{"id":84189,"date":"2021-09-21T09:00:34","date_gmt":"2021-09-21T03:30:34","guid":{"rendered":"https:\/\/techvidvan.com\/tutorials\/?p=84189"},"modified":"2021-09-21T09:00:34","modified_gmt":"2021-09-21T03:30:34","slug":"sparse-matrix-in-data-structure","status":"publish","type":"post","link":"https:\/\/techvidvan.com\/tutorials\/sparse-matrix-in-data-structure\/","title":{"rendered":"Sparse Matrix in Data Structure"},"content":{"rendered":"

In programming, we usually represent a 2-D array in the form of a matrix. However, if a matrix has most of its elements equal to zero, then the matrix is known as a sparse matrix. In the case of a sparse matrix, we don\u2019t store the zeros in the memory to reduce memory usage and make it more efficient. We only store the non-zero values of the sparse matrix inside the memory.<\/p>\n

For example, in the following 5*4 matrix, most of the numbers are zero. Only a few elements are non-zero which makes it a sparse matrix.<\/p>\n

\"Sparse<\/a><\/p>\n

Thus, a sparse matrix is a matrix in which the number of zeros is more than the number of non-zero elements. If we store this sparse matrix as it is, it will consume a lot of space. Therefore, we store only non-zero values in the memory in a more efficient way.<\/p>\n

Why Sparse Matrix:<\/h3>\n

There are mainly two reasons for using sparse matrices. These are:<\/p>\n

1. Computation time:<\/strong> If we store the sparse matrix in a memory-efficient manner, we can save a lot of computational time to perform operations on the matrix.<\/p>\n

2. Storage:<\/strong> When we store only non-zero elements, we can save a lot of memory\/space that we can use for storing other data structures or performing other operations.<\/p>\n

Memory Representation of Sparse Matrix:<\/h3>\n

There are two types of representations for sparse matrices. These are based on the type of data structure used to store the sparse matrix. Based on this, the representations are:<\/p>\n

1. Array representation
\n2. Linked list representation<\/p>\n

Array Representation:<\/h4>\n

In an array representation, we make use of arrays to store a sparse matrix. The sparse matrix is stored in a 2-D array having three rows as follows:<\/p>\n

1. Row:<\/strong> It stores the index of the row, where we have a non-zero element in the sparse matrix.<\/p>\n

2. Column:<\/strong> It stores the index of the column, where we have the non-zero element in the sparse matrix.<\/p>\n

3. Value:<\/strong> This variable consists of the actual non-zero value being stored.<\/p>\n

For example, the following diagram shows how we can represent a sparse matrix with the help of an array by storing only non-zero elements in the array along with their row number and column number.<\/p>\n

\"Array<\/a><\/p>\n

Linked List Representation:<\/h4>\n

A linked list is a combination of interconnected rows joined in a linear manner. In linked list representation, each node consists of four components:<\/p>\n

1. Row:<\/strong> It stores the index of the row, where we have a non-zero element in the sparse matrix.<\/p>\n

2. Column:<\/strong> It stores the index of the column, where we have the non-zero element in the sparse matrix.<\/p>\n

3. Value:<\/strong> This variable consists of the actual non-zero value being stored.<\/p>\n

4. Next node:<\/strong> It is a pointer to store the address of the next connected node.<\/p>\n

Thus, we can represent the node as follows:<\/p>\n

\"Sparse<\/a><\/p>\n

In the following diagram, we can see the linked list representation of a sparse matrix.<\/p>\n

