` `            ``n1 = n1.next; ` `        ``} ` `             `  `        ``n1.next = n2; ` `        ``n2.next = ``null``; ` `    ``} ` `         `  `    ``/* A utilty function that returns true if data is ` `    ``present in linked list else return false */` `    ``boolean` `isPresent (Node head, ``int` `data) ` `    ``{ ` `        ``Node t = head; ` `        ``while` `(t != ``null``) ` `        ``{ ` `            ``if` `(t.data == data) ` `                ``return` `true``; ` `            ``t = t.next; ` `        ``} ` `        ``return` `false``; ` `    ``} ` `     `  `LinkedList getIntersection(Node head1, Node head2) ` `{ ` `    ``HashSet hset = ``new` `HashSet<>(); ` `    ``Node n1 = head1; ` `    ``Node n2 = head2; ` `    ``LinkedList result = ``new` `LinkedList(); ` `     `  `    ``// loop stores all the elements of list1 in hset ` `    ``while``(n1 != ``null``) ` `    ``{ ` `        ``if``(hset.contains(n1.data)) ` `        ``{ ` `            ``hset.add(n1.data); ` `        ``} ` `        ``else` `        ``{ ` `            ``hset.add(n1.data); ` `        ``} ` `        ``n1 = n1.next; ` `    ``} ` `     `  `    ``//For every element of list2 present in hset ` `    ``//loop inserts the element into the result ` `    ``while``(n2 != ``null``) ` `    ``{ ` `        ``if``(hset.contains(n2.data)) ` `        ``{ ` `            ``result.push(n2.data); ` `        ``} ` `        ``n2 = n2.next; ` `    ``} ` `    ``return` `result; ` `} ` ` `  `LinkedList getUnion(Node head1, Node head2) ` `{ ` `    ``// HashMap that will store the  ` `    ``// elements of the lists with their counts ` `    ``HashMap hmap = ``new` `HashMap<>(); ` `    ``Node n1 = head1; ` `    ``Node n2 = head2; ` `    ``LinkedList result = ``new` `LinkedList(); ` `     `  `    ``// loop inserts the elements and the count of  ` `    ``// that element of list1 into the hmap ` `    ``while``(n1 != ``null``) ` `    ``{ ` `        ``if``(hmap.containsKey(n1.data)) ` `        ``{ ` `            ``int` `val = hmap.get(n1.data); ` `            ``hmap.put(n1.data, val + ``1``); ` `        ``} ` `        ``else` `        ``{ ` `            ``hmap.put(n1.data, ``1``); ` `        ``} ` `        ``n1 = n1.next; ` `    ``} ` `     `  `    ``// loop further adds the elements of list2 with  ` `    ``// their counts into the hmap  ` `    ``while``(n2 != ``null``) ` `    ``{ ` `        ``if``(hmap.containsKey(n2.data)) ` `        ``{ ` `            ``int` `val = hmap.get(n2.data); ` `            ``hmap.put(n2.data, val + ``1``); ` `        ``} ` `        ``else` `        ``{ ` `            ``hmap.put(n2.data, ``1``); ` `        ``} ` `        ``n2 = n2.next;  ` `    ``} ` `     `  `    ``// Eventually add all the elements ` `    ``// into the result that are present in the hmap ` `    ``for``(``int` `a:hmap.keySet()) ` `    ``{ ` `        ``result.append(a); ` `    ``} ` `    ``return` `result; ` `} ` ` `  `    ``/* Driver program to test above functions */` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``LinkedList llist1 = ``new` `LinkedList(); ` `        ``LinkedList llist2 = ``new` `LinkedList(); ` `        ``LinkedList union = ``new` `LinkedList(); ` `        ``LinkedList intersection = ``new` `LinkedList(); ` ` `  `        ``/*create a linked list 10->15->4->20 */` `        ``llist1.push(``20``); ` `        ``llist1.push(``4``); ` `        ``llist1.push(``15``); ` `        ``llist1.push(``10``); ` ` `  `        ``/*create a linked list 8->4->2->10 */` `        ``llist2.push(``10``); ` `        ``llist2.push(``2``); ` `        ``llist2.push(``4``); ` `        ``llist2.push(``8``); ` ` `  `        ``intersection = intersection.getIntersection(llist1.head, ` `                                                  ``llist2.head); ` `        ``union=union.getUnion(llist1.head, llist2.head); ` ` `  `        ``System.out.println(``"First List is"``); ` `        ``llist1.printList(); ` ` `  `        ``System.out.println(``"Second List is"``); ` `        ``llist2.printList(); ` ` `  `        ``System.out.println(``"Intersection List is"``); ` `        ``intersection.printList(); ` ` `  `        ``System.out.println(``"Union List is"``); ` `        ``union.printList(); ` `    ``}      ` `} ` `// This code is contributed by Kamal Rawal `

Output:

```First List is
10 15 4 20
Second List is
8 4 2 10
Intersection List is
10 4
Union List is
2 4 20 8 10 15
```

Time complexity of this method depends on the hashing technique used and the distribution of elements in input lists. In practical, this approach may turn out to be better than above 2 methods.