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 26Explanation:
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 Classstruct 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 classstruct 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 Codeint 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 Classclass 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 Classclass 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 classclass 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 Codegrid = [[13, 42, 93, 88], [26, 38, 66, 42], [75, 63, 78, 12]]# n is number of rowsn = len(grid)# m is number of columnm = len(grid[0])# creation of objectl = 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 approachusing System;// Node Classclass 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 Classclass 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 classclass 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 Codelet grid = [[13, 42, 93, 88], [26, 38, 66, 42], [75, 63, 78, 12]]// n is number of rowslet n = grid.length// m is number of columnlet m = grid[0].length// creation of objectlet 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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