# Sparse Matrix and its representations | Set 2 (Using List of Lists and Dictionary of keys)

In this post other two methods of sparse matrix representation are discussed.

1. List of Lists
2. Dictionary

List of Lists (LIL)

One of the possible representation of sparse matrix is List of Lists (LIL). Where one list is used to represent the rows and each row contains the list of triples: Column index, Value(non – zero element) and address field, for non – zero elements. For the best performance both lists should be stored in order of ascending keys.

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

 `// C program for Sparse Matrix Representation ` `// using List Of Lists ` `#include ` `#include ` `#define R 4 ` `#define C 5 ` ` `  `// Node to represent row - list ` `struct` `row_list ` `{ ` `    ``int` `row_number; ` `    ``struct` `row_list *link_down; ` `    ``struct` `value_list *link_right; ` `}; ` ` `  `// Node to represent triples ` `struct` `value_list ` `{ ` `    ``int` `column_index; ` `    ``int` `value; ` `    ``struct` `value_list *next; ` `}; ` ` `  `// Function to create node for non - zero elements ` `void` `create_value_node(``int` `data, ``int` `j, ``struct` `row_list **z) ` `{ ` `    ``struct` `value_list *temp, *d; ` ` `  `    ``// Create new node dynamically ` `    ``temp = (``struct` `value_list*)``malloc``(``sizeof``(``struct` `value_list)); ` `    ``temp->column_index = j+1; ` `    ``temp->value = data; ` `    ``temp->next = NULL; ` ` `  `    ``// Connect with row list ` `    ``if` `((*z)->link_right==NULL) ` `        ``(*z)->link_right = temp; ` `    ``else` `    ``{ ` `        ``// d points to data list node ` `        ``d = (*z)->link_right; ` `        ``while``(d->next != NULL) ` `            ``d = d->next; ` `        ``d->next = temp; ` `    ``} ` `} ` ` `  `// Function to create row list ` `void` `create_row_list(``struct` `row_list **start, ``int` `row, ` `                    ``int` `column, ``int` `Sparse_Matrix[R][C]) ` `{ ` `    ``// For every row, node is created ` `    ``for` `(``int` `i = 0; i < row; i++) ` `    ``{ ` `        ``struct` `row_list *z, *r; ` ` `  `        ``// Create new node dynamically ` `        ``z = (``struct` `row_list*)``malloc``(``sizeof``(``struct` `row_list)); ` `        ``z->row_number = i+1; ` `        ``z->link_down = NULL; ` `        ``z->link_right = NULL; ` `        ``if` `(i==0) ` `            ``*start = z; ` `        ``else` `        ``{ ` `            ``r = *start; ` `            ``while` `(r->link_down != NULL) ` `                ``r = r->link_down; ` `            ``r->link_down = z; ` `        ``} ` ` `  `        ``// Firstiy node for row is created, ` `        ``// and then travering is done in that row ` `        ``for` `(``int` `j = 0; j < 5; j++) ` `        ``{ ` `            ``if` `(Sparse_Matrix[i][j] != 0) ` `            ``{ ` `                ``create_value_node(Sparse_Matrix[i][j], j, &z); ` `            ``} ` `        ``} ` `    ``} ` `} ` ` `  `//Function display data of LIL ` `void` `print_LIL(``struct` `row_list *start) ` `{ ` `    ``struct` `row_list *r; ` `    ``struct` `value_list *z; ` `    ``r = start; ` ` `  `    ``// Traversing row list ` `    ``while` `(r != NULL) ` `    ``{ ` `        ``if` `(r->link_right != NULL) ` `        ``{ ` `            ``printf``(``"row=%d \n"``, r->row_number); ` `            ``z = r->link_right; ` ` `  `            ``// Traversing data list ` `            ``while` `(z != NULL) ` `            ``{ ` `                ``printf``(``"column=%d value=%d \n"``, ` `                     ``z->column_index, z->value); ` `                ``z = z->next; ` `            ``} ` `        ``} ` `        ``r = r->link_down; ` `    ``} ` `} ` ` `  `//Driver of the program ` `int` `main() ` `{ ` `    ``// Assume 4x5 sparse matrix ` `    ``int` `Sparse_Matrix[R][C] = ` `    ``{ ` `        ``{0 , 0 , 3 , 0 , 4 }, ` `        ``{0 , 0 , 5 , 7 , 0 }, ` `        ``{0 , 0 , 0 , 0 , 0 }, ` `        ``{0 , 2 , 6 , 0 , 0 } ` `    ``}; ` ` `  `    ``// Start with the empty List of lists ` `    ``struct` `row_list* start = NULL; ` ` `  `    ``//Function creating List of Lists ` `    ``create_row_list(&start, R, C, Sparse_Matrix); ` ` `  `    ``// Display data of List of lists ` `    ``print_LIL(start); ` `    ``return` `0; ` `} `

Output:

```row = 1
column = 3 value = 3
column = 5 value = 4
row = 2
column = 3 value = 5
column = 4 value = 7
row = 4
column = 2 value = 2
column = 3 value = 6
```

Dictionary of Keys

An alternative representation of sparse matrix is Dictionary. For the key field of the dictionary, pair of row and column index is used that maps with the non – zero element of the matrix. This method saves space but sequential access of items is costly.
In C++, dictionary is defined as map class of STL(Standard Template Library). To know more about map click the link below:
Basics of map

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

 `// C++ program for Sparse Matrix Representation ` `// using Dictionary ` `#include ` `using` `namespace` `std; ` `#define R 4 ` `#define C 5 ` ` `  `// Driver of the program ` `int` `main() ` `{ ` `    ``// Assume 4x5 sparse matrix ` `    ``int` `Sparse_Matrix[R][C] = ` `    ``{ ` `        ``{0 , 0 , 3 , 0 , 4 }, ` `        ``{0 , 0 , 5 , 7 , 0 }, ` `        ``{0 , 0 , 0 , 0 , 0 }, ` `        ``{0 , 2 , 6 , 0 , 0 } ` `    ``}; ` ` `  `    ``/* Declaration of map where first field(pair of ` `       ``row and column) represent key and second ` `       ``field represent value */` `    ``map< pair<``int``,``int``>, ``int` `> new_matrix; ` ` `  `    ``for` `(``int` `i = 0; i < R; i++) ` `        ``for` `(``int` `j = 0; j < C; j++) ` `            ``if` `(Sparse_Matrix[i][j] != 0) ` `                ``new_matrix[make_pair(i+1,j+1)] = ` `                                ``Sparse_Matrix[i][j] ; ` ` `  `    ``int` `c = 0; ` ` `  `    ``// Iteration over map ` `    ``for` `(``auto` `i = new_matrix.begin(); i != new_matrix.end(); i++ ) ` `    ``{ ` `        ``if` `(c != i->first.first) ` `        ``{ ` `            ``cout << ``"row = "` `<< i->first.first << endl ; ` `            ``c = i->first.first; ` `        ``} ` `        ``cout << ``"column = "` `<< i->first.second <<``" "``; ` `        ``cout << ``"value = "` `<< i->second << endl; ` `    ``} ` ` `  `    ``return` `0; ` `} `

Output:

```row = 1
column = 3 value = 3
column = 5 value = 4
row = 2
column = 3 value = 5
column = 4 value = 7
row = 4
column = 2 value = 2
column = 3 value = 6
```

References:
Wikipedia
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