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Form a Rectangle from boundary elements of Matrix using Linked List

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  • Difficulty Level : Hard
  • Last Updated : 22 Aug, 2022
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Given a Matrix grid[][] of size NxM where N is number of rows and M is number of columns. The task is to form a rectangle from boundary elements of grid[][] using linked list having four pointers namely prev, next, top and bottom. Print the final linked list. 

Examples:

Input: A = [[13, 42, 93, 88], 
                  [26, 38, 66, 42], 
                 [75, 63, 78, 12]]
Output: 13 42 93 88 42 12 78 63 75 26

Explanation:  
 

1. Make A[0][0] and head node
2. Traverse through 0th row and create node for each element and connect them through next pointer.
3. Traverse through (m-1)th column and create node for each element and connect them through bottom pointer.
4. Traverse through (n-1)th row and create node for each element and connect them through prev pointer.
5. Traverse through 0th column and create node for each element and connect them through top pointer.
6. Step 2, 3, 4, 5 is repeated till temp. The top become equal to head.

Input: A = [[1, 2, 3]
                  [8, 9, 4]
                 [7, 6, 5]]
Output: 1 2 3 4 5 6 7 8

Approach: This problem can be solved by Performing boundary traversal of matrix and creating nodes for each element and link them using next, prev, bottom or top and create a linked list. 

Follow the steps below:

Step 1: Make grid[0][0] as the head of the Linked list and initialize temp as the head.
Step 2: Traverse through the first row from j=1 to j=m-1 where i=0 and create a node for each element and link them through the next pointer.
Step 3: Traverse through the last column from i=0 to i=n-1 where j=m-1 and create a node for each element and link them through a bottom pointer.
Step 4: Traverse through the last row from j=m-1 to j=0 where i=n-1 and create a node for each element and link them through the prev pointer.
Step 5: Traverse through the first column from i=n-1 to i=0 where j=0 and create a node for each element and link them through the top pointer.
Step 6: Step 2, 3, 4, 5 is repeated till temp.top becomes equal to head.
Step 7: Print the required Linked List.

Below is the implementation of the above algorithm. 

C++




// C++ program for above approach
#include <bits/stdc++.h>
using namespace std;
 
// Node Class
struct Node {
    int data;
    Node* next;
    Node* prev;
    Node* top;
    Node* bottom;
 
    // Constructor to initialize the node object
    Node(int data)
    {
        this->data = data;
        next = NULL;
        prev = NULL;
        top = NULL;
        bottom = NULL;
    }
};
 
// Linked List class
struct LinkedList {
 
    // initialize head
    Node* head = NULL;
 
    // function to form square
    // linked list of matrix.
    void Quad(vector<vector<int> > grid, int n, int m)
    {
 
        // initialising A[0][0] as head.
        head = new Node(grid[0][0]);
 
        // head is assigned to head.
        Node* temp = head;
 
        // i is row index, j is column index
        int i = 0;
        int j = 1;
 
        // loop till temp.top become equal to head.
        while (temp != NULL and temp->top != head) {
            // as we iterating over boundary
            // of matrix so we will iterate
            // over first(0) and last(n-1) row
            // and first(0) and last(m-1) column.
 
            // iterating over first i.e 0th row
            // and connecting node.
            if (j < m && i == 0) {
                temp->next = new Node(grid[i][j]);
                temp = temp->next;
                j += 1;
            }
 
            // iterating over last i.e (m-1)th
            // column and connecting Node.
            else if (j == m && i < n - 1) {
                i = i + 1;
                temp->bottom = new Node(grid[i][j - 1]);
                temp = temp->bottom;
            }
 
            // iterating over last i.e (n-1)th row
            // and connecting Node.
            else if (i == n - 1 && j <= m && j >= 1) {
                if (j == m)
                    j = j - 1;
                j = j - 1;
                temp->prev = new Node(grid[i][j]);
                temp = temp->prev;
            }
 
            // iterating over first i.e 0th column
            // and connecting Node.
            else if (i <= n - 1 && j == 0) {
                i = i - 1;
                temp->top = new Node(grid[i][j]);
                temp = temp->top;
                if (i == 1)
                    temp->top = head;
            }
        }
    }
 
    // function to print Linked list.
    void printList(Node* root)
    {
 
        Node* temp = root;
 
        // printing head of linked list
        cout << temp->data << " ";
 
        // loop till temp.top
        // become equal to head
        while (temp->top != root) {
 
