Using the flattened array syntax in C++, crashes depending on width/height - c++

Question

I have read quite a few articles in SO and cplusplus.com and decided to give a try to the flattened, 1D array that mimics 2D and 3D.
I managed to get a prototype to work with some values, but there is something wrong with the indices, which has to be the formula. All I did was copy the formula from different places and applied to the code. Here it is:
#include <iostream>
using namespace std;
int main(void)
{
float *flat_2d_array, *flat_3d_array;
int width, height, depth, counter;
counter = 1;
width = 2;
height = 3;
depth = 4;
flat_2d_array = new float[width * height];
flat_3d_array = new float[width * height * depth];
// 2D part, works fine
for(int x = 0; x < width; x++)
for(int y = 0; y < height; y++)
flat_2d_array[y * width + x] = counter++;
for(int x = 0; x < width; x++)
for(int y = 0; y < height; y++)
cout << "Element [" << x << "]" << "[" << y << "] = " << flat_2d_array[y * width + x] << endl;
cout << endl;
// Resets the counter and runs the 3D part
counter = 1;
for(int x = 0; x < width; x++)
for(int y = 0; y < height; y++)
for(int z = 0; z < depth; z++)
flat_3d_array[z * height * depth + y * depth + x] = counter++;
for(int x = 0; x < width; x++)
for(int y = 0; y < height; y++)
for(int z = 0; z < depth; z++)
cout << "Element [" << x << "]" << "[" << y << "]" << "[" << z << "] = " << flat_3d_array[z * height * depth + y * depth + x] << endl;
delete[] flat_2d_array;
delete[] flat_3d_array;
return 0;
}
It just declares a few variables, allocates memory for the arrays, populates them with a counter in for() loops and prints the elements, then frees the memory.
If you copy/paste it will compile the way it is and will run fine.
However, if you change width to 3 and height to 2, then compile and run, it will crash after the element [2][1][3] in the 3D part.
So there seems to be indexing problem with this formula I'm using for the 3D:
3d_array[ X ][ Y ][ Z ] == flat_3d_array[ Z * height * depth + Y * depth + X ]
Can you guys see anything incorrect?

Answer 1

Can you guys see anything incorrect?
yes, your formula should be instead:
z * height * width + y * width + x
or more efficient form:
( z * height + y ) * width + x
and you should make loop on x inner, otherwise you iterate against CPU cache.
To make clear: making loop on x inner would not affect correctness of your program, it will make it more efficient (including iteration on 2d array as well). Your program crashes because you calculate linear index for 3d array by wrong formula.