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# C++ Program For Inserting Node In The Middle Of The Linked List

Given a linked list containing n nodes. The problem is to insert a new node with data x at the middle of the list. If n is even, then insert the new node after the (n/2)th node, else insert the new node after the (n+1)/2th node.

Examples:

```Input : list: 1->2->4->5
x = 3
Output : 1->2->3->4->5

Input : list: 5->10->4->32->16
x = 41
Output : 5->10->4->41->32->16```

Method 1(Using length of the linked list):
Find the number of nodes or length of the linked using one traversal. Let it be len. Calculate c = (len/2), if len is even, else c = (len+1)/2, if len is odd. Traverse again the first c nodes and insert the new node after the cth node.

## C++

 `// C++ implementation to insert node at the middle``// of the linked list``#include ` `using` `namespace` `std;` `// structure of a node``struct` `Node {``    ``int` `data;``    ``Node* next;``};` `// function to create and return a node``Node* getNode(``int` `data)``{``    ``// allocating space``    ``Node* newNode = (Node*)``malloc``(``sizeof``(Node));` `    ``// inserting the required data``    ``newNode->data = data;``    ``newNode->next = NULL;``    ``return` `newNode;``}` `// function to insert node at the middle``// of the linked list``void` `insertAtMid(Node** head_ref, ``int` `x)``{``    ``// if list is empty``    ``if` `(*head_ref == NULL)``        ``*head_ref = getNode(x);``    ``else` `{` `        ``// get a new node``        ``Node* newNode = getNode(x);` `        ``Node* ptr = *head_ref;``        ``int` `len = 0;` `        ``// calculate length of the linked list``        ``//, i.e, the number of nodes``        ``while` `(ptr != NULL) {``            ``len++;``            ``ptr = ptr->next;``        ``}` `        ``// 'count' the number of nodes after which``        ``//  the new node is to be inserted``        ``int` `count = ((len % 2) == 0) ? (len / 2) :``                                    ``(len + 1) / 2;``        ``ptr = *head_ref;` `        ``// 'ptr' points to the node after which``        ``// the new node is to be inserted``        ``while` `(count-- > 1)``            ``ptr = ptr->next;` `        ``// insert the 'newNode' and adjust the``        ``// required links``        ``newNode->next = ptr->next;``        ``ptr->next = newNode;``    ``}``}` `// function to display the linked list``void` `display(Node* head)``{``    ``while` `(head != NULL) {``        ``cout << head->data << ``" "``;``        ``head = head->next;``    ``}``}` `// Driver program to test above``int` `main()``{``    ``// Creating the list 1->2->4->5``    ``Node* head = NULL;``    ``head = getNode(1);``    ``head->next = getNode(2);``    ``head->next->next = getNode(4);``    ``head->next->next->next = getNode(5);` `    ``cout << ``"Linked list before insertion: "``;``    ``display(head);` `    ``int` `x = 3;``    ``insertAtMid(&head, x);` `    ``cout << "``Linked list after insertion: ";``    ``display(head);` `    ``return` `0;``}`

Output:

```Linked list before insertion: 1 2 4 5
Linked list after insertion: 1 2 3 4 5```

Time Complexity: O(n)

Space complexity: O(1) since using constant space

Method 2(Using two pointers):
Based on the tortoise and hare algorithm which uses two pointers, one known as slow and the other known as fast. This algorithm helps in finding the middle node of the linked list. It is explained in the front and black split procedure of this post. Now, you can insert the new node after the middle node obtained from the above process. This approach requires only a single traversal of the list.

## C++

 `// C++ implementation to insert node at the middle``// of the linked list``#include ` `using` `namespace` `std;` `// structure of a node``struct` `Node {``    ``int` `data;``    ``Node* next;``};` `// function to create and return a node``Node* getNode(``int` `data)``{``    ``// allocating space``    ``Node* newNode = (Node*)``malloc``(``sizeof``(Node));` `    ``// inserting the required data``    ``newNode->data = data;``    ``newNode->next = NULL;``    ``return` `newNode;``}` `// function to insert node at the middle``// of the linked list``void` `insertAtMid(Node** head_ref, ``int` `x)``{``    ``// if list is empty``    ``if` `(*head_ref == NULL)``        ``*head_ref = getNode(x);` `    ``else` `{``        ``// get a new node``        ``Node* newNode = getNode(x);` `        ``// assign values to the slow and fast``        ``// pointers``        ``Node* slow = *head_ref;``        ``Node* fast = (*head_ref)->next;` `        ``while` `(fast && fast->next) {` `            ``// move slow pointer to next node``            ``slow = slow->next;` `            ``// move fast pointer two nodes at a time``            ``fast = fast->next->next;``        ``}` `        ``// insert the 'newNode' and adjust the``        ``// required links``        ``newNode->next = slow->next;``        ``slow->next = newNode;``    ``}``}` `// function to display the linked list``void` `display(Node* head)``{``    ``while` `(head != NULL) {``        ``cout << head->data << ``" "``;``        ``head = head->next;``    ``}``}` `// Driver program to test above``int` `main()``{``    ``// Creating the list 1->2->4->5``    ``Node* head = NULL;``    ``head = getNode(1);``    ``head->next = getNode(2);``    ``head->next->next = getNode(4);``    ``head->next->next->next = getNode(5);` `    ``cout << ``"Linked list before insertion: "``;``    ``display(head);` `    ``int` `x = 3;``    ``insertAtMid(&head, x);` `    ``cout << "``Linked list after insertion: ";``    ``display(head);` `    ``return` `0;``}`

Output:

```Linked list before insertion: 1 2 4 5
Linked list after insertion: 1 2 3 4 5```

Time Complexity: O(n)

Space complexity: O(n) where n is size of linked list

Please refer complete article on Insert node into the middle of the linked list for more details!