我最近阅读的一本教科书讨论了行主要和列主要数组.这本书主要关注1维和2维数组,但没有真正讨论3维数组.我正在寻找一些很好的例子来帮助巩固我对使用行主列和列主数组在多维数组中寻址元素的理解.
+--+--+--+ |
/ / / /| |
+--+--+--+ + | +---+---+---+---+
/ / / /|/| | / / / / /|
+--+--+--+ + + | +---+---+---+---+ +
/ / / /|/|/| | / / / / /|/|
+--+--+--+ + + + | +---+---+---+---+ + +
/ / / /|/|/|/| | / / / / /|/|/|
+--+--+--+ + + + + | +---+---+---+---+ + + +
/ / / /|/|/|/|/ | |000|001|002|003|/|/|/|
+--+--+--+ + + + + | +---+---+---+---+ + + +
|00|01|02|/|/|/|/ | |004|005|006|007|/|/|/|
+--+--+--+ + + + | +---+---+---+---+ + + +
|03|04|05|/|/|/ | |008|009|00A|00B|/|/|/
+--+--+--+ + + | +---+---+---+---+ + +
|06|07|08|/|/ | |00C|00D|00E|00F|/|/
+--+--+--+ + | +---+---+---+---+ +
|09|0A|0B|/ | |010|011|012|013|/
+--+--+--+ | +---+---+---+---+
arr[5][3][4] | arr[3][4][5]
注意:原始问题错误地表示为arr [3] [4] [5].我了解到原始下标代表深度.已更正数据以反映预期的阵列表示.
Example hex data
+---+---+---+---+ +---+---+---+---+ +---+---+---+---+
|000|001|002|003| |100|101|102|103| |200|201|202|203|
+---+---+---+---+ +---+---+---+---+ +---+---+---+---+
|004|005|006|007| |104|105|106|107| |204|205|206|207|
+---+---+---+---+ +---+---+---+---+ +---+---+---+---+
|008|009|00A|00B| |108|109|10A|10B| |208|209|20A|20B|
+---+---+---+---+ +---+---+---+---+ +---+---+---+---+
|00C|00D|00E|00F| |10C|10D|10E|10F| |20C|20D|20E|20F|
+---+---+---+---+ +---+---+---+---+ +---+---+---+---+
|010|011|012|013| |110|111|112|113| |210|211|212|213|
+---+---+---+---+ +---+---+---+---+ +---+---+---+---+
slice 0 slice 1 slice 2
short Arr[3][4][5]; // assume array is filled with hex test data
arr[1][2][3] = 0x10B use slice 1, row 2, col 3
arr[2][3][4] = 0x210 use slice 2, row 3, col 4
resolves to row 4, col 0
行主要
{000,001,002,003,004,005,006,007,008,009,00A,00B,00C,00D,00E,00F,010011012013,100,101,102,103,104,105,106,107,108,109,10A,10B,10C,10D,10E,10F,110111112113,200,201,202,203,204,205,206,207,208,209,20A,20B,20C,20D,20E,20F,210211212213 }
专栏{000,004,008,00C,010,001,005,009,00D,011,002,006,00A,00E,012,003,007,00B,00F,013,100,104,108,10C,110,101,105,109,10D,111,102,106,10A,10E,112,103,107,10B,10F,113,200,204,208,20C ,210,201,205,209,20D,211,202,206,20A,20E,212,203,207,20B,20F,213}
Calculation offset for arr[1][2][3] using row major offset? Calculation offset for arr[1][2][3] using column major offset?
Cor*_*ker 10
我会看到Row-major order Wikipedia的文章.目前所描述的尺寸大于2也有一个很好的文章一节在这里.该文给出了使用行主要布局的三维数组的以下公式:
Address = Base + ((depthindex*col_size+colindex) * row_size + rowindex) * Element_Size
对于3D阵列:键入A [深度] [col] [行].基数是数组的起始偏移量.此外,大小变量是每个维度的不同大小.Element_Size变量表示数组组成的任何类型的大小.
假设你有一个由标准C++整数组成的行主阵列a [4] [6] [5].要计算1 [3] 2的偏移量,您可以将以下数字插入公式中:
Address = Base + ((1 * 6 + 3) * 5 + 2) * 4
对于具有列主要布局的三维数组,等式更像是:
Address = Base + ((rowindex*col_size+colindex) * depth_size + depthindex) * Element_Size
您将使用列主要布局插入上面示例的数字现在是这样的:
Address = Base + ((2 * 6 + 3) * 4 + 1) * 4
Tre*_*ith 10
不要通过专注于三维和二维来人为地约束自己.而是专注于学习解决n维数组的表达式.
表达n维寻址将巩固你对这个主题的把握,并且更容易记住一个公式,而不是单独的公式用于2d和3d寻址.
