# C++ Program For Removing Middle Points From a Linked List Of Line Segments

• Last Updated : 27 Dec, 2021

Given a linked list of coordinates where adjacent points either form a vertical line or a horizontal line. Delete points from the linked list which are in the middle of a horizontal or vertical line.
Examples:

```Input:   (0,10)->(1,10)->(5,10)->(7,10)
|
(7,5)->(20,5)->(40,5)
Output: Linked List should be changed to following
(0,10)->(7,10)
|
(7,5)->(40,5)
The given linked list represents a horizontal line from (0,10)
to (7, 10) followed by a vertical line from (7, 10) to (7, 5),
followed by a horizontal line from (7, 5) to (40, 5).

Input: (2,3)->(4,3)->(6,3)->(10,3)->(12,3)
Output: Linked List should be changed to following
(2,3)->(12,3)
There is only one vertical line, so all middle points are removed.```

The idea is to keep track of the current node, next node, and next-next node. While the next node is the same as the next-next node, keep deleting the next node. In this complete procedure, we need to keep an eye on the shifting of pointers and checking for NULL values.
Following are implementations of the above idea.

## C++

 `// C++ program to remove intermediate points``// in a linked list that represents horizontal``// and vertical line segments ``#include ``using` `namespace` `std; `` ` `// Node has 3 fields including x, y ``// coordinates and a pointer ``// to next node ``class` `Node ``{ ``    ``public``:``    ``int` `x, y; ``    ``Node *next; ``}; `` ` `/* Function to insert a node ``   ``at the beginning */``void` `push(Node ** head_ref, ``          ``int` `x,``int` `y) ``{ ``    ``Node* new_node =``new` `Node();``    ``new_node->x = x; ``    ``new_node->y = y; ``    ``new_node->next = (*head_ref); ``    ``(*head_ref) = new_node; ``} `` ` `/* Utility function to print ``   ``a singly linked list */``void` `printList(Node *head) ``{ ``    ``Node *temp = head; ``    ``while` `(temp != NULL) ``    ``{ ``        ``cout << ``"("` `<< temp->x << ``                ``","` `<< temp->y << ``")-> "``; ``        ``temp = temp->next; ``    ``} ``    ``cout << endl;``} `` ` `// Utility function to remove Next ``// from linked list and link nodes ``// after it to head ``void` `deleteNode(Node *head, ``                ``Node *Next) ``{ ``    ``head->next = Next->next; ``    ``Next->next = NULL; ``    ``free``(Next); ``} `` ` `// This function deletes middle nodes ``// in a sequence of horizontal and ``// vertical line segments represented ``// by linked list. ``Node* deleteMiddle(Node *head) ``{ ``    ``// If only one node or no node...``    ``// Return back ``    ``if` `(head == NULL || ``        ``head->next == NULL || ``        ``head->next->next == NULL) ``        ``return` `head; `` ` `    ``Node* Next = head->next; ``    ``Node *NextNext = Next->next ; `` ` `    ``// Check if this is a vertical line ``    ``// or horizontal line ``    ``if` `(head->x == Next->x) ``    ``{ ``        ``// Find middle nodes with same x ``        ``// value, and delete them ``        ``while` `(NextNext != NULL && ``               ``Next->x == NextNext->x) ``        ``{ ``            ``deleteNode(head, Next); `` ` `            ``// Update Next and NextNext ``            ``// for next iteration ``            ``Next = NextNext; ``            ``NextNext = NextNext->next; ``        ``} ``    ``} `` ` `    ``// If horizontal line ``    ``else` `if` `(head->y == Next->y) ``    ``{ ``        ``// Find middle nodes with same y ``        ``// value, and delete them ``        ``while` `(NextNext != NULL && ``               ``Next->y == NextNext->y) ``        ``{ ``            ``deleteNode(head, Next); `` ` `            ``// Update Next and NextNext for ``            ``// next iteration ``            ``Next = NextNext; ``            ``NextNext = NextNext->next; ``        ``} ``    ``} `` ` `    ``// Adjacent points must have either ``    ``// same x or same y ``    ``else` `    ``{ ``        ``puts``(``"Given linked list is not valid"``); ``        ``return` `NULL; ``    ``} `` ` `    ``// Recur for next segment ``    ``deleteMiddle(head->next); `` ` `    ``return` `head; ``} `` ` `// Driver code``int` `main() ``{ ``    ``Node *head = NULL; `` ` `    ``push(&head, 40,5); ``    ``push(&head, 20,5); ``    ``push(&head, 10,5); ``    ``push(&head, 10,8); ``    ``push(&head, 10,10); ``    ``push(&head, 3,10); ``    ``push(&head, 1,10); ``    ``push(&head, 0,10); ``    ``cout << ``"Given Linked List: "``; ``    ``printList(head); `` ` `    ``if` `(deleteMiddle(head) != NULL); ``    ``{ ``        ``cout << ``"Modified Linked List: "``; ``        ``printList(head); ``    ``} ``    ``return` `0; ``} ``// This is code is contributed by rathbhupendra`

Output:

```Given Linked List:
(0,10)-> (1,10)-> (3,10)-> (10,10)-> (10,8)-> (10,5)-> (20,5)-> (40,5)->