摘要：在平常的二位数组运用中，总是容易造成空间浪费，所以将矩阵压缩很有必要。
一、压缩矩阵转置 1、定义压缩矩阵存放原矩阵的行数、列数和有效数据的个数。
//定义的一个矩阵
typedef struct Triple{
int i;
int j;
elem e;
} Triple, *TriplePtr;
//压缩后的矩阵
typedef struct CompressedMatrix{
int rows,columns,numElements;
Triple* elements;
} CompressedMatrix, *CompressedMatrixPtr;
2、初始化
初始化是先动态分配一块动态的空间，然后将压缩后的矩阵传入并赋值。
CompressedMatrixPtr initCompressedMatrix(int paraRows, int paraColumns, int paraElements, int** paraData){
int i;
CompressedMatrixPtr resultPtr = (CompressedMatrixPtr)malloc(sizeof(struct CompressedMatrix));
resultPtr->rows = paraRows;
resultPtr->columns = paraColumns;
resultPtr->numElements = paraElements;
resultPtr->elements = (TriplePtr)malloc(paraElements * sizeof(struct Triple));
for(i = 0; i < paraElements; i ++){
resultPtr->elements[i].i = paraData[i][0];
resultPtr->elements[i].j = paraData[i][1];
resultPtr->elements[i].e = paraData[i][2];
}//Of for i
return resultPtr;
}// Of initCompressedMatrix
3、打印
void printCompressedMatrix(CompressedMatrixPtr paraPtr){
int i;
for(i = 0; i < paraPtr->numElements; i ++){
printf("(%d, %d): %drn", paraPtr->elements[i].i, paraPtr->elements[i].j, paraPtr->elements[i].e);
}//Of for i
}// Of printCompressedMatrix
4、压缩矩阵的转置
所谓矩阵的转置，就是把矩阵的行数转变为列数、把矩阵的列数转变为行数，但是数据元素不加改变。
CompressedMatrixPtr transposeCompressedMatrix(CompressedMatrixPtr paraPtr){
//Step 1. Allocate space.
int i, tempColumn, tempPosition;
int *tempColumnCounts = (int*)malloc(paraPtr->columns * sizeof(int));
int *tempOffsets = (int*)malloc(paraPtr->columns * sizeof(int));
for(i = 0; i < paraPtr->columns; i ++){
tempColumnCounts[i] = 0;
}//Of for i
CompressedMatrixPtr resultPtr = (CompressedMatrixPtr)malloc(sizeof(struct CompressedMatrix));
resultPtr->rows = paraPtr->columns;
resultPtr->columns = paraPtr->rows;
resultPtr->numElements = paraPtr->numElements;
resultPtr->elements = (TriplePtr)malloc(paraPtr->numElements * sizeof(struct Triple));
//Step 2. One scan to calculate offsets.
for(i = 0; i < paraPtr->numElements; i ++) {
tempColumnCounts[paraPtr->elements[i].j] ++;
}//Of for i
tempOffsets[0] = 0;
for(i = 1; i < paraPtr->columns; i ++){
tempOffsets[i] = tempOffsets[i - 1] + tempColumnCounts[i - 1];
printf("tempOffsets[%d] = %d rn", i, tempOffsets[i]);
}//Of for i
//Step 3. Another scan to fill data.
for(i = 0; i < paraPtr->numElements; i ++) {
tempColumn = paraPtr->elements[i].j;
tempPosition = tempOffsets[tempColumn];
resultPtr->elements[tempPosition].i = paraPtr->elements[i].j;
resultPtr->elements[tempPosition].j = paraPtr->elements[i].i;
resultPtr->elements[tempPosition].e = paraPtr->elements[i].e;
tempOffsets[tempColumn]++;
}//Of for i
return resultPtr;
}//Of transposeCompressedMatrix
5、测试函数
void compressedMatrixTest(){
CompressedMatrixPtr tempPtr1, tempPtr2;
int i, j, tempElements;
//Construct the first sample matrix.
