数据结构 5.2 压缩矩阵的转置

压缩矩阵：指为多个值相同的元素只分配一个存储空间，对零元素不分配存储空间。在对二维数组进行基本操作时，时间复杂度达到了n的三次方，在经过压缩之后，时间复杂度可以得到有效的降低，现在对压缩的代码进行展示。

第一步，创建

typedef int elem;

typedef struct Tripe {
	int i;
	int j;
	elem e;
}Triple,*TriplePtr;

第二步，初始化操作

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;
}

第三步，打印工作

void printCompressedMatrix(CompressedMatrixPtr paraPtr) {
	int i;
	for (i = 0; i < paraPtr->numElements; i++) {
		printf("(%d,%d):%drn", paraPtr->elements[i].i, paraPtr[i].j, paraPtr->elements[i].e);

	}//of for i
}//of printCompressedMatrix

第四步，压缩重要板块

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.
	//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

第五步，测试

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);
}

主函数

int main() {
	compressedMatrixTest();

	return 1;
}// Of main

在进行压缩式定义了两个存储单元，一个存储在转置之前，第i列一共有几个元素，另一个记录填入之后的初始位置。