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Suppose we have an array a[90][30][40] where first element starts from a[1][1][1] then what will be the index of a[20][20][30] in column major representation ?

According to me a[x][y][z] means x is depth, y is rows and z is columns.

So according to me, the index should be 19(30)(40) + (29)(30) + (20-1) = 23689.

I read https://eli.thegreenplace.net/2015/memory-layout-of-multi-dimensional-arrays/ which says that a[x][y][z] actually means x is rows, y is columns and z is depth.

I read all the existing answers here and also the above link and got confused.

Is my calculation correct?

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  • 2
    The first element is actually a[0][0][0]. Commented Oct 21, 2017 at 13:39
  • What did you try to sort it out yourself - probably nothing. Commented Oct 21, 2017 at 13:42
  • @PeterJ_01 what else you want me to sort out ? I showed the calculation and also the link I read. Commented Oct 21, 2017 at 13:45
  • To do some experiments. This is the proper way of learning Commented Oct 21, 2017 at 13:54
  • The formula is in the link you posted too, given an int a[rows][cols][layers];, element a[i][j][k] has an offset of k + layers * (j + cols * i). Commented Oct 21, 2017 at 14:08

2 Answers 2

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I have asked you in the comment what have you done to sort this puzzle out? Not your "calculations". It is enough to write three lines of the code to get the answer:

char a[10][10][10];


for (int i = 0; i < 10; i++)
    printf("&a[%1d][0][0] = %04zu\t\t&a[0][%1d][0] = %04zu\t\t&a[0][0][%1d] = %04zu\n", i, &a[i][0][0] - &a[0][0][0], i, &a[0][i][0] - &a[0][0][0], i, &a[0][0][i] - &a[0][0][0]);


&a[0][0][0] = 0000              &a[0][0][0] = 0000              &a[0][0][0] = 0000
&a[1][0][0] = 0100              &a[0][1][0] = 0010              &a[0][0][1] = 0001
&a[2][0][0] = 0200              &a[0][2][0] = 0020              &a[0][0][2] = 0002
&a[3][0][0] = 0300              &a[0][3][0] = 0030              &a[0][0][3] = 0003
&a[4][0][0] = 0400              &a[0][4][0] = 0040              &a[0][0][4] = 0004
&a[5][0][0] = 0500              &a[0][5][0] = 0050              &a[0][0][5] = 0005
&a[6][0][0] = 0600              &a[0][6][0] = 0060              &a[0][0][6] = 0006
&a[7][0][0] = 0700              &a[0][7][0] = 0070              &a[0][0][7] = 0007
&a[8][0][0] = 0800              &a[0][8][0] = 0080              &a[0][0][8] = 0008
&a[9][0][0] = 0900              &a[0][9][0] = 0090              &a[0][0][9] = 0009
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1 Comment

So was my calculation correct ? Even I took the representation as <depth,row,column>.
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Is my calculation correct?

No, since your basis is wrong.

The first element is a[0][0][0], since indexing starts from 0 in arrays, not 1.

Usually, the first dimension of a 3D array is the rows, the second the columns, and the third the depth.

There are two popular representation when it comes to arrays, row and column major order.

It seems like you are confused and talk about Fortran arrays (where the arrays are column major ordered, and the index starts from 1), rather than C ones.

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8 Comments

Then how will the calculation be ? I am not able to visualize the column major representation of 3d array.
If possible please help me in visualizing the column major representation. I am not interested in base index at the moment.
C is row major ordered when it comes to arrays @Zephyr. I am not sure what you are asking me.
visualizing the column major representation. First index is the page with the table, the second one is the row in the table on this page, the third is the column
@PeterJ_01 But in the website the representation is different. It's <row,column,depth>
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