transform matrix 2D to 1D

2019-02-17 05:15发布

站内文章 / C
11 0 0

问题:

I have an issue passing a matrix 2D to a vector(1D array)with function in C. There is the code of what i want to create:

#include <stdio.h>
#define N  64
#define A  8


int tab2[A][A];
int vect[N];
void fonc(int i,int j,int k,int l,int c,int **tab2,int *vect);

void fonc(int i,int j,int k,int l,int c,int **tab2,int *vect){

vect[k]=tab2[0][0];
printf("%d",vect[k]);
  while(i!=8 && j!=8)
    {
        //bas
        i=i;
    j=j+1;


    vect[k]++;
      printf("%d\t",vect[k]);
    //descente
    while(j !=0)
    {
     i=i+1;
     j=j-1;

     vect[k]++;
    }

    //droite
    i=i;
    j=j+1;

    vect[k]++;
     //montée
    while(i !=0)
    {
     i=i-1;
     j=j+1;

     vect[k]++;
    }
    }

}



int main (){
    int vect[64] ;
int tab2[8][8]={
{1, 2, 6, 7, 15, 16 ,28 ,1},
{3, 5, 8, 14, 17 ,27 ,29 ,1},
{4, 9, 13, 18, 26, 30, 39 ,1},
{10, 12, 19, 25, 31 ,38 ,40 ,1},
{11, 20 ,24, 32 ,37 ,41 ,46 ,1} ,
{21 ,23, 33, 36, 42, 45, 47 ,1},
{22, 34 ,35, 43, 44, 48, 49 ,1},
{22, 34 ,35, 43, 44, 48, 49 ,1}};
    int i;
    int j;
    int k;

fonc(i,j,k,8,8,tab2,vect);
//printf("%d\n", ) ;//limpide !
return 0;
}

i don't have errors but it debug i can't the result somoene have an idea how can i do , i use the function to applied a zigzag linear transform for jpeg compression RLE codingthank you for all i try to do this : 

0, 0
0, 1    1, 0
2, 0    1, 1    0, 2
0, 3    1, 2    2, 1    3, 0
4, 0    3, 1    2, 2    1, 3    0, 4
0, 5    1, 4    2, 3    3, 2    4, 1    5, 0
6, 0    5, 1    4, 2    3, 3    2, 4    1, 5    0, 6
0, 7    1, 6    2, 5    3, 4    4, 3    5, 2    6, 1    7, 0
7, 1    6, 2    5, 3    4, 4    3, 5    2, 6    1, 7
2, 7    3, 6    4, 5    5, 4    6, 3    7, 2

回答1:

Your function has 3 unnecessary parameters — i, j, k. The values passed in main() to the function are uninitialized; the values passed in i and j in the function are irrelevant because the code sets the variables on first use. The value in k is used but the value passed to the function is indeterminate. That needs to be changed so that there are three fewer parameters and they're just local variables in the function, and they all need to be set to zero. (k is the index in the vector where the next value from the matrix should be assigned; i and j are the subscripts of the array).

You should lose the two global variables; they're never referenced because the local variables in main() hide them and the parameters to the function hide them. The two #define values are never used either.

Although you pass l and c (lines and columns), you ignore them and assume the upper bounds are l = 8 and c = 8. Also, the type you try to pass to fonc is not int **tab2; it is int tab2[][8] or int tab2[8][8]. The function signature may as well become:

void fonc(int tab2[8][8], int *vect);

In your function, every assignment of the form vect[k]++; should be an assignment of the form vect[k++] = tab2[i][j];.

The zig-zag algorithm is fiddly to code. For an 8x8 fixed-size matrix, it is tempting just to pack the the sequence of indexes into an array. I'm assuming that the top-left corner of the zig-zag diagram is (0, 0) and the bottom-right is (7, 7). If that's wrong, you simply have to fix the initializer for the table.

static const struct ZigZag
{
    unsigned char y, x;  // Reversed from original
} zigzag[] =
{
    { 0, 0 }, { 1, 0 }, { 0, 1 }, { 0, 2 },
    { 1, 1 }, { 2, 0 }, { 3, 0 }, { 2, 1 },
    { 1, 2 }, { 0, 3 }, { 0, 4 }, { 1, 3 },
    ...
    { 7, 5 }, { 7, 6 }, { 6, 7 }, { 7, 7 },
};

The correct copying operation is then simple:

for (int i = 0; i < 64; i++)
    vect[i] = tab[zigzag[i].x][zigzag[i].y];

We can debate about writing 64 vs sizeof(zigzag)/sizeof(zigzag[0]). If you're really short of memory (the data is only 128 bytes at the moment, so I don't believe you), then you could pack the two coordinates into one byte for storage:

static const unsigned char zigzag[] =
{
    0x00, 0x10, 0x01, 0x02, ...
};

and then use a more complex subscripting expression:

vect[i] = tab[zigzag[i] >> 4][zigzag[i] & 0xF];

It might be faster due to fewer memory accesses — you'd have to measure.

