Find address of element in 3d array

Question

A is an array $[2.....6, 2.....8, 2.......10]$ of elements. The starting location is $500$. The location of an element $A(5, 5, 5)$ using column major order is __________.

Comments

Please explain how are you getting it. I want to know the approach.

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719 for rmo?

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i think correct answer is 713

Answer 1

A[x][y][z] = A[6-2+1][8-2+1][10-2+1]. So A[5][7][9] is our 3-D array.

It contains 2-D arrays (comprises of 5 rows and 7 columns) arranged in 9 layers making it a 3-D array.

In total we have 5 rows({2,3,4,5,6}) in the similar way we have 7 columns({2,3,4,5,6,7,8}) and 9 layers({2,3,4,5,6,7,8,9,10}).

So in the layer 1 ({2,3,4,5,6,7,8,9,10}) we have  7 Columns * 5 Rows = 35 Elements. In the similar way each of the remaining layers also contain 35 elements.

Here we have to use column major Order to find the address of A[5][5][5]. Base Address is 500.

Here the index of z is 5. so we can have the required element in the 4 th layer({2,3,4,5,6,7,8,9,10}). Upto 3 layers({2,3,4,5,6,7,8,9,10}) we will have (3 layers *35 elements) 105 elements.

Now in the 4th layer we can find the number in 4th column({2,3,4,5,6,7,8}) in 4th row({2,3,4,5,6}). As we have to look in column major order upto 3rd column ({2,3,4,5,6,7,8}) we will have (3 columns * 5 rows) 15 elements.

Then in the  4th column upto 4 rows we have 3 elements.

Let us consider the size of each element is of 1 Byte.

So the address of the element in the location A[5][5][5] is Base Address + (Total Number of elements ) * Size of each element (We add one to get to the current element)

LOCATION(A[5][5][5]) = 500 + (105 + 15 + 3 )*1 = 623.

Comments

yes, 623. I have corrected.

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ok..😀

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Please refer to : https://eli.thegreenplace.net/2015/memory-layout-of-multi-dimensional-arrays to get the correct and clear understanding of multi dimensional arrays, row and column major representations.You may also refer to the Wikipedia for the correct explanation

Answer 2

I considered the above as 9*(7x5) 2D arrays in that case to reach A[5], we need to cross 4*(7x5) 2D arrays ie. 140.

After that add 4*7 iterations + 4 to reach A[5][5] , this makes it- 28+4=32

So adding to the base address I got 500+172=672.

Answer 3

https://gateoverflow.in/?qa=blob&qa_blobid=9191013060072203721