# XOR Linked List – Find the middle node

• Difficulty Level : Medium
• Last Updated : 13 Oct, 2021

Given an XOR linked list, the task is to find the middle node of the given XOR linked list.

Examples:

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Input: 4 –> 7 –> 5
Output:
Explanation:
The middle node of the given XOR list is 7.

Input: 4 –> 7 –> 5 –> 1
Output: 7 5
Explanation:
The two middle nodes of the XOR linked list with even number of nodes are 7 and 5.

Approach: Follow the steps below to solve the problem:

• Traverse to (Length / 2)th node of the Linked List.
• If the number of nodes is found to be odd, then print (Length + 1) / 2 th node as the only middle node.
• If the number of nodes is found to be even, then print both Length / 2 th node and (Length / 2) + 1 th node as the middle nodes.

Below is the implementation of the above approach:

## C++

 `// C++ program to implement``// the above approach` `#include ``#include ``using` `namespace` `std;` `// Structure of a node``// in XOR linked list``struct` `Node {` `    ``// Stores data value``    ``// of a node``    ``int` `data;` `    ``// Stores XOR of previous``    ``// pointer and next pointer``    ``struct` `Node* nxp;``};` `// Function to find the XOR of two nodes``struct` `Node* XOR(``struct` `Node* a, ``struct` `Node* b)``{``    ``return` `(``struct` `Node*)((``uintptr_t``)(a) ^ (``uintptr_t``)(b));``}` `// Function to insert a node with``// given value at given position``struct` `Node* insert(``struct` `Node** head, ``int` `value)``{` `    ``// If XOR linked list is empty``    ``if` `(*head == NULL) {` `        ``// Initialize a new Node``        ``struct` `Node* node = ``new` `Node;` `        ``// Stores data value in``        ``// the node``        ``node->data = value;` `        ``// Stores XOR of previous``        ``// and next pointer``        ``node->nxp = XOR(NULL, NULL);` `        ``// Update pointer of head node``        ``*head = node;``    ``}` `    ``// If the XOR linked list``    ``// is not empty``    ``else` `{` `        ``// Stores the address``        ``// of current node``        ``struct` `Node* curr = *head;` `        ``// Stores the address``        ``// of previous node``        ``struct` `Node* prev = NULL;` `        ``// Initialize a new Node``        ``struct` `Node* node``            ``= ``new` `Node();` `        ``// Update curr node address``        ``curr->nxp = XOR(node, XOR(NULL, curr->nxp));` `        ``// Update new node address``        ``node->nxp = XOR(NULL, curr);` `        ``// Update head``        ``*head = node;` `        ``// Update data value of``        ``// current node``        ``node->data = value;``    ``}``    ``return` `*head;``}` `// Function to print the middle node``int` `printMiddle(``struct` `Node** head, ``int` `len)``{``    ``int` `count = 0;` `    ``// Stores XOR pointer``    ``// in current node``    ``struct` `Node* curr = *head;` `    ``// Stores XOR pointer of``    ``// in previous Node``    ``struct` `Node* prev = NULL;` `    ``// Stores XOR pointer of``    ``// in next node``    ``struct` `Node* next;` `    ``int` `middle = (``int``)len / 2;` `    ``// Traverse XOR linked list``    ``while` `(count != middle) {` `        ``// Forward traversal``        ``next = XOR(prev, curr->nxp);` `        ``// Update prev``        ``prev = curr;` `        ``// Update curr``        ``curr = next;` `        ``count++;``    ``}` `    ``// If the length of the``    ``// linked list is odd``    ``if` `(len & 1) {``        ``cout << curr->data << ``" "``;``    ``}` `    ``// If the length of the``    ``// linked list is even``    ``else` `{``        ``cout << prev->data << ``" "` `<< curr->data << ``" "``;``    ``}``}` `// Driver Code``int` `main()``{``    ``/* Create following XOR Linked List``    ``head --> 4 –> 7 –> 5 */``    ``struct` `Node* head = NULL;``    ``insert(&head, 4);``    ``insert(&head, 7);``    ``insert(&head, 5);` `    ``printMiddle(&head, 3);` `    ``return` `(0);``}`

## C

 `// C program to implement``// the above approach` `#include ``#include ``#include ` `// Structure of a node``// in XOR linked list``struct` `Node {` `    ``// Stores data value``    ``// of a node``    ``int` `data;` `    ``// Stores XOR of previous``    ``// pointer and next pointer``    ``struct` `Node* nxp;``};` `// Function to find the XOR of two nodes``struct` `Node* XOR(``struct` `Node* a,``                 ``struct` `Node* b)``{``    ``return` `(``struct` `Node*)((``uintptr_t``)(a)``                          ``^ (``uintptr_t``)(b));``}` `// Function to insert a node with``// given value at given position``struct` `Node* insert(``struct` `Node** head,``                    ``int` `value)``{` `    ``// If XOR linked list is empty``    ``if` `(*head == NULL) {` `        ``// Initialize a new Node``        ``struct` `Node* node``            ``= (``struct` `Node*)``malloc``(``                ``sizeof``(``struct` `Node));` `        ``// Stores data value in``        ``// the node``        ``node->data = value;` `        ``// Stores XOR of previous``        ``// and next pointer``        ``node->nxp = XOR(NULL, NULL);` `        ``// Update pointer of head node``        ``*head = node;``    ``}` `    ``// If the XOR linked list``    ``// is not empty``    ``else` `{` `        ``// Stores the address``        ``// of current node``        ``struct` `Node* curr = *head;` `        ``// Stores the address``        ``// of previous node``        ``struct` `Node* prev = NULL;` `        ``// Initialize a new Node``        ``struct` `Node* node``            ``= (``struct` `Node*)``malloc``(``                ``sizeof``(``struct` `Node));` `        ``// Update curr node address``        ``curr->nxp = XOR(``            ``node, XOR(NULL, curr->nxp));` `        ``// Update new node address``        ``node->nxp = XOR(NULL, curr);` `        ``// Update head``        ``*head = node;` `        ``// Update data value of``        ``// current node``        ``node->data = value;``    ``}``    ``return` `*head;``}` `// Function to print the middle node``int` `printMiddle(``struct` `Node** head, ``int` `len)``{``    ``int` `count = 0;` `    ``// Stores XOR pointer``    ``// in current node``    ``struct` `Node* curr = *head;` `    ``// Stores XOR pointer of``    ``// in previous Node``    ``struct` `Node* prev = NULL;` `    ``// Stores XOR pointer of``    ``// in next node``    ``struct` `Node* next;` `    ``int` `middle = (``int``)len / 2;` `    ``// Traverse XOR linked list``    ``while` `(count != middle) {` `        ``// Forward traversal``        ``next = XOR(prev, curr->nxp);` `        ``// Update prev``        ``prev = curr;` `        ``// Update curr``        ``curr = next;` `        ``count++;``    ``}` `    ``// If the length of the``    ``// linked list is odd``    ``if` `(len & 1) {``        ``printf``(``"%d"``, curr->data);``    ``}` `    ``// If the length of the``    ``// linked list is even``    ``else` `{``        ``printf``(``"%d %d"``, prev->data,``               ``curr->data);``    ``}``}` `// Driver Code``int` `main()``{``    ``/* Create following XOR Linked List``    ``head --> 4 –> 7 –> 5 */``    ``struct` `Node* head = NULL;``    ``insert(&head, 4);``    ``insert(&head, 7);``    ``insert(&head, 5);` `    ``printMiddle(&head, 3);` `    ``return` `(0);` `}`
Output:
`7`

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

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