This all assumes you're dealing with 8x8 fixed size square arrays. If you have to deal with any size of array and still do the job, then you probably have to encode things so that you specify the starting point, you go one step right, you go down diagonally left until you reach an edge (left or bottom), you go one step down or right, you go up diagonally right until you reach an edge (top or right), you go one step right or down, and repeat until you reach the end. That is fiddly to code neatly; the copying loop won't be two lines.

Instrumented code from question

Here is the code from the question, somewhat cleaned up but with the core algorithm in fonc() unchanged — at least, unchanged in the handling of i, j, and k except for initializing them. The main function prints out the matrix before, and the vector after, the call to fonc(). Each assignment in fonc() to the vector has been fixed and instrumented.

#include <stdio.h>

void fonc(int tab2[8][8], int *vect);

void fonc(int tab2[8][8], int *vect)
{
    int i = 0;
    int j = 0;
    int k = 0;

    vect[k] = tab2[i][j];
    printf("v[%2d] = m[%2d][%2d] = %d\n", k, i, j, tab2[i][j]);

    while (i != 8 && j != 8)
    {
        // bas
        i = i;
        j = j+1;
        vect[k++] = tab2[i][j];
        printf("v[%2d] = m[%2d][%2d] = %d\n", k, i, j, tab2[i][j]);

        // descente
        while (j != 0)
        {
            i = i+1;
            j = j-1;
            vect[k++] = tab2[i][j];
            printf("v[%2d] = m[%2d][%2d] = %d\n", k, i, j, tab2[i][j]);
        }

        // droite
        i = i;
        j = j+1;
        vect[k++] = tab2[i][j];
        printf("v[%2d] = m[%2d][%2d] = %d\n", k, i, j, tab2[i][j]);

        // montée
        while (i != 0)
        {
            i = i-1;
            j = j+1;
            printf("v[%2d] = m[%2d][%2d] = %d\n", k, i, j, tab2[i][j]);
            vect[k++] = tab2[i][j];
        }
    }
}

int main(void)
{
    int vect[64];
    int tab2[8][8] =
    {
        // Up to element value 28, the data should appear in
        // the order 1, 2, 3, ... in the output vector
        {1, 2, 6, 7, 15, 16, 28, 1},
        {3, 5, 8, 14, 17, 27, 29, 1},
        {4, 9, 13, 18, 26, 30, 39, 1},
        {10, 12, 19, 25, 31, 38, 40, 1},
        {11, 20, 24, 32, 37, 41, 46, 1},
        {21, 23, 33, 36, 42, 45, 47, 1},
        {22, 34, 35, 43, 44, 48, 49, 1},
        {22, 34, 35, 43, 44, 48, 49, 1}
    };

    for (int i = 0; i < 8; i++)
    {
        for (int j = 0; j < 8; j++)
            printf("%3d", tab2[i][j]);
        putchar('\n');
    }

    fonc(tab2, vect);

    for (int i = 0; i < 8 * 8; i++)
    {
        printf("%3d", vect[i]);
        if (i % 8 == 7)
            putchar('\n');
    }

    return 0;
}

Sample output:

