【数据结构】数组和字符串(一):矩阵的数组表示
矩阵是以按行优先次序将所有矩阵元素存放在一个一维数组中。但是对于特殊矩阵,如对称矩阵、三角矩阵、对角矩阵和稀疏矩阵等, 如果用这种方式存储,会出现大量存储空间存放重复信息或零元素的情况,这样会造成很大的空间浪费。为节约存储空间和算法(程序)运行时间,通常会采用压缩存储的方法。
【数据结构】数组和字符串(二):特殊矩阵的压缩存储:对角矩阵——一维数组
【数据结构】数组和字符串(三):特殊矩阵的压缩存储:三角矩阵、对称矩阵——一维数组
【数据结构】数组和字符串(四):特殊矩阵的压缩存储:稀疏矩阵——三元组表
压缩稀疏行(Compressed Sparse Row,CSR)是一种常用的稀疏矩阵存储格式。CSR存储格式通过压缩非零元素的行指针和列索引,以及存储非零元素的值,来有效地表示稀疏矩阵。它包含以下几个关键组成部分:
CSR存储格式的主要优点是有效地压缩了稀疏矩阵的存储空间,只存储非零元素及其对应的行和列信息。此外,CSR格式还支持高效的稀疏矩阵向量乘法和稀疏矩阵乘法等操作。
typedef struct {
int row;
int col;
int value;
} Element;
typedef struct {
int rows;
int cols;
int num_elements;
Element* elements;
int* row_ptr;
int* col_indices;
} CSRMatrix;
Element
结构体表示矩阵中的一个元素,包含三个成员变量:row
(行索引)、col
(列索引)和 value
(元素值)。
CSRMatrix
结构体表示一个CSR矩阵,包含了矩阵的行数 rows
、列数 cols
、非零元素的个数 num_elements
,以及三个指针成员变量 elements
、row_ptr
和 col_indices
。
CSRMatrix createCSRMatrix(int rows, int cols, int num_elements) {
CSRMatrix matrix;
matrix.rows = rows;
matrix.cols = cols;
matrix.num_elements = num_elements;
matrix.elements = (Element*)malloc(num_elements * sizeof(Element));
matrix.row_ptr = (int*)malloc((rows + 1) * sizeof(int));
matrix.col_indices = (int*)malloc(num_elements * sizeof(int));
return matrix;
}
createCSRMatrix
函数用于创建一个CSR矩阵。elements
、row_ptr
和 col_indices
分配内存空间,并将 row_ptr
数组的所有元素初始化为0,最后返回创建的矩阵。void setElement(CSRMatrix* matrix, int row, int col, int value) {
if (row < 0 || row >= matrix->rows) {
printf("Invalid row index.\n");
return;
}
int index = matrix->row_ptr[row];
matrix->elements[index].row = row;
matrix->elements[index].col = col;
matrix->elements[index].value = value;
matrix->col_indices[index] = col;
matrix->row_ptr[row]++; // 递增索引值
}
setElement
函数可用于设置(修改)CSR矩阵中某个位置的元素值。
matrix
,以及要设置的元素的行索引、列索引和值作为参数。col_indices
数组和 row_ptr
数组中的值。void initializeCSRMatrix(CSRMatrix* matrix, int* values, int* row_indices, int* col_indices, int num_elements) {
for (int i = 0; i < num_elements; i++) {
matrix->elements[i].value = values[i];
matrix->elements[i].row = row_indices[i];
matrix->elements[i].col = col_indices[i];
matrix->col_indices[i] = col_indices[i];
matrix->row_ptr[row_indices[i]]++;
}
int sum = 0;
for (int i = 0; i <= matrix->rows; i++) {
int temp = matrix->row_ptr[i];
matrix->row_ptr[i] = sum;
sum += temp;
}
}
initializeCSRMatrix
函数用于初始化CSR矩阵的数据。
matrix
,以及包含非零元素的值、行索引和列索引的数组,以及非零元素的个数作为参数。col_indices
数组和 row_ptr
数组中的值。row_ptr
数组的每个元素表示对应行的非零元素在 elements
数组中的起始位置,通过累加非零元素的个数来计算每行的结束位置。void printCSRMatrix(CSRMatrix matrix) {
printf("CSR Matrix:\n");
printf("Rows: %d, Cols: %d, Num Elements: %d\n", matrix.rows, matrix.cols, matrix.num_elements);
printf("Values: ");
for (int i = 0; i < matrix.num_elements; i++) {
printf("%d ", matrix.elements[i].value);
}
printf("\n");
printf("Row Pointer: ");
for (int i = 0; i <= matrix.rows; i++) {
printf("%d ", matrix.row_ptr[i]);
}
printf("\n");
printf("Column Indices: ");
for (int i = 0; i < matrix.num_elements; i++) {
printf("%d ", matrix.col_indices[i]);
}
printf("\n");
}
void printMatrixForm(CSRMatrix matrix) {
printf("Matrix Form:\n");
for (int i = 0; i < matrix.rows; i++) {
for (int j = 0; j < matrix.cols; j++) {
int value = 0;
for (int k = matrix.row_ptr[i]; k < matrix.row_ptr[i + 1]; k++) {
if (matrix.elements[k].col == j) {
value = matrix.elements[k].value;
break;
}
}
printf("%d ", value);
}
printf("\n");
}
}
printCSRMatrix
函数用于打印CSR矩阵的信息:它接受一个CSR矩阵作为参数,并打印矩阵的行数、列数、非零元素的个数以及 elements
、row_ptr
和 col_indices
数组的内容。printMatrixForm
函数用于以矩阵形式打印CSR矩阵。它接受一个CSR矩阵作为参数,并按矩阵的行数和列数遍历矩阵元素,通过遍历 row_ptr
数组和 col_indices
