Given a linked list of line segments, remove middle points

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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; 
        } 
    } 
    else if (head->y==Next->y) // If horizontal line 
    { 
        // 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; 
        } 
    } 
    else // Adjacent points must have either same x or same y 
    { 
        puts("Given linked list is not valid"); 
        return NULL; 
    } 
 
    // Recur for next segment 
    deleteMiddle(head->next); 
 
    return head; 
} 
 
// Driver program to test above functions 
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: \n"; 
    printList(head); 
 
    if (deleteMiddle(head) != NULL); 
    { 
        cout << "Modified Linked List: \n"; 
        printList(head); 
    } 
    return 0; 
} 
// This is code is contributed by rathbhupendra

C

// C program to remove intermediate points in a linked list 
// that represents horizontal and vertical line segments
#include <stdio.h>
#include <stdlib.h>
 
// Node has 3 fields including x, y coordinates and a pointer
// to next node
struct Node
{
    int x, y;
    struct Node *next;
};
 
/* Function to insert a node at the beginning */
void push(struct Node ** head_ref, int x,int y)
{
    struct Node* new_node = 
           (struct Node*) malloc(sizeof(struct 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(struct Node *head)
{
    struct Node *temp = head;
    while (temp != NULL)
    {
        printf("(%d,%d)-> ", temp->x,temp->y);
        temp = temp->next;
    }
    printf("\n");
 
}
 
// Utility function to remove Next from linked list 
// and link nodes after it to head
void deleteNode(struct Node *head, struct 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.
struct Node* deleteMiddle(struct Node *head)
{
    // If only one node or no node...Return back
    if (head==NULL || head->next ==NULL || head->next->next==NULL)
        return head;
 
    struct Node* Next = head->next;
    struct 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;
        }
    }
    else if (head->y==Next->y) // If horizontal line
    {
        // 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;
        }
    }
    else  // Adjacent points must have either same x or same y
    {
        puts("Given linked list is not valid");
        return NULL;
    }
 
    // Recur for next segment
    deleteMiddle(head->next);
 
    return head;
}
 
// Driver program to test above functions
int main()
{
    struct 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);
    printf("Given Linked List: \n");
    printList(head);
 
    if (deleteMiddle(head) != NULL);
    {
        printf("Modified Linked List: \n");
        printList(head);
    }
    return 0;
}

Java

// Java program to remove middle points in a linked list of
// line segments,
class LinkedList
{
    Node head;  // head of list
 
    /* Linked list Node*/
    class Node
    {
        int x,y;
        Node next;
        Node(int x, int y)
        {
            this.x = x;
            this.y = y;
            next = null;
        }
    }
 
    // This function deletes middle nodes in a sequence of
    // horizontal and vertical line segments represented
    // by linked list.
    Node deleteMiddle()
    {
        // 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 vertical or horizontal line
        if (head.x == Next.x)
        {
            // Find middle nodes with same value as x and
            // delete them.
            while (NextNext != null && Next.x == NextNext.x)
            {
                head.next = Next.next;
                Next.next = null;
 
                // Update NextNext for the next iteration
                Next = NextNext;
                NextNext = NextNext.next;
            }
        }
 
        // if horizontal
        else if (head.y == Next.y)
        {
            // find middle nodes with same value as y and
            // delete them
            while (NextNext != null && Next.y == NextNext.y)
            {
                head.next = Next.next;
                Next.next = null;
 
                // Update NextNext for the next iteration
                Next = NextNext;
                NextNext = NextNext.next;
            }
        }
 
        // Adjacent points should have same x or same y
        else
        {
            System.out.println("Given list is not valid");
            return null;
        }
 
        // recur for other segment
 
        // temporarily store the head and move head forward.
        Node temp = head;
        head = head.next;
 
        // call deleteMiddle() for next segment
        this.deleteMiddle();
 
        // restore head
        head = temp;
 
        // return the head
        return head;
    }
 
    /*  Given a reference (pointer to pointer) to the head
        of a list and an int, push a new node on the front
        of the list. */
    void push(int x, int y)
    {
        /* 1 & 2: Allocate the Node &
                  Put in the data*/
        Node new_node = new Node(x,y);
 
        /* 3. Make next of new Node as head */
        new_node.next = head;
 
        /* 4. Move the head to point to new Node */
        head = new_node;
    }
 
 
    void printList()
    {
        Node temp = head;
        while (temp != null)
        {
            System.out.print("("+temp.x+","+temp.y+")->");
            temp = temp.next;
        }
        System.out.println();
    }
 
