# Form a Rectangle from boundary elements of Matrix using Linked List

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.

## 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)` |

## 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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