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

Prerequisite : Sparse Matrix and its representations Set 1 (Using Arrays and Linked Lists)

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

- List of Lists
- 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.

`// C program for Sparse Matrix Representation` `// using List Of Lists` `#include<stdio.h>` `#include<stdlib.h>` `#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

`// C++ program for Sparse Matrix Representation` `// using Dictionary` `#include<bits/stdc++.h>` `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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