\"Linked<\/a><\/p>\n

Array Implementation in C:<\/h3>\n
int main()\n{\n  int sparse_matrix[5][4] =\n  {\n    {0, 0, 3, 0},\n    {0, 0, 5, 7},\n    {0, 0, 0, 0},\n    {0, 2, 6, 0},\n    {4, 0, 0, 0}\n  };\n\n  int size = 0;\n  for (int i = 0; i < 5; i++)\n    for (int j = 0; j < 4; j++)\n      if (sparse_matrix[i][j] != 0)\n        size++;\n\n  int new_matrix[3][size];\n  int k = 0;\n  for (int i = 0; i < 5; i++)\n    for (int j = 0; j < 4; j++)\n      if (sparse_matrix[i][j] != 0)\n      {\n        new_matrix[0][k] = i;\n        new_matrix[1][k] = j;\n        new_matrix[2][k] = sparse_matrix[i][j];\n        k++;\n      }\n  for (int i=0; i<3; i++)\n  {\n    for (int j=0; j<size; j++)\n      printf(\"%d \", new_matrix[i][j]);\n    printf(\"\\n\");\n  }\n  return 0;\n}\n<\/pre>\n
Output:<\/strong><\/p>\n
0 1 1 3 3 4
\n2 2 3 1 2 0
\n3 5 7 2 6 4<\/div>\n
Array Implementation in C++:<\/h3>\n
#include<bits\/stdc++o.h>\n\nint main()\n{\n  int sparse_matrix[5][4] =\n  {\n    {0, 0, 3, 0},\n    {0, 0, 5, 7},\n    {0, 0, 0, 0},\n    {0, 2, 6, 0},\n    {4, 0, 0, 0}\n  };\n\n  int size = 0;\n  for (int i = 0; i < 5; i++)\n    for (int j = 0; j < 4; j++)\n      if (sparse_matrix[i][j] != 0)\n        size++;\n\n  int new_matrix[3][size];\n  int k = 0;\n  for (int i = 0; i < 5; i++)\n    for (int j = 0; j < 4; j++)\n      if (sparse_matrix[i][j] != 0)\n      {\n        new_matrix[0][k] = i;\n        new_matrix[1][k] = j;\n        new_matrix[2][k] = sparse_matrix[i][j];\n        k++;\n      }\n  for (int i=0; i<3; i++)\n  {\n    for (int j=0; j<size; j++)\n      cout << new_matrix[i][j];\n    cout << endl;\n  }\n  return 0;\n}\n<\/pre>\n
Output:<\/strong><\/p>\n
0 1 1 3 3 4
\n2 2 3 1 2 0
\n3 5 7 2 6 4<\/div>\n
Array Implementation in Java:<\/h3>\n
class TechVidvan\n{\n\n  public static void main(String[] args)\n  {\n    int sparse_matrix[][]\n        = {\n          {0, 0, 3, 0},\n               \t\t\t{0, 0, 5, 7},\n                \t\t{0, 0, 0, 0},\n                \t\t{0, 2, 6, 0},\n               \t\t\t {4, 0, 0, 0}\n        };\n\n    int size = 0;\n    for (int i = 0; i < 5; i++)\n    {\n      for (int j = 0; j < 4; j++)\n      {\n        if (sparse_matrix[i][j] != 0)\n          size++;\n      }\n    }\n\n    int new_matrix[][] = new int[3][size];\n    int k = 0;\n    for (int i = 0; i < 4; i++)\n    {\n      for (int j = 0; j < 5; j++)\n      {\n        if (sparse_matrix[i][j] != 0)\n        {\n          new_matrix[0][k] = i;\n          new_matrix[1][k] = j;\n          new_matrix[2][k] = sparse_matrix[i][j];\n          k++;\n        }\n      }\n    }\n\n    for (int i = 0; i < 3; i++)\n    {\n      for (int j = 0; j < size; j++)\n      {\n        System.out.print(\"%d \", new_matrix[i][j]);\n      }\n      System.out.print(\"\\n\");\n    }\n  }\n}\n<\/pre>\n
Output:<\/strong><\/p>\n
0 1 1 3 3 4
\n2 2 3 1 2 0
\n3 5 7 2 6 4<\/div>\n
Array Implementation in Python:<\/h3>\n
sparse_matrix = [[0,0,3,0],[0,0,5,7],[0,0,0,0],[0,2,6,0],[4,0,0,0]]\n\nsize = 0\n\nfor i in range(5):\n  for j in range(4):\n    if (sparse_matrix[i][j] != 0):\n      size += 1\n\n\nrows, cols = (3, size)\nnew_matrix = [[0 for i in range(cols)] for j in range(rows)]\n\nk = 0\nfor i in range(5):\n  for j in range(4):\n    if (sparse_matrix[i][j] != 0):\n      new_matrix[0][k] = i\n      new_matrix[1][k] = j\n      new_matrix[2][k] = sparse_matrix[i][j]\n      k += 1\n\nfor i in new_matrix:\n  print(i)\n<\/pre>\n