这是我对n维寻址的尝试:
#define LEN 10
int getValue_nDimensions( int * baseAddress, int * indexes, int nDimensions ) {
int i;
int offset = 0;
for( i = 0; i < nDimensions; i++ ) {
offset += pow(LEN,i) * indexes[nDimensions - (i + 1)];
}
return *(baseAddress + offset);
}
int main() {
int i;
int * baseAddress;
int val1;
int val2;
// 1 dimensions
int array1d[LEN];
int array1d_indexes[] = {2};
int array1d_nDimensions = 1;
baseAddress = &array1d[0];
for(i = 0; i < LEN; i++) { baseAddress[i] = i; }
val1 = array1d[2];
val2 = getValue_nDimensions( // Equivalent to: val1 = array1d[2];
baseAddress,
&array1d_indexes[0],
array1d_nDimensions
);
printf("SANITY CHECK: %d %d\n",val1,val2);
// 3 dimensions
int array3d[LEN][LEN][LEN];
int array3d_indexes[] = {2,3,4};
int array3d_nDimensions = 3;
baseAddress = &array3d[0][0][0];
for(i = 0; i < LEN*LEN*LEN; i++) { baseAddress[i] = i; }
val1 = array3d[2][3][4];
val2 = getValue_nDimensions( // Equivalent to: val1 = array3d[2][3][4];
baseAddress,
&array3d_indexes[0],
array3d_nDimensions
);
printf("SANITY CHECK: %d %d\n",val1,val2);
// 5 dimensions
int array5d[LEN][LEN][LEN][LEN][LEN];
int array5d_indexes[] = {2,3,4,5,6};
int array5d_nDimensions = 5;
baseAddress = &array5d[0][0][0][0][0];
for(i = 0; i < LEN*LEN*LEN*LEN*LEN; i++) { baseAddress[i] = i; }
val1 = array5d[2][3][4][5][6];
val2 = getValue_nDimensions( // Equivalent to: val1 = array5d[2][3][4][5][6];
baseAddress,
&array5d_indexes[0],
array5d_nDimensions
);
printf("SANITY CHECK: %d %d\n",val1,val2);
return 0;
}
输出:
SANITY CHECK: 2 2
SANITY CHECK: 234 234
SANITY CHECK: 23456 23456
当我问这个问题时，我希望找到一些好的 3 维数组示例。特别是代码示例。由于我没有找到任何可以理解的内容，因此我决定创建一个小 C 程序来帮助展示这个概念。它在 3x4x5 数组中使用相同的测试数据。它还包括 5x5x5 阵列的测试数据。它从行主数组创建列主数组，以便可以验证偏移计算。
数组偏移方法有：
//
// Arrays.cpp :
// Purpose: Display rowMajor & colMajor data and calculations.
//
#include "stdafx.h"
#define _show_Arrays 1 // 1=display rowMajor & colMajor arrays
#define _square_array 0 // 1=use arr[5][5][5], 0=use arr[3][4][5]
#if (_square_array == 1)
const int depthSz = 5;
const int rowSz = 5;
const int colSz = 5;
/*
+---+---+---+---+---+
|x00|x01|x02|x03|x04|
+---+---+---+---+---+
|x05|x06|x07|x08|x09|
+---+---+---+---+---+
|x0A|x0B|x0C|x0D|x0E|
+---+---+---+---+---+
|x0F|x10|x11|x12|x13|
+---+---+---+---+---+
|x14|x15|x16|x17|x18|
+---+---+---+---+---+
slice x
*/
short row_arr[depthSz][colSz][rowSz] = {
{ /* slice 0 */
{0x000,0x001,0x002,0x003,0x004},
{0x005,0x006,0x007,0x008,0x009},
{0x00A,0x00B,0x00C,0x00D,0x00E},
{0x00F,0x010,0x011,0x012,0x013},
{0x014,0x015,0x016,0x017,0x018}},
{ /* slice 1 */
{0x100,0x101,0x102,0x103,0x104},
{0x105,0x106,0x107,0x108,0x109},
{0x10A,0x10B,0x10C,0x10D,0x10E},
{0x10F,0x110,0x111,0x112,0x113},
{0x114,0x115,0x116,0x117,0x118}},
{ /* slice 2 */
{0x200,0x201,0x202,0x203,0x204},
{0x205,0x206,0x207,0x208,0x209},
{0x20A,0x20B,0x20C,0x20D,0x20E},
{0x20F,0x210,0x211,0x212,0x213},
{0x214,0x215,0x216,0x217,0x218}},
{ /* slice 3 */
{0x300,0x301,0x302,0x303,0x304},
{0x305,0x306,0x307,0x308,0x309},
{0x30A,0x30B,0x30C,0x30D,0x30E},
{0x30F,0x310,0x311,0x312,0x313},
{0x314,0x315,0x316,0x317,0x318}},
{ /* slice 4 */
{0x400,0x401,0x402,0x403,0x404},
{0x405,0x406,0x407,0x408,0x409},
{0x40A,0x40B,0x40C,0x40D,0x40E},
{0x40F,0x410,0x411,0x412,0x413},
{0x414,0x415,0x416,0x417,0x418}}
};
#else
const int depthSz = 3;
const int rowSz = 4;
const int colSz = 5;
/*
+---+---+---+---+
|000|001|002|003|
+---+---+---+---+
|004|005|006|007|
+---+---+---+---+