数组来获取每个位置的元素值,并打印出矩阵的形式。void destroyCSRMatrix(CSRMatrix* matrix) {
free(matrix->elements);
free(matrix->row_ptr);
free(matrix->col_indices);
matrix->elements = NULL;
matrix->row_ptr = NULL;
matrix->col_indices = NULL;
}
int main() {
int rows = 9;
int cols = 3;
int num_elements = 5;
CSRMatrix matrix = createCSRMatrix(rows, cols, num_elements);
int col_indices[] = {0, 0, 0, 0, 1};
int row_indices[] = {3, 5, 7, 8, 7};
int values[] = {2, 1, 3, 1, 4};
initializeCSRMatrix(&matrix, values, row_indices, col_indices, num_elements);
printCSRMatrix(matrix);
printMatrixForm(matrix);
destroyCSRMatrix(&matrix);
return 0;
}
#include
#include
#include
typedef struct {
int row;
int col;
int value;
} Element;
typedef struct {
int rows;
int cols;
int num_elements;
Element* elements;
int* row_ptr;
int* col_indices;
} CSRMatrix;
CSRMatrix createCSRMatrix(int rows, int cols, int num_elements) {
CSRMatrix matrix;
matrix.rows = rows;
matrix.cols = cols;
matrix.num_elements = num_elements;
matrix.elements = (Element*)malloc(num_elements * sizeof(Element));
matrix.row_ptr = (int*)malloc((rows + 1) * sizeof(int));
matrix.col_indices = (int*)malloc(num_elements * sizeof(int));
memset(matrix.row_ptr, 0, (rows + 1) * sizeof(int));
return matrix;
}
void initializeCSRMatrix(CSRMatrix* matrix, int* values, int* row_indices, int* col_indices, int num_elements) {
for (int i = 0; i < num_elements; i++) {
matrix->elements[i].value = values[i];
matrix->elements[i].row = row_indices[i];
matrix->elements[i].col = col_indices[i];
matrix->col_indices[i] = col_indices[i];
matrix->row_ptr[row_indices[i]]++;
}
int sum = 0;
for (int i = 0; i <= matrix->rows; i++) {
int temp = matrix->row_ptr[i];
matrix->row_ptr[i] = sum;
sum += temp;
}
}
void setElement(CSRMatrix* matrix, int row, int col, int value) {
if (row < 0 || row >= matrix->rows) {
printf("Invalid row index.\n");
return;
}
int index = matrix->row_ptr[row];
matrix->elements[index].row = row;
matrix->elements[index].col = col;
matrix->elements[index].value = value;
matrix->col_indices[index] = col;
matrix->row_ptr[row]++; // 递增索引值
}
void printCSRMatrix(CSRMatrix matrix) {
printf("CSR Matrix:\n");
printf("Rows: %d, Cols: %d, Num Elements: %d\n", matrix.rows, matrix.cols, matrix.num_elements);
printf("Values: ");
for (int i = 0; i < matrix.num_elements; i++) {
printf("%d ", matrix.elements[i].value);
}
printf("\n");
printf("Row Pointer: ");
for (int i = 0; i <= matrix.rows; i++) {
printf("%d ", matrix.row_ptr[i]);
}
printf("\n");
printf("Column Indices: ");
for (int i = 0; i < matrix.num_elements; i++) {
printf("%d ", matrix.col_indices[i]);
}
printf("\n");
}
void printMatrixForm(CSRMatrix matrix) {
printf("Matrix Form:\n");
for (int i = 0; i < matrix.rows; i++) {
for (int j = 0; j < matrix.cols; j++) {
int value = 0;
for (int k = matrix.row_ptr[i]; k < matrix.row_ptr[i + 1]; k++) {
if (matrix.elements[k].col == j) {
value = matrix.elements[k].value;
break;
}
}
printf("%d ", value);
}
printf("\n");
}
}
void destroyCSRMatrix(CSRMatrix* matrix) {
free(matrix->elements);
free(matrix->row_ptr);
free(matrix->col_indices);
matrix->elements = NULL;
matrix->row_ptr = NULL;
matrix->col_indices = NULL;
}
int main() {
int rows = 9;
int cols = 3;
int num_elements = 5;
CSRMatrix matrix = createCSRMatrix(rows, cols, num_elements);
int col_indices[] = {0, 0, 0, 0, 1};
int row_indices[] = {3, 5, 7, 8, 7};
int values[] = {2, 1, 3, 1, 4};
initializeCSRMatrix(&matrix, values, row_indices, col_indices, num_elements);
printCSRMatrix(matrix);
printMatrixForm(matrix);
destroyCSRMatrix(&matrix);
return 0;
}