  1  2  6  7 15 16 28  1
  3  5  8 14 17 27 29  1
  4  9 13 18 26 30 39  1
 10 12 19 25 31 38 40  1
 11 20 24 32 37 41 46  1
 21 23 33 36 42 45 47  1
 22 34 35 43 44 48 49  1
 22 34 35 43 44 48 49  1
v[ 0] = m[ 0][ 0] = 1
v[ 1] = m[ 0][ 1] = 2
v[ 2] = m[ 1][ 0] = 3
v[ 3] = m[ 1][ 1] = 5
v[ 3] = m[ 0][ 2] = 6
v[ 5] = m[ 0][ 3] = 7
v[ 6] = m[ 1][ 2] = 8
v[ 7] = m[ 2][ 1] = 9
v[ 8] = m[ 3][ 0] = 10
v[ 9] = m[ 3][ 1] = 12
v[ 9] = m[ 2][ 2] = 13
v[10] = m[ 1][ 3] = 14
v[11] = m[ 0][ 4] = 15
v[13] = m[ 0][ 5] = 16
v[14] = m[ 1][ 4] = 17
v[15] = m[ 2][ 3] = 18
v[16] = m[ 3][ 2] = 19
v[17] = m[ 4][ 1] = 20
v[18] = m[ 5][ 0] = 21
v[19] = m[ 5][ 1] = 23
v[19] = m[ 4][ 2] = 24
v[20] = m[ 3][ 3] = 25
v[21] = m[ 2][ 4] = 26
v[22] = m[ 1][ 5] = 27
v[23] = m[ 0][ 6] = 28
v[25] = m[ 0][ 7] = 1
v[26] = m[ 1][ 6] = 29
v[27] = m[ 2][ 5] = 30
v[28] = m[ 3][ 4] = 31
v[29] = m[ 4][ 3] = 32
v[30] = m[ 5][ 2] = 33
v[31] = m[ 6][ 1] = 34
v[32] = m[ 7][ 0] = 22
v[33] = m[ 7][ 1] = 34
v[33] = m[ 6][ 2] = 35
v[34] = m[ 5][ 3] = 36
v[35] = m[ 4][ 4] = 37
v[36] = m[ 3][ 5] = 38
v[37] = m[ 2][ 6] = 39
v[38] = m[ 1][ 7] = 1
v[39] = m[ 0][ 8] = 3
  2  3  5  6  7  8  9 10
 12 13 14 15 16 17 18 19
 20 21 23 24 25 26 27 28
  1 29 30 31 32 33 34 22
 34 35 36 37 38 39  1  3
  0  0  0  0  0  0  0  0
  0  0  0  0  0  0  0  0
  0  0  0  0  0  0  0  0

Note that:

  1. You access tab2[0][8] which is out of bounds.
  2. Your algorithm runs into problems when your diagonal motions hit the bottom or right side of the matrix.
  3. If you don't have C99 and VLA support, handling variable NxM arrays will be a pain.

Table-driven Program

#include <stdio.h>

void fonc(int tab2[8][8], int vect[8]);

void fonc(int tab2[8][8], int vect[8])
{
    static const struct ZigZag
    {
        unsigned char y, x;
    } zigzag[8*8] =
    {
        { 0, 0 }, { 1, 0 }, { 0, 1 }, { 0, 2 },
        { 1, 1 }, { 2, 0 }, { 3, 0 }, { 2, 1 },
        { 1, 2 }, { 0, 3 }, { 0, 4 }, { 1, 3 },
        { 2, 2 }, { 3, 1 }, { 4, 0 }, { 5, 0 },
        { 4, 1 }, { 3, 2 }, { 2, 3 }, { 1, 4 },
        { 0, 5 }, { 0, 6 }, { 1, 5 }, { 2, 4 },
        { 3, 3 }, { 4, 2 }, { 5, 1 }, { 6, 0 },
        { 7, 0 }, { 6, 1 }, { 5, 2 }, { 4, 3 },
        { 3, 4 }, { 2, 5 }, { 1, 6 }, { 0, 7 },
        { 1, 7 }, { 2, 6 }, { 3, 5 }, { 4, 4 },
        { 5, 3 }, { 6, 2 }, { 7, 1 }, { 7, 2 },
        { 6, 3 }, { 5, 4 }, { 4, 5 }, { 3, 6 },
        { 2, 7 }, { 3, 7 }, { 4, 6 }, { 5, 5 },
        { 6, 4 }, { 7, 3 }, { 7, 4 }, { 6, 5 },
        { 5, 6 }, { 4, 7 }, { 5, 7 }, { 6, 6 },
        { 7, 5 }, { 7, 6 }, { 6, 7 }, { 7, 7 },
    };