tempElements = 4;
int** tempMatrix1 = (int**)malloc(tempElements * sizeof(int*));
for(i = 0; i < tempElements; i ++){
tempMatrix1[i] = (int*)malloc(3 * sizeof(int));
}//Of for i
int tempMatrix2[4][3] = {{0, 0, 2}, {0, 2, 3}, {2, 0, 5}, {2, 1, 6}};
for(i = 0; i < tempElements; i ++){
for(j = 0; j < 3; j ++) {
tempMatrix1[i][j] = tempMatrix2[i][j];
}//Of for j
}//Of for i
tempPtr1 = initCompressedMatrix(2, 3, 4, tempMatrix1);
printf("After initialization.rn");
printCompressedMatrix(tempPtr1);
tempPtr2 = transposeCompressedMatrix(tempPtr1);
printf("After transpose.rn");
printCompressedMatrix(tempPtr2);
}// Of main
6、完整代码
#include7、运行结果#include typedef int elem; //定义的一个矩阵 typedef struct Triple{ int i; int j; elem e; } Triple, *TriplePtr; //压缩后的矩阵 typedef struct CompressedMatrix{ int rows,columns,numElements; Triple* elements; } CompressedMatrix, *CompressedMatrixPtr; CompressedMatrixPtr initCompressedMatrix(int paraRows, int paraColumns, int paraElements, int** paraData){ int i; CompressedMatrixPtr resultPtr = (CompressedMatrixPtr)malloc(sizeof(struct CompressedMatrix)); resultPtr->rows = paraRows; resultPtr->columns = paraColumns; resultPtr->numElements = paraElements; resultPtr->elements = (TriplePtr)malloc(paraElements * sizeof(struct Triple)); for(i = 0; i < paraElements; i ++){ resultPtr->elements[i].i = paraData[i][0]; resultPtr->elements[i].j = paraData[i][1]; resultPtr->elements[i].e = paraData[i][2]; }//Of for i return resultPtr; }// Of initCompressedMatrix void printCompressedMatrix(CompressedMatrixPtr paraPtr){ int i; for(i = 0; i < paraPtr->numElements; i ++){ printf("(%d, %d): %drn", paraPtr->elements[i].i, paraPtr->elements[i].j, paraPtr->elements[i].e); }//Of for i }// Of printCompressedMatrix CompressedMatrixPtr transposeCompressedMatrix(CompressedMatrixPtr paraPtr){ //Step 1. Allocate space. int i, tempColumn, tempPosition; int *tempColumnCounts = (int*)malloc(paraPtr->columns * sizeof(int)); int *tempOffsets = (int*)malloc(paraPtr->columns * sizeof(int)); for(i = 0; i < paraPtr->columns; i ++){ tempColumnCounts[i] = 0; }//Of for i CompressedMatrixPtr resultPtr = (CompressedMatrixPtr)malloc(sizeof(struct CompressedMatrix)); resultPtr->rows = paraPtr->columns; resultPtr->columns = paraPtr->rows; resultPtr->numElements = paraPtr->numElements; resultPtr->elements = (TriplePtr)malloc(paraPtr->numElements * sizeof(struct Triple)); //Step 2. One scan to calculate offsets. for(i = 0; i < paraPtr->numElements; i ++) { tempColumnCounts[paraPtr->elements[i].j] ++; }//Of for i tempOffsets[0] = 0; for(i = 1; i < paraPtr->columns; i ++){ tempOffsets[i] = tempOffsets[i - 1] + tempColumnCounts[i - 1]; printf("tempOffsets[%d] = %d rn", i, tempOffsets[i]); }//Of for i //Step 3. Another scan to fill data. for(i = 0; i < paraPtr->numElements; i ++) { tempColumn = paraPtr->elements[i].j; tempPosition = tempOffsets[tempColumn]; resultPtr->elements[tempPosition].i = paraPtr->elements[i].j; resultPtr->elements[tempPosition].j = paraPtr->elements[i].i; resultPtr->elements[tempPosition].e = paraPtr->elements[i].e; tempOffsets[tempColumn]++; }//Of for i return resultPtr; }//Of transposeCompressedMatrix void compressedMatrixTest(){ CompressedMatrixPtr tempPtr1, tempPtr2; int i, j, tempElements; //Construct the first sample matrix. tempElements = 4; int** tempMatrix1 = (int**)malloc(tempElements * sizeof(int*)); for(i = 0; i < tempElements; i ++){ tempMatrix1[i] = (int*)malloc(3 * sizeof(int)); }//Of for i int tempMatrix2[4][3] = {{0, 0, 2}, {0, 2, 3}, {2, 0, 5}, {2, 1, 6}}; for(i = 0; i < tempElements; i ++){ for(j = 0; j < 3; j ++) { tempMatrix1[i][j] = tempMatrix2[i][j]; }//Of for j }//Of for i tempPtr1 = initCompressedMatrix(2, 3, 4, tempMatrix1); printf("After initialization.rn"); printCompressedMatrix(tempPtr1); tempPtr2 = transposeCompressedMatrix(tempPtr1); printf("After transpose.rn"); printCompressedMatrix(tempPtr2); }// Of main int main(){ compressedMatrixTest(); return 1; }// Of main
After initialization. (0, 0): 2 (0, 2): 3 (2, 0): 5 (2, 1): 6 tempOffsets[1] = 2 tempOffsets[2] = 3 After transpose. (0, 0): 2 (0, 2): 5 (1, 2): 6 (2, 0): 3
总结：在实现压缩矩阵的转置中，代码中有多次的for循环的运用，在不同的代码块理解起来有一定的难道，所以强烈建议读者朋友们画一画图，在不能理解的地方多次跟踪。
