Construct a linked list from 2D matrix

Given a matrix. Convert it into a linked list matrix such that each node is connected to its next right and down node.

Input : 2D matrix
1 2 3
4 5 6
7 8 9
Output :
1 -> 2 -> 3 -> NULL
|        |     |
v       v    v
4 -> 5 -> 6 -> NULL
|        |     |
v      v     v
7 -> 8 -> 9 -> NULL
|       |       |
v     v       v
NULL NULL NULL

Question Source: Factset Interview Experience | Set 9

Approach: The problem can be solved based on the following idea:

Connect every cell to its right cell of the same row and to its bottom cell in the same column and also for each cell and keep track of those created node.

Follow the steps mentioned below to solve this problem:

• First create a variable of Node type, which will store address of its right and bottom Node corresponding to cell in the matrix.
• Recursively do the following steps for any cell in the matrix:
• If Node is not created for any corresponding cell in the matrix, then create a new Node and store it.
• Else we reach at some cell which has already been created for its corresponding cell in the matrix then return that stored Node.
• Attach Node to its right and bottom cell which is created and return the current Node.
• Finally return the root Node.

Below is the implementation of the above approach:

C++

 `// CPP program to construct a linked list``// from given 2D matrix``#include ``using` `namespace` `std;``// struct node of linked list``struct` `Node {``    ``int` `data;``    ``Node *right, *down;``};``// returns head pointer of linked list``// constructed from 2D matrix``Node* construct(``int` `arr[][4], ``int` `i, ``int` `j, ``int` `m, ``int` `n,``                ``vector >& visited)``{``    ``// return if i or j is out of bounds``    ``if` `(i > m - 1 || j > n - 1)``        ``return` `NULL;``    ``// Check if node is previously created then,``    ``// don't need to create new/``    ``if` `(visited[i][j]) {``        ``return` `visited[i][j];``    ``}``    ``// create a new node for current i and j``    ``// and recursively allocate its down and``    ``// right pointers``    ``Node* temp = ``new` `Node();``    ``visited[i][j] = temp;``    ``temp->data = arr[i][j];``    ``temp->right = construct(arr, i, j + 1, m, n, visited);``    ``temp->down = construct(arr, i + 1, j, m, n, visited);``    ``return` `temp;``}``// utility function for displaying``// linked list data``void` `display(Node* head)``{``    ``// pointer to move right``    ``Node* Rp;``    ``// pointer to move down``    ``Node* Dp = head;``    ``// loop till node->down is not NULL``    ``while` `(Dp) {``        ``Rp = Dp;``        ``// loop till node->right is not NULL``        ``while` `(Rp) {``            ``cout << Rp->data << ``" "``;``            ``Rp = Rp->right;``        ``}``        ``cout << ``"\n"``;``        ``Dp = Dp->down;``    ``}``}``// driver program``int` `main()``{``    ``// 2D matrix``    ``int` `arr[][4] = { { 1, 2, 3, 0 },``                     ``{ 4, 5, 6, 1 },``                     ``{ 7, 8, 9, 2 },``                     ``{ 7, 8, 9, 2 } };``    ``int` `m = 4, n = 4;``    ``vector > visited(m, vector(n));``    ``Node* head = construct(arr, 0, 0, m, n, visited);``    ``display(head);``    ``return` `0;``}`