            // printing the node
            if (temp->next) {
                cout << temp->next->data << " ";
                temp = temp->next;
            }
            if (temp->prev) {
                cout << temp->prev->data << " ";
                temp = temp->prev;
            }
            if (temp->bottom) {
                cout << temp->bottom->data << " ";
                temp = temp->bottom;
            }
            if (temp->top) {
                cout << temp->top->data << " ";
                temp = temp->top;
            }
        }
    }
};
 
// Driver Code
int main()
{
    vector<vector<int> > grid = { { 13, 42, 93, 88 },
                                  { 26, 38, 66, 42 },
                                  { 75, 63, 78, 12 } };
 
    // n is number of rows
    int n = grid.size();
     
    // m is number of columns
    int m = grid[0].size();
   
    // creation of object
    LinkedList* l = new LinkedList();
 
    // Call Quad method to create Linked List.
    l->Quad(grid, n, m);
 
    // Call Quad method to create Linked List.
    l->printList(l->head);
 
    return 0;
}
 
// The code is contributed by Gautam goel (gautamgoel962)


Java




// Java program for above approach
 
// Node Class
class Node {
    int data;
    Node next;
    Node prev;
    Node top;
    Node bottom;
    // Constructor to initialize the node object
    Node(int data)
    {
        this.data = data;
        next = null;
        prev = null;
        top = null;
        bottom = null;
    }
}
 
class GFG {
 
    // initialize head
    public Node head = null;
 
    // function to form square linked list of matrix.
    public void Quad(int[][] grid, int n, int m)
    {
 
        // initialising A[0][0] as head.
        head = new Node(grid[0][0]);
 
        // head is assigned to head.
        Node temp = head;
 
        // i is row index, j is column index
        int i = 0;
        int j = 1;
 
        // loop till temp.top become equal to head.
        while (temp.top != head) {
            // as we iterating over boundary
            // of matrix so we will iterate
            // over first(0) and last(n-1) row
            // and first(0) and last(m-1) column.
 
            // iterating over first i.e 0th row
            // and connecting node.
            if (j < m && i == 0) {
                temp.next = new Node(grid[i][j]);
                temp = temp.next;
                j += 1;
            }
 
            // iterating over last i.e (m-1)th
            // column and connecting Node.
            else if (j == m && i < n - 1) {
                i = i + 1;
                temp.bottom = new Node(grid[i][j - 1]);
                temp = temp.bottom;
            }
 
            // iterating over last i.e (n-1)th row
            // and connecting Node.
            else if (i == n - 1 && j <= m && j >= 1) {
                if (j == m) {
                    j = j - 1;
                }
                j = j - 1;
                temp.prev = new Node(grid[i][j]);
                temp = temp.prev;
            }
 
            // iterating over first i.e 0th column
            // and connecting Node.
            else if (i <= n - 1 && j == 0) {
                i = i - 1;
                temp.top = new Node(grid[i][j]);
                temp = temp.top;
                if (i == 1) {
                    temp.top = head;
                }
            }
        }
    }
 
    // function to print Linked list.
    public void printList(Node root)
    {
        Node temp = root;
 
        // printing head of linked list
        System.out.print(temp.data + " ");
 
        // loop till temp.top
        // become equal to head
        while (temp.top != root) {
 
            // printing the node
            if (temp.next != null) {
                System.out.print(temp.next.data + " ");
                temp = temp.next;
            }
            if (temp.prev != null) {
                System.out.print(temp.prev.data + " ");
                temp = temp.prev;
            }
            if (temp.bottom != null) {
                System.out.print(temp.bottom.data + " ");
                temp = temp.bottom;
            }
            if (temp.top != null) {
                System.out.print(temp.top.data + " ");
                temp = temp.top;
            }
        }
    }
 
    public static void main(String[] args)
    {
 
        int[][] grid = new int[][] { { 13, 42, 93, 88 },
                                     { 26, 38, 66, 42 },
                                     { 75, 63, 78, 12 } };
 
        // n is number of rows
        int n = grid.length;
 
        // m is number of columns
        int m = grid[0].length;
 
        GFG l = new GFG();
 
        // Call Quad method to create Linked List.
        l.Quad(grid, n, m);
 
        // Call Quad method to create Linked List.
        l.printList(l.head);
    }
}
 
// This code is contributed by lokesh (lokeshmvs21).