    for (int i = 0; i < 64; i++)
        vect[i] = tab2[zigzag[i].x][zigzag[i].y];
}

// The output vector should be in order 1..64
int main(void)
{
    int vect[64];
    int tab2[8][8] =
    {
        {  1,  2,  6,  7, 15, 16, 28, 29 },
        {  3,  5,  8, 14, 17, 27, 30, 43 },
        {  4,  9, 13, 18, 26, 31, 42, 44 },
        { 10, 12, 19, 25, 32, 41, 45, 54 },
        { 11, 20, 24, 33, 40, 46, 53, 55 },
        { 21, 23, 34, 39, 47, 52, 56, 61 },
        { 22, 35, 38, 48, 51, 57, 60, 62 },
        { 36, 37, 49, 50, 58, 59, 63, 64 }
    };

    puts("Matrix:");
    for (int i = 0; i < 8; i++)
    {
        for (int j = 0; j < 8; j++)
            printf("%3d", tab2[i][j]);
        putchar('\n');
    }

    fonc(tab2, vect);

    puts("Vector:");
    for (int i = 0; i < 8 * 8; i++)
    {
        printf("%3d", vect[i]);
        if (i % 8 == 7)
            putchar('\n');
    }

    return 0;
}

Sample output:

Matrix:
  1  2  6  7 15 16 28 29
  3  5  8 14 17 27 30 43
  4  9 13 18 26 31 42 44
 10 12 19 25 32 41 45 54
 11 20 24 33 40 46 53 55
 21 23 34 39 47 52 56 61
 22 35 38 48 51 57 60 62
 36 37 49 50 58 59 63 64
Vector:
  1  2  3  4  5  6  7  8
  9 10 11 12 13 14 15 16
 17 18 19 20 21 22 23 24
 25 26 27 28 29 30 31 32
 33 34 35 36 37 38 39 40
 41 42 43 44 45 46 47 48
 49 50 51 52 53 54 55 56
 57 58 59 60 61 62 63 64

Instrumented version of code by Anonymous

Anonymous provided an answer. It's very interesting in concept, but I'm not sure it is accurate. Instrumenting it so that it prints its input and output is not conclusive, so I put in the same table as in the code above which should yield the vector 1..64. The code and output are:

#include <stdio.h>

#define max(a, b) ((a) > (b) ? (a) : (b))
#define min(a, b) ((a) > (b) ? (b) : (a))

void dezigzag(int out[64], int in[8][8])
{
    int n = 0;
    for (int diag = 0; diag < 15; diag++)
    {
        for (int i = max(0, diag - 7); i <= min(7, diag); i++)
            out[n++] = diag % 2 ? in[diag - i][i] : in[i][diag - i];
    }
}

int main(void)
{
    int out[64] = {-1};
    int in[8][8];

    for (int i = 0; i < 64; i++)
        in[i % 8][i / 8] = i;

    puts("Matrix:");
    for (int i = 0; i < 8; i++)
    {
        for (int j = 0; j < 8; j++)
            printf("%3d", in[i][j]);
        putchar('\n');
    }

    dezigzag(out, in);

    puts("Vector:");
    for (int i = 0; i < 8 * 8; i++)
    {
        printf("%3d", out[i]);
        if (i % 8 == 7)
            putchar('\n');
    }

    //for (int i = 0; i < 64; i++) {
    //    printf("%d: %d\n", i, out[i]);
    //}

    int tab2[8][8] =
    {
        {  1,  2,  6,  7, 15, 16, 28, 29 },
        {  3,  5,  8, 14, 17, 27, 30, 43 },
        {  4,  9, 13, 18, 26, 31, 42, 44 },
        { 10, 12, 19, 25, 32, 41, 45, 54 },
        { 11, 20, 24, 33, 40, 46, 53, 55 },
        { 21, 23, 34, 39, 47, 52, 56, 61 },
        { 22, 35, 38, 48, 51, 57, 60, 62 },
        { 36, 37, 49, 50, 58, 59, 63, 64 },
    };

    puts("Matrix:");
    for (int i = 0; i < 8; i++)
    {
        for (int j = 0; j < 8; j++)
            printf("%3d", tab2[i][j]);
        putchar('\n');
    }

    dezigzag(out, tab2);

    puts("Vector:");
    for (int i = 0; i < 8 * 8; i++)
    {
        printf("%3d", out[i]);
        if (i % 8 == 7)
            putchar('\n');
    }

    return 0;
}

Output:

