特殊矩阵压缩存储的代码实现

为了更好地理解特殊矩阵的压缩存储，下面提供一些C语言的代码示例，展示如何实现这些矩阵的压缩存储和操作。

1. 稀疏矩阵的三元组表示

#include <stdio.h>#define MAX_TERMS 100typedef struct {int row;int col;int value;
} Triple;typedef struct {Triple data[MAX_TERMS];int rows;int cols;int terms;
} SparseMatrix;// 创建一个稀疏矩阵
void createSparseMatrix(SparseMatrix *m, int rows, int cols, int elements[][3], int num) {m->rows = rows;m->cols = cols;m->terms = num;for (int i = 0; i < num; i++) {m->data[i].row = elements[i][0];m->data[i].col = elements[i][1];m->data[i].value = elements[i][2];}
}// 打印稀疏矩阵
void printSparseMatrix(SparseMatrix *m) {for (int i = 0; i < m->terms; i++) {printf("(%d, %d, %d)\n", m->data[i].row, m->data[i].col, m->data[i].value);}
}int main() {SparseMatrix m;int elements[][3] = {{0, 2, 3},{1, 0, 4},{2, 1, 5}};createSparseMatrix(&m, 3, 3, elements, 3);printSparseMatrix(&m);return 0;
}

2. 对称矩阵的压缩存储

#include <stdio.h>#define MAX_SIZE 100typedef struct {int data[MAX_SIZE];int n;
} SymmetricMatrix;// 创建一个对称矩阵
void createSymmetricMatrix(SymmetricMatrix *m, int n, int elements[]) {m->n = n;for (int i = 0; i < n * (n + 1) / 2; i++) {m->data[i] = elements[i];}
}// 获取对称矩阵中的元素
int getElement(SymmetricMatrix *m, int i, int j) {if (i >= j) {return m->data[i * (i + 1) / 2 + j];} else {return m->data[j * (j + 1) / 2 + i];}
}// 打印对称矩阵
void printSymmetricMatrix(SymmetricMatrix *m) {for (int i = 0; i < m->n; i++) {for (int j = 0; j < m->n; j++) {printf("%d ", getElement(m, i, j));}printf("\n");}
}int main() {SymmetricMatrix m;int elements[] = {1, 2, 3, 4, 5, 6};createSymmetricMatrix(&m, 3, elements);printSymmetricMatrix(&m);return 0;
}

3. 上三角矩阵的压缩存储

#include <stdio.h>#define MAX_SIZE 100typedef struct {int data[MAX_SIZE];int n;
} UpperTriangularMatrix;// 创建一个上三角矩阵
void createUpperTriangularMatrix(UpperTriangularMatrix *m, int n, int elements[]) {m->n = n;for (int i = 0; i < n * (n + 1) / 2; i++) {m->data[i] = elements[i];}
}// 获取上三角矩阵中的元素
int getElement(UpperTriangularMatrix *m, int i, int j) {if (i > j) {return 0;} else {return m->data[i * m->n - i * (i - 1) / 2 + j - i];}
}// 打印上三角矩阵
void printUpperTriangularMatrix(UpperTriangularMatrix *m) {for (int i = 0; i < m->n; i++) {for (int j = 0; j < m->n; j++) {printf("%d ", getElement(m, i, j));}printf("\n");}
}int main() {UpperTriangularMatrix m;int elements[] = {1, 2, 3, 4, 5, 6};createUpperTriangularMatrix(&m, 3, elements);printUpperTriangularMatrix(&m);return 0;
}

通过这些代码示例，我们可以更清楚地理解特殊矩阵的压缩存储方法，并在实际应用中实现高效的存储和操作。