|008|009|00A|00B|
+---+---+---+---+
|00C|00D|00E|00F|
+---+---+---+---+
|010|011|012|013|
+---+---+---+---+
slice x
*/
short row_arr[depthSz][colSz][rowSz] = {
{ /* slice 0 */
{0x000,0x001,0x002,0x003},
{0x004,0x005,0x006,0x007},
{0x008,0x009,0x00A,0x00B},
{0x00C,0x00D,0x00E,0x00F},
{0x010,0x011,0x012,0x013}},
{ /* slice 1 */
{0x100,0x101,0x102,0x103},
{0x104,0x105,0x106,0x107},
{0x108,0x109,0x10A,0x10B},
{0x10C,0x10D,0x10E,0x10F},
{0x110,0x111,0x112,0x113}},
{ /* slice 2 */
{0x200,0x201,0x202,0x203},
{0x204,0x205,0x206,0x207},
{0x208,0x209,0x20A,0x20B},
{0x20C,0x20D,0x20E,0x20F},
{0x210,0x211,0x212,0x213}}
};
#endif
short col_arr[depthSz*colSz*rowSz]; //
char *calc_RowMajor(char *Base, int elemSz, int depth_idx, int row_idx, int col_idx)
{ // row major slice is navigated by rows
char *address;
int lbound = 0; // lower bound (0 for zero-based arrays)
address = Base /* use base passed */
+ ((depth_idx-lbound)*(colSz*rowSz*elemSz)) /* select slice */
+ ((row_idx-lbound)*rowSz*elemSz) /* select row */
+ ((col_idx-lbound)*elemSz); /* select col */
return address;
}
char *calc_ColMajor(char *Base, int elemSz, int depth_idx, int col_idx, int row_idx)
{ // col major slice is navigated by columns
char *address;
int lbound = 0; // lower bound (0 for zero-based arrays)
int pageSz = colSz*rowSz*elemSz;
int offset;
offset = (col_idx-lbound)*(colSz*elemSz) /* select column */
+ (row_idx-lbound)*(elemSz); /* select row */
if (offset >= pageSz)
{ // page overflow, rollover
offset -= (pageSz-elemSz); /* ajdust offset back onto page */
}
address = Base /* use base passed */
+ ((depth_idx-lbound)*pageSz) /* select slice */
+ offset;
return address;
}
void disp_slice(char *pStr, short *pArr,int slice,int cols, int rows)
{
printf("== %s slice %d == %p\r\n",pStr, slice,pArr+(slice*rows*cols));
for(int x=0;x<rows;x++)
{
for(int y=0;y<cols;y++)
printf("%03X ",*(pArr+(slice*rows*cols)+(x*cols)+y));
printf("\r\n");
}
}
int _tmain(int argc, _TCHAR* argv[])
{
// initialize col based array using row based array data
{ // convert row_arr into col_arr
short *pSrc = &row_arr[0][0][0];
short *pDst = &col_arr[0];
for(int d=0;d<depthSz;d++)
for(int r=0;r<rowSz;r++)
for(int c=0;c<colSz;c++)
{
*pDst++ = *(pSrc+((d*rowSz*colSz)+(c*rowSz)+r));
}
}
printf("Using Array[%d][%d][%d]\r\n",depthSz,rowSz,colSz);
#if (_show_Arrays == 1)
{ for(int x=0;x<depthSz;x++) {disp_slice("rowMajor",&row_arr[0][0][0],x,rowSz,colSz);}}
{ for(int x=0;x<depthSz;x++) {disp_slice("colMajor",&col_arr[0],x,rowSz,colSz);}}
#endif
int d = 2; // depth
int r = 3; // row
int c = 4; // column
for(d=0;d<depthSz;d++)
{
c = r = d; // simple access test pattern arr[0][0][0],arr[1][1][1],arr[2][2][2],...
{ // retrieve Array element
printf(" row_arr[%d][%d][%d] = %x\t",d,r,c,row_arr[d][r][c]);
printf("&row_arr[%d][%d][%d] = %p\r\n",d,r,c,&row_arr[d][r][c]);
}
{ // retrieve RowMajor element
short *pRowMajor = (short*)calc_RowMajor((char*)&row_arr[0][0][0],sizeof(short),d,r,c);
printf("calc_RowMajor(%d,%d,%d) = %x\t\t",d,r,c,*pRowMajor);
printf("pRowMajor = %p\r\n",pRowMajor);
}
{ // retrieve ColMajor element
short *pColMajor = (short*)calc_ColMajor((char*)&col_arr[0],sizeof(short),d,c,r);
printf("calc_ColMajor(%d,%d,%d) = %x\t\t",d,r,c,*pColMajor);
printf("pColMajor = %p\r\n",pColMajor);
}
} // for
getchar(); // just to hold the console while looking at the information
return 0;
}
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