 
    /* Driver program to test above functions */
    public static void main(String args[])
    {
        LinkedList llist = new LinkedList();
 
        llist.push(40,5);
        llist.push(20,5);
        llist.push(10,5);
        llist.push(10,8);
        llist.push(10,10);
        llist.push(3,10);
        llist.push(1,10);
        llist.push(0,10);
 
        System.out.println("Given list");
        llist.printList();
 
        if (llist.deleteMiddle() != null)
        {
            System.out.println("Modified Linked List is");
            llist.printList();
        }
    }
} /* This code is contributed by Rajat Mishra */

Python3

# Python program to remove middle points in a linked list of
# line segments,
class LinkedList(object):
    def __init__(self):
        self.head = None
 
    # Linked list Node
    class Node(object):
        def __init__(self, x, y):
            self.x = x
            self.y = y
            self.next = None
 
    # This function deletes middle nodes in a sequence of
    # horizontal and vertical line segments represented
    # by linked list.
    def deleteMiddle(self):
        # If only one node or no node...Return back
        if self.head == None or self.head.next == None or self.head.next.next == None:
            return self.head
        Next = self.head.next
        NextNext = Next.next
        # check if this is vertical or horizontal line
        if self.head.x == Next.x:
            # Find middle nodes with same value as x and
            # delete them.
            while NextNext != None and Next.x == NextNext.x:
                self.head.next = Next.next
                Next.next = None
                # Update NextNext for the next iteration
                Next = NextNext
                NextNext = NextNext.next
        elif self.head.y == Next.y:
            # find middle nodes with same value as y and
            # delete them
            while NextNext != None and Next.y == NextNext.y:
                self.head.next = Next.next
                Next.next = None
                # Update NextNext for the next iteration
                Next = NextNext
                NextNext = NextNext.next
        else:
            # Adjacent points should have same x or same y
            print ("Given list is not valid")
            return None
        # recur for other segment
        # temporarily store the head and move head forward.
        temp = self.head
        self.head = self.head.next
        # call deleteMiddle() for next segment
        self.deleteMiddle()
        # restore head
        self.head = temp
        # return the head
        return self.head
 
    # Given a reference (pointer to pointer) to the head
    # of a list and an int, push a new node on the front
    # of the list.
    def push(self, x, y):
        # 1 & 2: Allocate the Node &
        # Put in the data
        new_node = self.Node(x, y)
        # 3. Make next of new Node as head
        new_node.next = self.head
        # 4. Move the head to point to new Node
        self.head = new_node
 
    def printList(self):
        temp = self.head
        while temp != None:
            print ("(" + str(temp.x) + "," + str(temp.y) + ")->",end=" ")
            temp = temp.next
        print ()
 
# Driver program
llist = LinkedList()
llist.push(40,5)
llist.push(20,5)
llist.push(10,5)
llist.push(10,8)
llist.push(10,10)
llist.push(3,10)
llist.push(1,10)
llist.push(0,10)
 
print ("Given list")
llist.printList()
 
if llist.deleteMiddle() != None:
    print ("Modified Linked List is")
    llist.printList()
 
# This code is contributed by BHAVYA JAIN

C#

// C# program to remove middle
// points in a linked list of
// line segments,
using System;
 
public class LinkedList
{
    Node head; // head of list
 
    /* Linked list Node*/
    class Node
    {
        public int x,y;
        public Node next;
        public Node(int x, int y)
        {
            this.x = x;
            this.y = y;
            next = null;
        }
    }
 
    // This function deletes middle 
    // nodes in a sequence of horizontal and 
    // vertical line segments represented
    // by linked list.
    Node deleteMiddle()
    {
        // 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 vertical or horizontal line
        if (head.x == Next.x)
        {
            // Find middle nodes with same
            //  value as x and delete them.
            while (NextNext != null && 
                    Next.x == NextNext.x)
            {
                head.next = Next.next;
                Next.next = null;
 
                // Update NextNext for
                // the next iteration
                Next = NextNext;
                NextNext = NextNext.next;
            }
        }
 
        // if horizontal
        else if (head.y == Next.y)
        {
            // find middle nodes with same 
            // value as y and delete them
            while (NextNext != null && Next.y == NextNext.y)
            {
                head.next = Next.next;
                Next.next = null;
 
                // Update NextNext for the next iteration
                Next = NextNext;
                NextNext = NextNext.next;
            }
        }
 