Matrix:
  0  8 16 24 32 40 48 56
  1  9 17 25 33 41 49 57
  2 10 18 26 34 42 50 58
  3 11 19 27 35 43 51 59
  4 12 20 28 36 44 52 60
  5 13 21 29 37 45 53 61
  6 14 22 30 38 46 54 62
  7 15 23 31 39 47 55 63
Vector:
  0  1  8 16  9  2  3 10
 17 24 32 25 18 11  4  5
 12 19 26 33 40 48 41 34
 27 20 13  6  7 14 21 28
 35 42 49 56 57 50 43 36
 29 22 15 23 30 37 44 51
 58 59 52 45 38 31 39 46
 53 60 61 54 47 55 62 63
Matrix:
  1  2  6  7 15 16 28 29
  3  5  8 14 17 27 30 43
  4  9 13 18 26 31 42 44
 10 12 19 25 32 41 45 54
 11 20 24 33 40 46 53 55
 21 23 34 39 47 52 56 61
 22 35 38 48 51 57 60 62
 36 37 49 50 58 59 63 64
Vector:
  1  3  2  6  5  4 10  9
  8  7 15 14 13 12 11 21
 20 19 18 17 16 28 27 26
 25 24 23 22 36 35 34 33
 32 31 30 29 43 42 41 40
 39 38 37 49 48 47 46 45
 44 54 53 52 51 50 58 57
 56 55 61 60 59 63 62 64

That result isn't quite right, but I'm sure it is the correct direction. (Equally clearly, this is too complex to put in a comment to Anonymous's question — hence this addition here.)

Conceptually, the code is turning the square matrix so that it is standing on its points, and then scanning horizontally back and forth over the (8 + 8 - 1) lines.

ASCII art for a 3x3 scan:

   /\
  /\/\
 /\/\/\
 \/\/\/
  \/\/
   \/

There are (3 + 3 - 1) = 5 scan rows. In the table driven code, there is a regularity to the data that corresponds to this.

To fix Anonymous's code

In the function dezigzag(), the assignment line needs to invert the condition. The existing code is equivalent to:

out[n++] = (diag % 2 == 1) ? in[diag - i][i] : in[i][diag - i];

The correct code is:

out[n++] = (diag % 2 == 0) ? in[diag - i][i] : in[i][diag - i];

The output is then:

Matrix:
  0  8 16 24 32 40 48 56
  1  9 17 25 33 41 49 57
  2 10 18 26 34 42 50 58
  3 11 19 27 35 43 51 59
  4 12 20 28 36 44 52 60
  5 13 21 29 37 45 53 61
  6 14 22 30 38 46 54 62
  7 15 23 31 39 47 55 63
Vector:
  0  8  1  2  9 16 24 17
 10  3  4 11 18 25 32 40
 33 26 19 12  5  6 13 20
 27 34 41 48 56 49 42 35
 28 21 14  7 15 22 29 36
 43 50 57 58 51 44 37 30
 23 31 38 45 52 59 60 53
 46 39 47 54 61 62 55 63
Matrix:
  1  2  6  7 15 16 28 29
  3  5  8 14 17 27 30 43
  4  9 13 18 26 31 42 44
 10 12 19 25 32 41 45 54
 11 20 24 33 40 46 53 55
 21 23 34 39 47 52 56 61
 22 35 38 48 51 57 60 62
 36 37 49 50 58 59 63 64
Vector:
  1  2  3  4  5  6  7  8
  9 10 11 12 13 14 15 16
 17 18 19 20 21 22 23 24
 25 26 27 28 29 30 31 32
 33 34 35 36 37 38 39 40
 41 42 43 44 45 46 47 48
 49 50 51 52 53 54 55 56
 57 58 59 60 61 62 63 64

Code to handle MxN arrays

#include <stdio.h>

static inline int max(int a, int b) { return (a > b) ? a : b; }
static inline int min(int a, int b) { return (a < b) ? a : b; }

static void print_info(int rows, int cols)
{
    int n = rows + cols - 1;
    printf("R = %d, C = %d, N = %d\n", rows, cols, n);
    for (int i = 0; i < n; i++)
    {
        int max_x = min(i, cols-1);
        int min_x = max(0, i - n + cols);
        int max_y = min(i, rows-1);
        int min_y = max(0, i - n + rows);
        printf("i = %d, min_x = %d, max_x = %d, min_y = %d, max_y = %d\n",
                i, min_x, max_x, min_y, max_y);
    }

