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

Examples:

Input: List1: 10 -> 15 -> 4 -> 20 list2: 8 -> 4 -> 2 -> 10 Output: Intersection List: 4 -> 10 Union List: 2 -> 8 -> 20 -> 4 -> 15 -> 10

We have already discussed Method-1 and Method-2 of this question.

In this post, its Method-3 (Using Hashing) is discussed with a Time Complexity of O(m+n) i.e. better than both methods discussed earlier.

Implementation:1- Start traversing both the lists. a) Store the current element of both lists with its occurrence in the map. 2- For Union: Store all the elements of the map in the resultant list. 3- For Intersection: Store all the elements only with an occurrence of 2 as 2 denotes that they are present in both the lists.

Below is C++ implementation of above steps.

// C++ program to find union and intersection of // two unsorted linked lists in O(m+n) time. #include<bits/stdc++.h> using namespace std; /* Link list node */ struct Node { int data; struct Node* next; }; /* 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; } /* Utility function to store the elements of both list */ void storeEle(struct Node* head1, struct Node *head2, unordered_map<int, int> &eleOcc) { struct Node* ptr1 = head1; struct Node* ptr2 = head2; // Traverse both lists while (ptr1 != NULL || ptr2 != NULL) { // store element in the map if (ptr1!=NULL) { eleOcc[ptr1->data]++; ptr1=ptr1->next; } // store element in the map if (ptr2 != NULL) { eleOcc[ptr2->data]++; ptr2=ptr2->next; } } } /* Function to get union of two linked lists head1 and head2 */ struct Node *getUnion(unordered_map<int, int> eleOcc) { struct Node *result = NULL; // Push all the elements into the resultant list for (auto it=eleOcc.begin(); it!=eleOcc.end(); it++) push(&result, it->first); return result; } /* Function to get intersection of two linked lists head1 and head2 */ struct Node *getIntersection(unordered_map<int, int> eleOcc) { struct Node *result = NULL; // Push a node with an element having occurrence // of 2 as that means the current element is present // in both the lists for (auto it=eleOcc.begin(); it!=eleOcc.end(); it++) if (it->second == 2) push(&result, it->first); // return resultant list return result; } /* A utility function to print a linked list*/ void printList(struct Node *node) { while (node != NULL) { printf ("%d ", node->data); node = node->next; } } // Prints union and intersection of lists with head1 // and head2. void printUnionIntersection(Node *head1, Node *head2) { // Store all the elements of both lists in the map unordered_map<int, int> eleOcc; storeEle(head1, head2, eleOcc); Node *intersection_list = getIntersection(eleOcc); Node *union_list = getUnion(eleOcc); printf("\nIntersection list is \n"); printList(intersection_list); printf("\nUnion list is \n"); printList(union_list); } /* Drier program to test above function*/ int main() { /* Start with the empty list */ struct Node* head1 = NULL; struct Node* head2 = NULL; /* create a linked lits 11->10->15->4->20 */ push(&head1, 1); push(&head1, 2); push(&head1, 3); push(&head1, 4); push(&head1, 5); /* create a linked lits 8->4->2->10 */ push(&head2, 1); push(&head2, 3); push(&head2, 5); push(&head2, 6); printf("First list is \n"); printList(head1); printf("\nSecond list is \n"); printList(head2); printUnionIntersection(head1, head2); return 0; }

Output:

First list is 5 4 3 2 1 Second list is 6 5 3 1 Intersection list is 3 5 1 Union list is 3 4 6 5 2 1

We can also handle the case of duplicates by maintaining separate Hash for both the lists.

Time Complexity : O(m + n)

Auxiliary Space : O(m + n)

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