稀疏矩阵及其表示 |设置 2（使用列表列表和键字典）

先决条件：稀疏矩阵及其表示集 1（使用数组和链表）
在这篇文章中，我们讨论了其他两种稀疏矩阵表示方法。

1. 列表列表
2. 字典

列表列表 (LIL)

稀疏矩阵的一种可能表示形式是列表列表 (LIL)。其中一个列表用于表示行，每一行包含三元组列表：列索引、值（非零元素）和地址字段，用于非零元素。为了获得最佳性能，两个列表都应按键的升序存储。

C++

// C++ program for Sparse Matrix Representation
// using List Of Lists
#include
using namespace std;
#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 = new 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 = new 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 traversing 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)
        {
            cout<<"row="<row_number<link_right;
 
            // Traversing data list
            while (z != NULL)
            {
                cout<<"column="<column_index<<" value="<value<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;
}
 
// This code is contributed by rutvik_56.

C

// 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 traversing 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;
}

输出：

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 

钥匙词典

稀疏矩阵的另一种表示是字典。对于字典的关键字段，使用与矩阵的非零元素映射的行和列索引对。这种方法可以节省空间，但顺序访问项目的成本很高。
在 C++ 中，字典被定义为 STL（标准模板库）的映射类。想了解更多地图请点击以下链接：
地图基础

CPP

// 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 > 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;
}

Python3

# Python program for Sparse Matrix Representation
# using Dictionary
R = 4
C = 5
 
# Driver of the program
 
# Assume 4x5 sparse matrix
Sparse_Matrix=[[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 '''
new_matrix = {}
 
for i in range(R):
    for j in range(C):
        if (Sparse_Matrix[i][j] != 0):
            new_matrix[(i + 1, j + 1)] = Sparse_Matrix[i][j]
c = 0
 
# Iteration over map
for i in new_matrix:
    if (c != i[0]):
        print("row =", i[0])
        c = i[0]
         
    print("column =", i[1], end = " ")
    print("value =", new_matrix[i])
 
# This code is contributed by Shubham Singh

输出：

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