Java

 `// Java program to construct a linked list``// from given 2D matrix``public` `class` `Linked_list_2D_Matrix {``    ``// node of linked list``    ``static` `class` `Node {``        ``int` `data;``        ``Node right;``        ``Node down;``    ``};``    ``// returns head pointer of linked list``    ``// constructed from 2D matrix``    ``static` `Node construct(``int` `arr[][], ``int` `i, ``int` `j, ``int` `m,``                          ``int` `n, Node[][] visited)``    ``{``        ``// return if i or j is out of bounds``        ``if` `(i > m - ``1` `|| j > n - ``1``)``            ``return` `null``;``        ``// Check if node is previously created then,``        ``// don't need to create new/``        ``if` `(visited[i][j] != ``null``) {``            ``return` `visited[i][j];``        ``}``        ``// create a new node for current i and j``        ``// and recursively allocate its down and``        ``// right pointers``        ``Node temp = ``new` `Node();``        ``visited[i][j] = temp;``        ``temp.data = arr[i][j];``        ``temp.right``            ``= construct(arr, i, j + ``1``, m, n, visited);``        ``temp.down = construct(arr, i + ``1``, j, m, n, visited);``        ``return` `temp;``    ``}``    ``// utility function for displaying``    ``// linked list data``    ``static` `void` `display(Node head)``    ``{``        ``// pointer to move right``        ``Node Rp;``        ``// pointer to move down``        ``Node Dp = head;``        ``// loop till node->down is not NULL``        ``while` `(Dp != ``null``) {``            ``Rp = Dp;``            ``// loop till node->right is not NULL``            ``while` `(Rp != ``null``) {``                ``System.out.print(Rp.data + ``" "``);``                ``Rp = Rp.right;``            ``}``            ``System.out.println();``            ``Dp = Dp.down;``        ``}``    ``}``    ``// driver program``    ``public` `static` `void` `main(String args[])``    ``{``        ``// 2D matrix``        ``int` `arr[][] = { { ``1``, ``2``, ``3``, ``0` `},``                        ``{ ``4``, ``5``, ``6``, ``1` `},``                        ``{ ``7``, ``8``, ``9``, ``2` `},``                        ``{ ``7``, ``8``, ``9``, ``2` `} };``        ``int` `m = ``4``, n = ``4``;``        ``// List> arr = new``        ``// ArrayList>();``        ``Node[][] visited = ``new` `Node[m][n];``        ``Node head = construct(arr, ``0``, ``0``, m, n, visited);``        ``display(head);``    ``}``}``// This code is contributed by Sumit Ghosh`

Python3

 `# Python program to construct a linked list``# from given 2D matrix` `# Node class to represent a node in the linked list``class` `Node:``    ``def` `__init__(``self``, data``=``None``, right``=``None``, down``=``None``):``        ``self``.data ``=` `data``        ``self``.right ``=` `right``        ``self``.down ``=` `down` `# Function to construct the linked list from the given 2D matrix``def` `construct(arr, i, j, m, n, visited):``    ``# Return if i or j is out of bounds``    ``if` `i > m ``-` `1` `or` `j > n ``-` `1``:``        ``return` `None` `    ``# Check if node is previously created, then don't create new``    ``if` `visited[i][j]:``        ``return` `visited[i][j]` `    ``# Create a new node for current i and j and``    ``# recursively allocate its down and right pointers``    ``node ``=` `Node(arr[i][j])``    ``visited[i][j] ``=` `node``    ``node.right ``=` `construct(arr, i, j ``+` `1``, m, n, visited)``    ``node.down ``=` `construct(arr, i ``+` `1``, j, m, n, visited)` `    ``return` `node` `# Utility function for displaying linked list data``def` `display(head):``    ``# Pointer to move right``    ``Rp ``=` `head``    ``# Pointer to move down``    ``Dp ``=` `head` `    ``# Loop till node.down is not None``    ``while` `Dp:``        ``Rp ``=` `Dp``        ``# Loop till node.right is not None``        ``while` `Rp:``            ``print``(Rp.data, end``=``" "``)``            ``Rp ``=` `Rp.right``        ``print``()``        ``Dp ``=` `Dp.down` `# Driver program``if` `__name__ ``=``=` `"__main__"``:``    ``# 2D matrix``    ``arr ``=` `[[``1``, ``2``, ``3``, ``0``],``           ``[``4``, ``5``, ``6``, ``1``],``           ``[``7``, ``8``, ``9``, ``2``],``           ``[``7``, ``8``, ``9``, ``2``]]``    ``m ``=` `4``    ``n ``=` `4``    ``visited ``=` `[[``None``] ``*` `n ``for` `_ ``in` `range``(m)]``    ``head ``=` `construct(arr, ``0``, ``0``, m, n, visited)``    ``display(head)`