        // Adjacent points should have same x or same y
        else
        {
            Console.WriteLine("Given list is not valid");
            return null;
        }
 
        // recur for other segment
 
        // temporarily store the 
        // head and move head forward.
        Node temp = head;
        head = head.next;
 
        // call deleteMiddle() for next segment
        this.deleteMiddle();
 
        // restore head
        head = temp;
 
        // return the head
        return head;
    }
 
    /* Given a reference (pointer to pointer) to the head
        of a list and an int, push a new node on the front
        of the list. */
    void push(int x, int y)
    {
        /* 1 & 2: Allocate the Node &
                Put in the data*/
        Node new_node = new Node(x,y);
 
        /* 3. Make next of new Node as head */
        new_node.next = head;
 
        /* 4. Move the head to point to new Node */
        head = new_node;
    }
 
 
    void printList()
    {
        Node temp = head;
        while (temp != null)
        {
            Console.Write("("+temp.x + "," + temp.y + ")->");
            temp = temp.next;
        }
        Console.WriteLine();
    }
 
 
    /* Driver code */
    public static void Main(String []args)
    {
        LinkedList llist = new LinkedList();
 
        llist.push(40,5);
        llist.push(20,5);
        llist.push(10,5);
        llist.push(10,8);
        llist.push(10,10);
        llist.push(3,10);
        llist.push(1,10);
        llist.push(0,10);
 
        Console.WriteLine("Given list");
        llist.printList();
 
        if (llist.deleteMiddle() != null)
        {
            Console.WriteLine("Modified Linked List is");
            llist.printList();
        }
    }
}
 
// This code is contributed by Rajput-Ji

Javascript

<script>
 
// Javascript program to remove middle 
// points in a linked list of
// line segments,
var  head; // head of list
 
    /* Linked list Node */
    class Node {
 
constructor(x , y) {
            this.x = x;
            this.y = y;
            this.next = null;
        }
    }
 
    // This function deletes middle
    // nodes in a sequence of
    // horizontal and vertical line
    // segments represented
    // by linked list.
    function deleteMiddle() {
        // If only one node or no 
        // node...Return back
        if (head == null || head.next == null ||
        head.next.next == null)
            return head;
 
var Next = head.next;
var NextNext = Next.next;
 
        // check if this is vertical or
        // horizontal line
        if (head.x == Next.x) {
            // Find middle nodes with same
            // value as x and
            // delete them.
            while (NextNext != null && 
            Next.x == NextNext.x) 
            {
                head.next = Next.next;
                Next.next = null;
 
                // Update NextNext for the next iteration
                Next = NextNext;
                NextNext = NextNext.next;
            }
        }
 
        // if horizontal
        else if (head.y == Next.y) {
            // find middle nodes with same value as y and
            // delete them
            while (NextNext != null && 
            Next.y == NextNext.y) {
                head.next = Next.next;
                Next.next = null;
 
                // Update NextNext for the next iteration
                Next = NextNext;
                NextNext = NextNext.next;
            }
        }
 
        // Adjacent points should have same x or same y
        else {
            document.write("Given list is not valid");
            return null;
        }
 
        // recur for other segment
 
        // temporarily store the head and move head forward.
var temp = head;
        head = head.next;
 
        // call deleteMiddle() for next segment
        this.deleteMiddle();
 
        // restore head
        head = temp;
 
        // return the head
        return head;
    }
 
    /*
     Given a reference (pointer to pointer) to 
     the head of a list and an int, push
     a new node on the front of the list.
     */
    function push(x , y) {
        /*
         1 & 2: Allocate the Node & Put in the data
         */
var new_node = new Node(x, y);
 
        /* 3. Make next of new Node as head */
        new_node.next = head;
 
        /* 4. Move the head to point to new Node */
        head = new_node;
    }
 
    function printList() {
var temp = head;
        while (temp != null) {
            document.write("(" + temp.x + "," + 
            temp.y + ")->");
            temp = temp.next;
        }
        document.write("<br/>");
    }
 
    /* Driver program to test above functions */
     
 
        push(40, 5);
        push(20, 5);
        push(10, 5);
        push(10, 8);
        push(10, 10);
        push(3, 10);
        push(1, 10);
        push(0, 10);
 
        document.write("Given list<br/>");
        printList();
 
        if (deleteMiddle() != null) {
            document.write("Modified Linked List is<br/>");
            printList();
        }
 
// This code contributed by gauravrajput1
 
</script>

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) because it is using constant space

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

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