Python3




# Python program for above approach
# Node Class
class Node:
 
    # Constructor to initialize the node object
    def __init__(self, val):
        self.data = val
        self.next = None
        self.prev = None
        self.top = None
        self.bottom = None
 
 
# Linked List class
class LinkedList:
 
    # Constructor to initialize head
    def __init__(self):
        self.head = None
 
    # function to form square
    # linked list of matrix.
    def Quad(self, grid, n, m):
 
        # initialising A[0][0] as head.
        self.head = Node(grid[0][0])
 
        # head is assigned to head.
        temp = self.head
 
        # i is row index, j is column index
        i = 0
        j = 1
 
        # loop till temp.top become equal to head.
        while temp.top != self.head:
            # as we iterating over boundary
            # of matrix so we will iterate
            # over first(0) and last(n-1) row
            # and first(0) and last(m-1) column.
 
            # iterating over first i.e 0th row
            # and connecting node.
            if j < m and i == 0:
                temp.next = Node(grid[i][j])
                temp = temp.next
                j += 1
 
            # iterating over last i.e (m-1)th
            # column and connecting Node.
            elif j == m and i < n - 1:
                i = i + 1
                temp.bottom = Node(grid[i][j - 1])
                temp = temp.bottom
 
            # iterating over last i.e (n-1)th row
            # and connecting Node.
            elif i == n - 1 and j <= m and j >= 1:
                if j == m: j = j - 1
                j = j - 1
                temp.prev = Node(grid[i][j])
                temp = temp.prev
 
            # iterating over first i.e 0th column
            # and connecting Node.
            elif i <= n - 1 and j == 0:
                i = i - 1
                temp.top = Node(grid[i][j])
                temp = temp.top
                if i == 1:
                    temp.top = self.head
 
    # function to print Linked list.
    def printList(self, root):
         
        temp = root
         
        # printing head of linked list
        print(temp.data, end =" ")
         
        # loop till temp.top
        # become equal to head
        while temp.top != root:
           
          # printing the node
            if temp.next:
                print(temp.next.data, end =" ")
                temp = temp.next
            if temp.prev:
                print(temp.prev.data, end =" ")
                temp = temp.prev
            if temp.bottom:
                print(temp.bottom.data, end =" ")
                temp = temp.bottom
            if temp.top:
                print(temp.top.data, end =" ")
                temp = temp.top
 
# Driver Code
grid = [[13, 42, 93, 88],   
        [26, 38, 66, 42],
        [75, 63, 78, 12]]
 
# n is number of rows
n = len(grid)
 
# m is number of column
m = len(grid[0])
 
# creation of object
l = LinkedList()
 
# Call Quad method to create Linked List.
l.Quad(grid, n, m)
 
# Call printList method to print list.
l.printList(l.head)


C#




// C# program for above approach
using System;
 
// Node Class
class Node {
  public int data;
  public Node next;
  public Node prev;
  public Node top;
  public Node bottom;
 
  // Constructor to initialize the node object
  public Node(int data)
  {
    this.data = data;
    this.next = null;
    this.prev = null;
    this.top = null;
    this.bottom = null;
  }
}
 
public class GFG {
 
  // initialize head
  Node head = null;
 
  // function to form square linked list of matrix.
  public void Quad(int[, ] grid, int n, int m)
  {
 
    // initialising A[0][0] as head.
    head = new Node(grid[0, 0]);
 
    // head is assigned to head.
    Node temp = head;
 
    // i is row index, j is column index
    int i = 0;
    int j = 1;
 
    // loop till temp.top become equal to head.
    while (temp.top != head)
    {
       
      // as we iterating over boundary
      // of matrix so we will iterate
      // over first(0) and last(n-1) row
      // and first(0) and last(m-1) column.
 
      // iterating over first i.e 0th row
      // and connecting node.
      if (j < m && i == 0) {
        temp.next = new Node(grid[i, j]);
        temp = temp.next;
        j += 1;
      }
 
      // iterating over last i.e (m-1)th
      // column and connecting Node.
      else if (j == m && i < n - 1) {
        i = i + 1;
        temp.bottom = new Node(grid[i, j - 1]);
        temp = temp.bottom;
      }
 
      // iterating over last i.e (n-1)th row
      // and connecting Node.
      else if (i == n - 1 && j <= m && j >= 1) {
        if (j == m) {
          j = j - 1;
        }
        j = j - 1;
        temp.prev = new Node(grid[i, j]);
        temp = temp.prev;
      }
 
      // iterating over first i.e 0th column
      // and connecting Node.
      else if (i <= n - 1 && j == 0) {
        i = i - 1;
        temp.top = new Node(grid[i, j]);
        temp = temp.top;
        if (i == 1) {
          temp.top = head;
        }
      }
    }
  }
 