C#

 `// C#  program to construct a linked list``// from given 2D matrix``using` `System;``using` `System.Collections.Generic;` `// node of linked list``class` `Node {``  ``public` `int` `data;``  ``public` `Node right;``  ``public` `Node down;``}` `class` `Linked_list_2D_Matrix``{` `  ``// returns head pointer of linked list``  ``// constructed from 2D matrix``  ``static` `Node construct(``int``[, ] arr, ``int` `i, ``int` `j, ``int` `m,``                        ``int` `n, Node[, ] visited)``  ``{``    ``// return if i or j is out of bounds``    ``if` `(i > m - 1 || j > n - 1)``      ``return` `null``;` `    ``// Check if node is previously created then,``    ``// don't need to create new/``    ``if` `(visited[i, j] != ``null``) {``      ``return` `visited[i, j];``    ``}` `    ``// create a new node for current i and j``    ``// and recursively allocate its down and``    ``// right pointers``    ``Node temp = ``new` `Node();``    ``visited[i, j] = temp;``    ``temp.data = arr[i, j];``    ``temp.right``      ``= construct(arr, i, j + 1, m, n, visited);``    ``temp.down = construct(arr, i + 1, j, m, n, visited);``    ``return` `temp;``  ``}` `  ``// utility function for displaying``  ``// linked list data``  ``static` `void` `display(Node head)``  ``{` `    ``// pointer to move right``    ``Node Rp;` `    ``// pointer to move down``    ``Node Dp = head;` `    ``// loop till node->down is not NULL``    ``while` `(Dp != ``null``) {``      ``Rp = Dp;` `      ``// loop till node->right is not NULL``      ``while` `(Rp != ``null``) {``        ``Console.Write(Rp.data + ``" "``);``        ``Rp = Rp.right;``      ``}``      ``Console.WriteLine();``      ``Dp = Dp.down;``    ``}``  ``}` `  ``// driver program``  ``public` `static` `void` `Main(``string``[] args)``  ``{` `    ``// 2D matrix``    ``int``[, ] arr = { { 1, 2, 3, 0 },``                   ``{ 4, 5, 6, 1 },``                   ``{ 7, 8, 9, 2 },``                   ``{ 7, 8, 9, 2 } };``    ``int` `m = 4, n = 4;` `    ``// List> arr = new``    ``// ArrayList>();``    ``Node[, ] visited = ``new` `Node[m, n];``    ``Node head = construct(arr, 0, 0, m, n, visited);``    ``display(head);``  ``}``}` `// This code is contributed by phasing17`

Javascript

 `// Javascript program to construct a linked list``      ``// from given 2D matrix` `      ``//node of linked list``      ``class Node {``        ``constructor() {``          ``this``.data;``          ``this``.right;``          ``this``.down;``        ``}``      ``}``      ``// returns head pointer of linked list``      ``// constructed from 2D matrix``      ``function` `construct(arr, i, j, m, n, visited) {``        ``// return if i or j is out of bounds``        ``if` `(i > m - 1 || j > n - 1) ``return` `null``;``        ``// Check if node is previously created then,``        ``// don't need to create new/``        ``if` `(visited[i][j]) {``          ``return` `visited[i][j];``        ``}``        ``// create a new node for current i and j``        ``// and recursively allocate its down and``        ``// right pointers``        ``let temp = ``new` `Node();``        ``visited[i][j] = temp;``        ``temp.data = arr[i][j];``        ``temp.right = construct(arr, i, j + 1, m, n, visited);``        ``temp.down = construct(arr, i + 1, j, m, n, visited);``        ``return` `temp;``      ``}``      ``// utility function for displaying``      ``// linked list data``      ``function` `display(head) {``        ``// pointer to move right``        ``let Rp;``        ``// pointer to move down``        ``let Dp = head;``        ``// loop till node.down is not NULL``        ``while` `(Dp) {``          ``Rp = Dp;``          ``// loop till node.right is not NULL``          ``while` `(Rp) {``            ``console.log(Rp.data + ``" "``);``            ``Rp = Rp.right;``          ``}` `          ``Dp = Dp.down;``        ``}``      ``}``      ``// driver program` `      ``// 2D matrix``      ``var` `arr = [``        ``[1, 2, 3, 0],``        ``[4, 5, 6, 1],``        ``[7, 8, 9, 2],``        ``[7, 8, 9, 2],``      ``];``      ``let m = 4,``        ``n = 4;``      ``let visited = Array.from(Array(m), () => ``new` `Array(n));``      ``var` `head = construct(arr, 0, 0, m, n, visited);``      ``display(head);`