Output:<\/strong><\/p>\n
0 1 1 3 3 4
\n2 2 3 1 2 0
\n3 5 7 2 6 4<\/div>\n
Linked List Implementation in C:<\/h3>\n
#include<stdio.h>\n#include<stdlib.h>\n\nstruct Node\n{\n  int key;\n  int row_position;\n  int col_postion;\n  struct Node *Next;\n};\n\nvoid create_new_node(struct Node** head, int non_zero_element,\n          int row_index, int col_index )\n{\n  struct Node *temp, *r;\n  temp = *head;\n  if (temp == NULL)\n  {\n    temp = (struct Node *) malloc (sizeof(struct Node));\n    temp->key = non_zero_element;\n    temp->row_position = row_index;\n    temp->col_postion = col_index;\n    temp->Next = NULL;\n    *head = temp;\n\n  }\n  else\n  {\n    while (temp->Next != NULL)\n      temp = temp->Next;\n    r = (struct Node *) malloc (sizeof(struct Node));\n    r->key = non_zero_element;\n    r->row_position = row_index;\n    r->col_postion = col_index;\n    r->Next = NULL;\n    temp->Next = r;\n\n  }\n}\n\nvoid Print_list(struct Node* head)\n{\n  struct Node *temp, *r, *s;\n  temp = r = s = head;\n\n  printf(\"row_position: \");\n  while(temp != NULL)\n  {\n\n    printf(\"%d \", temp->row_position);\n    temp = temp->Next;\n  }\n  printf(\"\\n\");\n\n  printf(\"col_postion: \");\n  while(r != NULL)\n  {\n    printf(\"%d \", r->col_postion);\n    r = r->Next;\n  }\n  printf(\"\\n\");\n  printf(\"Value: \");\n  while(s != NULL)\n  {\n    printf(\"%d \", s->key);\n    s = s->Next;\n  }\n  printf(\"\\n\");\n}\n\nint main()\n{\n  int sparse_matric[5][4] =\n  {\n    {0, 0, 3, 0},\n    {0, 0, 5, 7},\n    {0, 0, 0, 0},\n    {0, 2, 6, 0},\n    {4, 0, 0, 0}\n  };\n\n  struct Node* start = NULL;\n\n  for (int i = 0; i < 5; i++)\n    for (int j = 0; j < 4; j++)\n      if (sparse_matric[i][j] != 0)\n        create_new_node(&head, sparse_matric[i][j], i, j);\n\n  Print_list(head);\n\n  return 0;\n}\n<\/pre>\n
Linked List Implementation in C++:<\/h3>\n
#include<bits\/stdc++.h>\n\nstruct Node\n{\n  int key;\n  int row_position;\n  int col_postion;\n  struct Node *Next;\n};\n\nvoid create_new_node(struct Node** head, int non_zero_element,\n          int row_index, int col_index )\n{\n  struct Node *temp, *r;\n  temp = *head;\n  if (temp == NULL)\n  {\n    temp = (struct Node *) malloc (sizeof(struct Node));\n    temp->key = non_zero_element;\n    temp->row_position = row_index;\n    temp->col_postion = col_index;\n    temp->Next = NULL;\n    *head = temp;\n\n  }\n  else\n  {\n    while (temp->Next != NULL)\n      temp = temp->Next;\n    r = (struct Node *) malloc (sizeof(struct Node));\n    r->key = non_zero_element;\n    r->row_position = row_index;\n    r->col_postion = col_index;\n    r->Next = NULL;\n    temp->Next = r;\n\n  }\n}\n\nvoid Print_list(struct Node* head)\n{\n  struct Node *temp, *r, *s;\n  temp = r = s = head;\n\n  cout << \"row_position: \";\n  while(temp != NULL)\n  {\n\n    cout << temp->row_position;\n    temp = temp->Next;\n  }\n  cout << endl;\n\n  cout << \"col_postion: \";\n  while(r != NULL)\n  {\n    cout << r->col_postion;\n    r = r->Next;\n  }\n  cout << endl;\n  cout << \"Value: \";\n  while(s != NULL)\n  {\n    cout << s->key;\n    s = s->Next;\n  }\n  cout << endl;\n}\n\nint main()\n{\n  int sparse_matric[5][4] =\n  {\n    {0, 0, 3, 0},\n    {0, 0, 5, 7},\n    {0, 0, 0, 0},\n    {0, 2, 6, 0},\n    {4, 0, 0, 0}\n  };\n\n  struct Node* start = NULL;\n\n  for (int i = 0; i < 5; i++)\n    for (int j = 0; j < 4; j++)\n      if (sparse_matric[i][j] != 0)\n        create_new_node(&head, sparse_matric[i][j], i, j);\n\n  Print_list(head);\n\n  return 0;\n}\n<\/pre>\n