  // function to print Linked list.
  void printList(Node root)
  {
    Node temp = root;
 
    // printing head of linked list
    Console.Write(temp.data + " ");
 
    // loop till temp.top
    // become equal to head
    while (temp.top != root) {
 
      // printing the node
      if (temp.next != null) {
        Console.Write(temp.next.data + " ");
        temp = temp.next;
      }
      if (temp.prev != null) {
        Console.Write(temp.prev.data + " ");
        temp = temp.prev;
      }
      if (temp.bottom != null) {
        Console.Write(temp.bottom.data + " ");
        temp = temp.bottom;
      }
      if (temp.top != null) {
        Console.Write(temp.top.data + " ");
        temp = temp.top;
      }
    }
  }
 
  static public void Main()
  {
 
    // Code
    int[, ] grid = { { 13, 42, 93, 88 },
                    { 26, 38, 66, 42 },
                    { 75, 63, 78, 12 } };
 
    // n is number of rows
    int n = grid.GetLength(0);
 
    // m is number of columns
    int m = grid.GetLength(1);
 
    GFG l = new GFG();
 
    // Call Quad method to create Linked List.
    l.Quad(grid, n, m);
 
    // Call Quad method to create Linked List.
    l.printList(l.head);
  }
}
 
// This code is contributed by lokesh (lokeshmvs21).


Javascript




<script>
// Javascript program for above approach
// Node Class
class Node{
 
    // Constructor to initialize the node object
    constructor(val){
        this.data = val
        this.next = null
        this.prev = null
        this.top = null
        this.bottom = null
    }
}
 
// Linked List class
class LinkedList{
 
    // Constructor to initialize head
    constructor(){
        this.head = null
    }
 
    // function to form square
    // linked list of matrix.
    Quad(grid, n, m){
 
        // initialising A[0][0] as head.
        this.head = new Node(grid[0][0])
 
        // head is assigned to head.
        let temp = this.head
 
        // i is row index, j is column index
        let i = 0
        let j = 1
 
        // loop till temp.top become equal to head.
        while(temp.top != this.head){
            // as we iterating over boundary
            // of matrix so we will iterate
            // over first(0) and last(n-1) row
            // and first(0) and last(m-1) column.
 
            // iterating over first i.e 0th row
            // and connecting node.
            if(j < m && i == 0){
                temp.next = new Node(grid[i][j])
                temp = temp.next
                j += 1
            }
 
            // iterating over last i.e (m-1)th
            // column and connecting Node.
            else if (j == m && i < n - 1){
                i = i + 1
                temp.bottom = new Node(grid[i][j - 1])
                temp = temp.bottom
            }
 
            // iterating over last i.e (n-1)th row
            // and connecting Node.
            else if (i == n - 1 && j <= m && j >= 1){
                if (j == m) j = j - 1
                j = j - 1
                temp.prev = new Node(grid[i][j])
                temp = temp.prev
            }
 
            // iterating over first i.e 0th column
            // and connecting Node.
            else if (i <= n - 1 && j == 0){
                i = i - 1
                temp.top = new Node(grid[i][j])
                temp = temp.top
                if(i == 1)
                    temp.top = this.head
            }
        }
    }
 
    // function to print Linked list.
    printList(root){
         
        let temp = root
         
        // printing head of linked list
        document.write(temp.data + " ")
         
        // loop till temp.top
        // become equal to head
        while(temp.top != root){
           
          // printing the node
            if(temp.next){
               document.write(temp.next.data + " ")
                temp = temp.next
            }
            if(temp.prev){
               document.write(temp.prev.data + " ")
                temp = temp.prev
            }
            if(temp.bottom){
               document.write(temp.bottom.data + " ")
                temp = temp.bottom
            }
            if(temp.top){
               document.write(temp.top.data + " ")
                temp = temp.top
            }
        }
    }
}
 
// Driver Code
let grid = [[13, 42, 93, 88],   
        [26, 38, 66, 42],
        [75, 63, 78, 12]]
 
// n is number of rows
let n = grid.length
 
// m is number of column
let m = grid[0].length
 
// creation of object
let l = new LinkedList()
 
// Call Quad method to create Linked List.
l.Quad(grid, n, m)
 
// Call printList method to print list.
l.printList(l.head)
 
// This code is contributed by gfgking.
</script>


Output

13 42 93 88 42 12 78 63 75 26 

Time Complexity: O(N*M) 
Auxiliary Space: O(N*M)


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