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

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.

Source: Microsoft Interview Experience

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 <bits/stdc++.h>
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)->
Modified Linked List:
(0,10)-> (10,10)-> (10,5)-> (40,5)-> 

Time Complexity of the above solution is O(n) where n is a number of nodes in the given linked list.

Auxiliary Space: O(1)
Exercise: 
The above code is recursive, write an iterative code for the same problem. Please see below for the solution.
Iterative approach for removing middle points in a linked list of line segments Please refer complete article on Given a linked list of line segments, remove middle points for more details!