    for (int i = 0; i < n; i++)
    {
        printf("%2d:", i);
        if (i % 2 == 0)
        {
            int max_x = min(i, cols-1);
            int min_x = max(0, i - n + cols);
            for (int j = min_x; j <= max_x; j++)
                /* (row,col) */
                printf(" (r=%d,c=%d)", i - j, j);
        }
        else
        {
            int max_y = min(i, rows-1);
            int min_y = max(0, i - n + rows);
            for (int j = min_y; j <= max_y; j++)
                printf(" (r=%d,c=%d)", j, i - j);
        }
        putchar('\n');
    }
}

static void set_zigzag(int rows, int cols, int matrix[rows][cols])
{
    int x = 0;
    int n = rows + cols - 1;
    for (int i = 0; i < n; i++)
    {
        if (i % 2 == 0)
        {
            int max_x = min(i, cols-1);
            int min_x = max(0, i - n + cols);
            for (int j = min_x; j <= max_x; j++)
                matrix[i-j][j] = x++;
        }
        else
        {
            int max_y = min(i, rows-1);
            int min_y = max(0, i - n + rows);
            for (int j = min_y; j <= max_y; j++)
                matrix[j][i-j] = x++;
        }
    }
}

static void zigzag(int rows, int cols, int matrix[rows][cols], int vector[rows*cols])
{
    int n = rows + cols - 1;
    int v = 0;
    for (int i = 0; i < n; i++)
    {
        if (i % 2 == 0)
        {
            int max_x = min(i, cols-1);
            int min_x = max(0, i - n + cols);
            for (int j = min_x; j <= max_x; j++)
                vector[v++] = matrix[i-j][j];
        }
        else
        {
            int max_y = min(i, rows-1);
            int min_y = max(0, i - n + rows);
            for (int j = min_y; j <= max_y; j++)
                vector[v++] = matrix[j][i-j];
        }
    }
}

static void dump_matrix(const char *tag, int rows, int cols, int matrix[rows][cols])
{
    printf("%s (%d x %d):\n", tag, rows, cols);
    for (int i = 0; i < rows; i++)
    {
        for (int j = 0; j < cols; j++)
            printf("%3d", matrix[i][j]);
        putchar('\n');
    }
}

static void dump_vector(const char *tag, int rows, int cols, int vector[rows * cols])
{
    printf("%s (%d : %d):\n", tag, rows, cols);
    for (int i = 0; i < rows * cols; i++)
    {
        printf("%3d", vector[i]);
        if (i % cols == cols - 1)
            putchar('\n');
    }
}

static void test_rows_x_cols(int rows, int cols)
{
    int vector[rows * cols];
    int matrix[rows][cols];

    printf("\nTest %dx%d\n\n", rows, cols);
    print_info(rows, cols);
    set_zigzag(rows, cols, matrix);
    dump_matrix("Matrix", rows, cols, matrix);
    zigzag(rows, cols, matrix, vector);
    dump_vector("Vector", rows, cols, vector);
}

int main(void)
{
    struct
    {
        int rows;
        int cols;
    } test[] =
    {
        { 4, 4 }, { 6, 4 }, { 4, 7 }, { 7, 14 }, { 6, 16 }, { 3, 33 },
    };
    enum { NUM_TEST = sizeof(test) / sizeof(test[0]) };

    for (int i = 0; i < NUM_TEST; i++)
        test_rows_x_cols(test[i].rows, test[i].cols);

    return 0;
}

Code using iterator structure

The iterator structure is fairly complex. The use of multiple one-line inline functions is extreme, but avoids repeating expressions. There is room for cleanup, I'm sure, but it was time to stop having fun.

#include <assert.h>
#include <limits.h>
#include <stdbool.h>
#include <stdio.h>

typedef struct RC
{
    int row;
    int col;
} RC;

typedef struct RLE
{
    RC  curr;
    RC  size;
    int zigzag;
    int sequence;
} RLE;

static inline int max(int a, int b) { return (a > b) ? a : b; }
static inline int min(int a, int b) { return (a < b) ? a : b; }

static inline int get_num_zigzags(const RLE *rle)
{
    return rle->size.row + rle->size.col - 1;
}

static inline int get_max_row(const RLE *rle)
{
    return min(rle->zigzag, rle->size.row - 1);
}

static inline int get_min_row(const RLE *rle)
{
    return max(0, rle->zigzag - get_num_zigzags(rle) + rle->size.row);
}

static inline int get_max_col(const RLE *rle)
{
    return min(rle->zigzag, rle->size.col - 1);
}