Output
```1 2 3 0
4 5 6 1
7 8 9 2
7 8 9 2 ```

Time complexity: O(N*M), where N is the number of row and M is the number of column.
Auxiliary space: O(N*M)

Use a pre-allocated array of nodes instead of allocating new nodes:

This will reduce the overhead of dynamic memory allocation and deallocation, which can be significant in some cases. The nodeCounter variable keeps track of the next available node in the array. A sentinel node is used to simplify the linked list construction logic, and eliminates the need for special cases when creating the first node.

Here is an example implementation that incorporates these optimizations:

C++

 `#include ``using` `namespace` `std;` `const` `int` `MAXN = 100;` `struct` `Node``{``    ``int` `data;``    ``Node *next;``};` `Node nodes[MAXN];``int` `nodeCounter = 0;` `Node *constructLinkedList(``int` `matrix[][4], ``int` `rows, ``int` `columns)``{``    ``Node *sentinel = &nodes[nodeCounter++];``    ``sentinel->next = NULL;``    ``Node *current = sentinel;` `    ``for` `(``int` `i = 0; i < rows; i++)``    ``{``        ``for` `(``int` `j = 0; j < columns; j++)``        ``{``            ``Node *newNode = &nodes[nodeCounter++];``            ``newNode->data = matrix[i][j];``            ``newNode->next = NULL;` `            ``current->next = newNode;``            ``current = current->next;``        ``}``    ``}` `    ``return` `sentinel->next;``}` `void` `printLinkedList(Node *head)``{``    ``while` `(head != NULL)``    ``{``        ``cout << head->data << ``" "``;``        ``head = head->next;``    ``}``    ``cout << endl;``}` `int` `main()``{``    ``int` `matrix[3][4] = {{1, 2, 3, 4},``                        ``{5, 6, 7, 8},``                        ``{9, 10, 11, 12}};` `    ``Node *head = constructLinkedList(matrix, 3, 4);``    ``printLinkedList(head);` `    ``return` `0;``}`

Java

 `// Java code to implement the approach` `import` `java.util.*;` `// Node class definition``class` `Node {``    ``public` `int` `data;``    ``public` `Node next;``}` `// LinkedListFromMatrix class definition``class` `LinkedListFromMatrix {` `    ``// This method constructs a linked list from a 2D array``    ``static` `Node constructLinkedList(``int``[][] matrix,``                                    ``int` `rows, ``int` `columns)``    ``{``        ``Node sentinel = ``new` `Node();``        ``sentinel.next = ``null``;``        ``Node current = sentinel;` `        ``// Iterating over the rows``        ``for` `(``int` `i = ``0``; i < rows; i++) {``            ``// Iterating over the columns``            ``for` `(``int` `j = ``0``; j < columns; j++) {``                ``// Adding node to linked list``                ``Node newNode = ``new` `Node();``                ``newNode.data = matrix[i][j];``                ``newNode.next = ``null``;` `                ``current.next = newNode;``                ``current = current.next;``            ``}``        ``}` `        ``return` `sentinel.next;``    ``}` `    ``// This function displays the linked list``    ``static` `void` `printLinkedList(Node head)``    ``{``        ``while` `(head != ``null``) {``            ``System.out.print(head.data + ``" "``);``            ``head = head.next;``        ``}``        ``System.out.println(``" "``);``    ``}` `    ``// Driver code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``int``[][] matrix = ``new` `int``[][] { { ``1``, ``2``, ``3``, ``4` `},``                                       ``{ ``5``, ``6``, ``7``, ``8` `},``                                       ``{ ``9``, ``10``, ``11``, ``12` `} };` `        ``// Function calls``        ``Node head = constructLinkedList(matrix, ``3``, ``4``);``        ``printLinkedList(head);``    ``}``}`

C#

