数据结构第八天——二维数组及矩阵乘法，还有压缩矩阵的转置

第一首先是矩阵乘法

#include
#include


 
typedef struct TwoDArray{
	int rows;
	int columns;
	int **elements;
} TwoDArray, *TwoDArrayPtr;


 
typedef struct TwoDStaticArray{
	int rows;
	int columns;
	int elements[4][5];
} TwoDStaticArray, *TwoDStaticArrayPtr;


 
TwoDArrayPtr initTwoDArray(int paraRows, int paraColumns) {
	int i;
	TwoDArrayPtr resultPtr = (TwoDArrayPtr)malloc(sizeof(TwoDArray));
	resultPtr->rows = paraRows;
	resultPtr->columns = paraColumns;
	resultPtr->elements = (int **)malloc(sizeof(int *) * paraRows);
	for (i = 0; i < paraRows; i ++) {
		resultPtr->elements[i] = (int *)malloc(sizeof(int) * paraColumns);
	}
	
	return resultPtr;
}


 
void randomizeTwoDArray(TwoDArrayPtr paraPtr, int paraLowerBound, int paraUpperBound) {
	int i, j;
	for (i = 0; i < paraPtr->rows; i ++) {
		for (j = 0; j < paraPtr->columns; j ++) {
			paraPtr->elements[i][j] = rand() % (paraUpperBound - paraLowerBound) + paraLowerBound;
		}
	}
}


 
void printTwoDArray(TwoDArrayPtr paraPtr) {
	int i, j;
	for (i = 0; i < paraPtr->rows; i ++) {
		for (j = 0; j < paraPtr->columns; j ++) {
			printf("%d, ", paraPtr->elements[i][j]);
		}
		printf("n");
	}
}


 
TwoDArrayPtr matrixMultiply(TwoDArrayPtr paraPtr1, TwoDArrayPtr paraPtr2) {
	int i, j, k, sum;
	if (paraPtr1->columns != paraPtr2->rows) {
		printf("Matrices cannot be multiplied.n");
		return NULL;
	}
	
	TwoDArrayPtr resultPtr = initTwoDArray(paraPtr1->rows, paraPtr2->columns);
	
	for (i = 0; i < paraPtr1->rows; i ++) {
		for (j = 0; j < paraPtr2->columns; j ++) {
			sum = 0;
			for (k = 0; k < paraPtr1->columns; k ++) {
				sum += paraPtr1->elements[i][k] * paraPtr2->elements[k][j];
			}
			resultPtr->elements[i][j] = sum;
			printf("sum = %d, ", sum);
		}
		printf("n");
	}
	
	return resultPtr;
}

void twoDArrayTest() {
	TwoDArrayPtr tempPtr1, tempPtr2, tempPtr3;
	tempPtr1 = initTwoDArray(3, 2);
	randomizeTwoDArray(tempPtr1, 1, 5);
	printf("The first matrix:n");
	printTwoDArray(tempPtr1);
	
	tempPtr2 = initTwoDArray(2, 4);
	randomizeTwoDArray(tempPtr2, 4, 9);
	printf("The second matrix:n");
	printTwoDArray(tempPtr2);
	
	tempPtr3 = matrixMultiply(tempPtr1, tempPtr2);
	printf("The result:n");
	printTwoDArray(tempPtr3);
}


 
TwoDStaticArrayPtr initTwoDStaticArray() {
	int i, j;
	TwoDStaticArrayPtr resultPtr = (TwoDStaticArrayPtr)malloc(sizeof(TwoDStaticArray));
	resultPtr->rows = 4;
	resultPtr->columns = 5;
	for (i = 0; i < 4; i ++) {
		for (j = 0; j < 5; j ++) {
			resultPtr->elements[i][j] = i * 10 + j;
			printf("(%d, %d): %pn", i, j, &(resultPtr->elements[i][j]));
		}
	}
	
	return resultPtr;
}

int main() {
	twoDArrayTest();
	TwoDStaticArrayPtr tempPtr = initTwoDStaticArray();
	
	return 0;
}

运行结果

The first matrix:
2, 4,
3, 1,
2, 1,
The second matrix:
7, 7, 6, 8,
4, 4, 5, 6,
sum = 30, sum = 30, sum = 32, sum = 40,
sum = 25, sum = 25, sum = 23, sum = 30,
sum = 18, sum = 18, sum = 17, sum = 22,
The result:
30, 30, 32, 40,
25, 25, 23, 30,
18, 18, 17, 22,
(0, 0): 00000000001E15B8
(0, 1): 00000000001E15BC
(0, 2): 00000000001E15C0
(0, 3): 00000000001E15C4
(0, 4): 00000000001E15C8
(1, 0): 00000000001E15CC
(1, 1): 00000000001E15D0
(1, 2): 00000000001E15D4
(1, 3): 00000000001E15D8
(1, 4): 00000000001E15DC
(2, 0): 00000000001E15E0
(2, 1): 00000000001E15E4
(2, 2): 00000000001E15E8
(2, 3): 00000000001E15EC
(2, 4): 00000000001E15F0
(3, 0): 00000000001E15F4
(3, 1): 00000000001E15F8
(3, 2): 00000000001E15FC
(3, 3): 00000000001E1600
(3, 4): 00000000001E1604

首先是创建了一个静态和一个动态的二维数组，然后通过静态的二维数组可以看到，在内存空间中，二维数组是一行一行存储的

还有动态二维数组在申请空间的时候，首先是给这个整体二维数组申请了空间，然后又给其中的数组申请，给数组申请时，分为两部分，我的理解是第一部分是申请的行，第二部分申请的空间是列，这样就构成一个二维数组了