Output:<\/strong><\/p>\n
row_position: 0 1 1 3 3 4
\ncol_position: 2 2 3 1 2 0
\nkey: 3 5 7 2 6 4<\/div>\n
Linked List Implementation in Python:<\/h3>\n
class Node:\n  __slots__ = \"row\", \"col\", \"key\", \"Next\"\n  def __init__(self, row=0, col=0, key=0, Next=None):\n\n    self.row = row\n    self.col = col\n    self.key = key\n    self.Next = Next\n\nclass Sparse:\n  def __init__(self):\n    self.head = None\n    self.temp = None\n    self.size = 0\n  def __len__(self):\n    return self.size\n    \n  def is_empty(self):\n    return self.size == 0\n\n  def create_new_node(self, row, col, key):\n    new_node = Node(row, col, key, None)\n    if self.is_empty():\n      self.head = new_node\n    else:\n      self.temp.Next = new_node\n    self.temp = new_node\n    self.size += 1\n\n  def Print_list(self):\n    temp = r = s = self.head\n    print(\"row_position:\", end=\" \")\n    while temp != None:\n      print(temp.row, end=\" \")\n      temp = temp.Next\n    print()\n    print(\"col_postion:\", end=\" \")\n    while r != None:\n      print(r.col, end=\" \")\n      r = r.Next\n    print()\n    print(\"Value:\", end=\" \")\n    while s != None:\n      print(s.key, end=\" \")\n      s = s.Next\n    print()\n\nif __name__ == \"__main__\":\n  s = Sparse()\n  sparse_matrix = [[0, 0, 3, 0],\n          [0, 0, 5, 7],\n          [0, 0, 0, 0],\n          [0, 2, 6, 0],\n          [4, 0, 0, 0]]\n  for i in range(5):\n    for j in range(4):\n      if sparse_matric[i][j] != 0:\n        s.create_new_node(i, j, sparse_matric[i][j])\n  s.Print_list()\n<\/pre>\n
Output:<\/strong><\/p>\n
row_position: 0 1 1 3 3 4
\ncol_position: 2 2 3 1 2 0
\nkey: 3 5 7 2 6 4<\/div>\n
Conclusion:<\/h3>\n
In this article, we have discussed what is a sparse matrix, how do we define it, what is the need for a sparse matrix and how we can implement it in various programming languages. Thus, a sparse matrix is a very beneficial way of representing matrices as it reduces the computational time to a great extent.<\/p>\n","protected":false},"excerpt":{"rendered":"
In programming, we usually represent a 2-D array in the form of a matrix. However, if a matrix has most of its elements equal to zero, then the matrix is known as a sparse...<\/p>\n","protected":false},"author":1,"featured_media":84893,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3555],"tags":[4265,4266],"class_list":["post-84189","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-data-structure","tag-sparse-matrix","tag-sparse-matrix-in-data-structure"],"yoast_head":"\nSparse Matrix in Data Structure - TechVidvan<\/title>\n<meta name=\"description\" content=\"Learn what is a sparse matrix, how to define it, what is its need and how we can implement it in various programming languages.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/techvidvan.com\/tutorials\/sparse-matrix-in-data-structure\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Sparse Matrix in Data Structure - 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