 `// C# code to implement the approach` `using` `System;` `// Node class definition``class` `Node``{``    ``public` `int` `data;``    ``public` `Node next;``}` `class` `LinkedListFromMatrix``{``    ``// This function constructs a linked list from a 2D array``    ``static` `Node ConstructLinkedList(``int``[,] matrix, ``int` `rows, ``int` `columns)``    ``{``        ``Node sentinel = ``new` `Node();``        ``sentinel.next = ``null``;``        ``Node current = sentinel;``        ` `        ``// Iterating over the rows``        ``for` `(``int` `i = 0; i < rows; i++)``        ``{``            ``// Iterating over the columns``            ``for` `(``int` `j = 0; j < columns; j++)``            ``{``                ``// Adding node to linked list``                ``Node newNode = ``new` `Node();``                ``newNode.data = matrix[i, j];``                ``newNode.next = ``null``;` `                ``current.next = newNode;``                ``current = current.next;``            ``}``        ``}` `        ``return` `sentinel.next;``    ``}``    ` `    ``// This function prints the linked list``    ``static` `void` `PrintLinkedList(Node head)``    ``{``        ``while` `(head != ``null``)``        ``{``            ``Console.Write(head.data + ``" "``);``            ``head = head.next;``        ``}``        ``Console.WriteLine(``" "``);``    ``}``    ` `    ``// Driver code``    ``static` `void` `Main(``string``[] args)``    ``{``        ``int``[,] matrix = ``new` `int``[3, 4] {{1, 2, 3, 4},``                                       ``{5, 6, 7, 8},``                                       ``{9, 10, 11, 12}};``        ` `        ``// Function calls``        ``Node head = ConstructLinkedList(matrix, 3, 4);``        ``PrintLinkedList(head);``    ``}``}`

Python3

 `# GFG ``# Python program to construct a linked list``# from given 2D matrix``# Pre-allocated array of nodes instead of allocating new nodes` `class` `Node:``    ``def` `__init__(``self``, data``=``None``):``        ``self``.data ``=` `data``        ``self``.``next` `=` `None`  `def` `construct_linked_list(matrix):``    ``sentinel ``=` `Node()``    ``current ``=` `sentinel` `    ``for` `row ``in` `matrix:``        ``for` `element ``in` `row:``            ``new_node ``=` `Node(element)``            ``current.``next` `=` `new_node``            ``current ``=` `current.``next` `    ``return` `sentinel.``next`  `def` `print_linked_list(head):``    ``while` `head ``is` `not` `None``:``        ``print``(head.data, end``=``" "``)``        ``head ``=` `head.``next``    ``print``()`  `if` `__name__ ``=``=` `"__main__"``:``    ``matrix ``=` `[[``1``, ``2``, ``3``, ``4``],``              ``[``5``, ``6``, ``7``, ``8``],``              ``[``9``, ``10``, ``11``, ``12``]]` `    ``head ``=` `construct_linked_list(matrix)``    ``print_linked_list(head)``# This code is written by Sundaram`

Javascript

 `// Javascript program to construct a linked list``// from given 2D matrix``// Pre-allocated array of nodes instead of allocating new nodes``class Node {``    ``constructor(data) {``        ``this``.data = data;``        ``this``.next = ``null``;``    ``}``}` `function` `constructLinkedList(matrix) {``    ``const sentinel = ``new` `Node();``    ``let current = sentinel;``    ``for` `(const row of matrix) {``        ``for` `(const element of row) {``            ``const newNode = ``new` `Node(element);``            ``current.next = newNode;``            ``current = current.next;``        ``}``    ``}` `    ``return` `sentinel.next;``}` `function` `printLinkedList(head) {``    ``let currentNode = head;``    ``let temp = []``    ``while` `(currentNode !== ``null``) {``        ``temp.push(currentNode.data);``        ``currentNode = currentNode.next;``    ``}``    ``console.log(temp.join(``' '``));``}` `const matrix = [``    ``[1, 2, 3, 4],``    ``[5, 6, 7, 8],``    ``[9, 10, 11, 12]``];` `const head = constructLinkedList(matrix);``printLinkedList(head);` `// Contributed by adityasharmadev01`

Output
`1 2 3 4 5 6 7 8 9 10 11 12 `

Time complexity: O(N*M)
Auxiliary space: O(N*M)

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