二、压缩矩阵的转置

核心：转置代码

CompressedMatrixPtr transposeCompressedMatrix(CompressedMatrixPtr paraPtr) {
	int i, tempColumn, tempPosition;
	int *tempColumnCounts = (int *)malloc(sizeof(int) * paraPtr->columns);
	int *tempOffsets = (int *)malloc(sizeof(int) * paraPtr->columns);
	for (i = 0; i < paraPtr->columns; i ++) {
		tempColumnCounts[i] = 0;
	}
	
	CompressedMatrixPtr resultPtr = (CompressedMatrixPtr)malloc(sizeof(CompressedMatrix));
	resultPtr->rows = paraPtr->columns;
	resultPtr->columns = paraPtr->rows;
	resultPtr->numElements = paraPtr->numElements;
	
	resultPtr->elements = (TriplePtr)malloc(sizeof(Triple) * paraPtr->numElements);
	
	for (i = 0; i < paraPtr->numElements; i ++) {
		tempColumnCounts[paraPtr->elements[i].j] ++;
	}
	
	tempOffsets[0] = 0;
	for (i = 1; i < paraPtr->columns; i ++) {
		tempOffsets[i] = tempOffsets[i - 1] + tempColumnCounts[i - 1];
		printf("tempOffsets[%d] = %dn", i, tempOffsets[i]);
	}
	
	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] ++;
	}
	
	return resultPtr;
}

总代码

#include
#include


 
typedef struct Tripe{
	int i;
	int j;
	int e;
} Triple, *TriplePtr;
 
typedef struct CompressedMatrix{
	int rows, columns, numElements;
	TriplePtr elements;
} CompressedMatrix, *CompressedMatrixPtr;


 
CompressedMatrixPtr initCompressedMatrix(int paraRows, int paraColumns, int paraElements, int **paraData) {
	int i;
	CompressedMatrixPtr resultPtr = (CompressedMatrixPtr)malloc(sizeof(CompressedMatrix));
	resultPtr->rows = paraRows;
	resultPtr->columns = paraColumns;
	resultPtr->numElements = paraElements;
	resultPtr->elements = (TriplePtr)malloc(sizeof(Triple) * paraElements);
	
	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];
	}
	
	return resultPtr;
}


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


 
CompressedMatrixPtr transposeCompressedMatrix(CompressedMatrixPtr paraPtr) {
	int i, tempColumn, tempPosition;
	int *tempColumnCounts = (int *)malloc(sizeof(int) * paraPtr->columns);
	int *tempOffsets = (int *)malloc(sizeof(int) * paraPtr->columns);
	for (i = 0; i < paraPtr->columns; i ++) {
		tempColumnCounts[i] = 0;
	}
	
	CompressedMatrixPtr resultPtr = (CompressedMatrixPtr)malloc(sizeof(CompressedMatrix));
	resultPtr->rows = paraPtr->columns;
	resultPtr->columns = paraPtr->rows;
	resultPtr->numElements = paraPtr->numElements;
	
	resultPtr->elements = (TriplePtr)malloc(sizeof(Triple) * paraPtr->numElements);
	
	for (i = 0; i < paraPtr->numElements; i ++) {
		tempColumnCounts[paraPtr->elements[i].j] ++;
	}
	
	tempOffsets[0] = 0;
	for (i = 1; i < paraPtr->columns; i ++) {
		tempOffsets[i] = tempOffsets[i - 1] + tempColumnCounts[i - 1];
		printf("tempOffsets[%d] = %dn", i, tempOffsets[i]);
	}
	
	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] ++;
	}
	
	return resultPtr;
}

void compressedMatrixTest() {
	CompressedMatrixPtr tempPtr1, tempPtr2;
	int i, j, tempElements;
	
	tempElements = 4;
	int ** tempMatrix1 = (int **)malloc(sizeof(int *) * tempElements);
	for (i = 0; i < tempElements; i ++) {
		tempMatrix1[i] = (int *)malloc(sizeof(int) * 3);
	}
	
	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];
		}
	}
	
	tempPtr1 = initCompressedMatrix(2, 3, 4, tempMatrix1);
	
	printf("After initializationn");
	printCompressedMatrix(tempPtr1);
	
	tempPtr2 = transposeCompressedMatrix(tempPtr1);
	printf("After transpose.n");
	printCompressedMatrix(tempPtr2);
}

int main() {
	compressedMatrixTest();
	
	return 0;
}

运行结果

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

 难点就在于tempColumnCounts和tempOffsets这两个数组

首先是tempColumnCounts，我认为，它就是用来存储原矩阵中不同的列（也就是j）的个数，如测试给出的例子，第0列的有两个，第1列的有一个，第2列的有一个，为什么要用它呢，主要是因为转置后，原矩阵的列就变成了转置矩阵的行，所以在后面排序并转置的过程中，能方便我们使用

然后是tempOffsets这个数组，首先说是这个数组代表什么意思，这个数组其实就是给转置之后的数组，给对应的行（也就是i）的数提供对应的位子，然后每当一个数找到位子后，这个位子就要往后挪一个，因为原位子已经被占了，所以就要+1

tempColumnCounts数组中，第0列的数有2个，变成转置矩阵后，那就是第0行的数了，而第0行的数肯定就是从0号位置开始，而第1列的数有一个，变成转置矩阵后，就是第1行的数，那肯定就是排完第0行的数再来排第1行的数，一行一行的排列，所以在tempOffsets中，第1行的开始位子就是2了，因为第0行占了位子0和1，所以第1行只能从位子2开始排