static inline int get_min_col(const RLE *rle)
{
    return max(0, rle->zigzag - get_num_zigzags(rle) + rle->size.col);
}

static inline int get_row_from_col(const RLE *rle)
{
    return rle->zigzag - rle->curr.col;
}

static inline int get_col_from_row(const RLE *rle)
{
    return rle->zigzag - rle->curr.row;
}

static RLE RLE_init(int rows, int cols)
{
    RLE rle;
    assert(rows > 0 && cols > 0);
    assert(INT_MAX / rows >= cols);
    rle.curr.row = 0;
    rle.curr.col = 0;
    rle.size.row = rows;
    rle.size.col = cols;
    rle.zigzag = 0;
    rle.sequence = 0;
    return(rle);
}

static inline RC RLE_position(const RLE *rle)
{
    return rle->curr;
}

static inline int RLE_row(const RLE *rle)
{
    return rle->curr.row;
}

static inline int RLE_col(const RLE *rle)
{
    return rle->curr.col;
}

static inline int RLE_sequence(const RLE *rle)
{
    return rle->sequence;
}

static inline int RLE_zigzag(const RLE *rle)
{
    return rle->zigzag;
}

static inline RC RLE_size(const RLE *rle)
{
    return rle->size;
}

static inline bool RLE_finished(const RLE *rle)
{
    return(rle->sequence == rle->size.row * rle->size.col);
}

static void RLE_check(const RLE *rle)
{
    assert(rle->size.row > 0);
    assert(rle->size.col > 0);
    assert(rle->curr.row < rle->size.row && rle->curr.row >= 0);
    assert(rle->curr.col < rle->size.col && rle->curr.col >= 0);
    assert(rle->zigzag >= 0 && rle->zigzag < rle->size.row + rle->size.col - 1);
    assert(rle->sequence >= 0 && rle->sequence <= rle->size.row * rle->size.col);
}

#if defined(REL_DUMP_REQUIRED)
static void RLE_dump(const char *tag, const RLE *rle)
{
    printf("Dump RLE (%s):", tag);
    RC size = RLE_size(rle);
    assert(size.row == rle->size.row);
    assert(size.col == rle->size.col);
    printf("    Rows = %2d, Cols = %2d, Zigzags = %2d; ",
           rle->size.row, rle->size.col, rle->size.row + rle->size.col - 1);
    RC posn = RLE_position(rle);
    assert(posn.row == rle->curr.row);
    assert(posn.col == rle->curr.col);
    assert(posn.row == RLE_row(rle));
    assert(posn.col == RLE_col(rle));
    printf(" Position: r = %d, c = %d; ", RLE_row(rle), RLE_col(rle));
    assert(RLE_zigzag(rle) == rle->zigzag);
    assert(RLE_sequence(rle) == rle->sequence);
    printf(" Zigzag = %d, Sequence = %d\n", rle->zigzag, rle->sequence);
    RLE_check(rle);
}
#endif

static void RLE_next(RLE *rle)
{
    RLE_check(rle);

    /* Already finished? */
    if (RLE_finished(rle))
        return;
    rle->sequence++;
    /* Finished now? */
    if (RLE_finished(rle))
        return;

    if (rle->zigzag % 2 == 0)
    {
        if (rle->curr.col < get_max_col(rle))
        {
            /* Same zigzag */
            rle->curr.col++;
            rle->curr.row = get_row_from_col(rle);
        }
        else
        {
            /* Next zigzag */
            rle->zigzag++;
            rle->curr.row = get_min_row(rle);
            rle->curr.col = get_col_from_row(rle);
        }
    }
    else
    {
        if (rle->curr.row < get_max_row(rle))
        {
            /* Same zigzag */
            rle->curr.row++;
            rle->curr.col = get_col_from_row(rle);
        }
        else
        {
            /* Next zigzag */
            rle->zigzag++;
            rle->curr.col = get_min_col(rle);
            rle->curr.row = get_row_from_col(rle);
        }
    }
}

static void print_info(int rows, int cols)
{
    int n = rows + cols - 1;
    printf("R = %d, C = %d, N = %d\n", rows, cols, n);

    for (int zigzag = 0; zigzag < n; zigzag++)
    {
        int max_col = min(zigzag, cols-1);
        int min_col = max(0, zigzag - n + cols);
        int max_row = min(zigzag, rows-1);
        int min_row = max(0, zigzag - n + rows);
        printf("zigzag = %2d, min_col = %2d, max_col = %2d, min_row = %2d, max_row = %2d\n",
                zigzag, min_col, max_col, min_row, max_row);
    }

    for (int zigzag = 0; zigzag < n; zigzag++)
    {
        printf("%d:", zigzag);
        if (zigzag % 2 == 0)
        {
            int max_col = min(zigzag, cols-1);
            int min_col = max(0, zigzag - n + cols);
            for (int col = min_col; col <= max_col; col++)
                /* (row,col) */
                printf(" (r=%d,c=%d)", zigzag - col, col);
        }
        else
        {
            int max_row = min(zigzag, rows-1);
            int min_row = max(0, zigzag - n + rows);
            for (int row = min_row; row <= max_row; row++)
                printf(" (r=%d,c=%d)", row, zigzag - row);
        }
        putchar('\n');
    }
}

static void dump_matrix(const char *tag, int rows, int cols, int matrix[rows][cols])
{
    printf("%s (%d x %d):\n", tag, rows, cols);
    for (int i = 0; i < rows; i++)
    {
        for (int j = 0; j < cols; j++)
            printf("%3d", matrix[i][j]);
        putchar('\n');
    }
}

static void dump_vector(const char *tag, int rows, int cols, int vector[rows * cols])
{
    printf("%s (%d : %d):\n", tag, rows, cols);
    for (int i = 0; i < rows * cols; i++)
    {
        printf("%3d", vector[i]);
        if (i % cols == cols - 1)
            putchar('\n');
    }
}

static void RLE_demonstration(int rows, int cols)
{
    int matrix[rows][cols];
    int vector[rows*cols];

    /* Set matrix */
    for (RLE rle = RLE_init(rows, cols); !RLE_finished(&rle); RLE_next(&rle))
    {
        //RLE_dump("Set Matrix", &rle);
        RC rc = RLE_position(&rle); 
        matrix[rc.row][rc.col] = RLE_sequence(&rle);
    }
    dump_matrix("Matrix", rows, cols, matrix);

    /* Convert matrix to vector */
    for (RLE rle = RLE_init(rows, cols); !RLE_finished(&rle); RLE_next(&rle))
    {
        //RLE_dump("Get Matrix", &rle);
        RC rc = RLE_position(&rle); 
        vector[RLE_sequence(&rle)] = matrix[rc.row][rc.col];
    }
    dump_vector("Vector", rows, cols, vector);
}

int main(int argc, char **argv)
{
    struct
    {
        int rows;
        int cols;
    } test[] =
    {
        { 4, 4 }, { 6, 4 },  { 4, 7 }, { 7, 14 }, { 6, 16 }, { 3, 33 },
    };
    enum { NUM_TEST = sizeof(test) / sizeof(test[0]) };

    /* argv != 0 avoids unused variable warning */
    int verbose = (argv != 0 && argc > 1) ? 1 : 0;

    for (int i = 0; i < NUM_TEST; i++)
    {
        if (verbose)
            print_info(test[i].rows, test[i].cols);
        RLE_demonstration(test[i].rows, test[i].cols);
    }

    return 0;
}


回答2:

This is how you do it in 17 times less lines:

#define N 8

int mat2d[N][N] = { /* stuff */ };
int vec1d[N * N];
memcpy(vec1d, mat2d, sizeof vec1d);


回答3:

Iterate over the diagonals of the square, alternating direction each time.

Here's a complete, working example (in c99).

#include <stdio.h>

#define max(a, b) ((a) > (b) ? (a) : (b))
#define min(a, b) ((a) > (b) ? (b) : (a))

void dezigzag(int out[64], int in[8][8]) {
    int n = 0;
    for (int diag = 0; diag < 15; diag++) {
        for (int i = max(0, diag - 7); i <= min(7, diag); i++) {
            out[n++] = diag % 2 ? in[diag - i][i] : in[i][diag - i];
        }
    }
}

int main(int argc, char *argv[]) {
    int out[64] = {-1};
    int in[8][8];
    for (int i = 0; i < 64; i++) {
        in[i % 8][i / 8] = i;
    }
    dezigzag(out, in);
    for (int i = 0; i < 64; i++) {
        printf("%d: %d\n", i, out[i]);
    }
    return 0;
}


标签： c vector matrix
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