IterateOverACube | Topcoder Archive

Problem Statement

We use the following pseudocode to visit each cell of an N x N x N cube exactly once:

for sum = 0 .. 3*N-3:
    for x = 0 .. N-1:
        for y = 0 .. N-1:
            for z = 0 .. N-1:
                if x+y+z == sum:
                    visit (x,y,z)

You are given the int N and the long index: a 0-based index into the sequence of cells visited by the above pseudocode. Return a int[] containing the coordinates of that cell.

Definition

Class:: IterateOverACube
Method:: findCell
Parameters:: int, long
Returns:: int[]
Method signature:: int[] findCell(int N, long index)
(be sure your method is public)

Constraints

N will be between 1 and 10^6, inclusive.
index will be between 0 and N^3 - 1, inclusive.

Examples

```
3
```
```
9
```
```
Returns: {2, 0, 0 }
```
The first ten cells visited are (0,0,0), (0,0,1), (0,1,0), (1,0,0), (0,0,2), (0,1,1), (0,2,0), (1,0,1), (1,1,0), and (2,0,0).
```
3
```
```
10
```
```
Returns: {0, 1, 2 }
```
The next visited cell is (0,1,2).

106968940722

Returns: {4746, 4746, 4746 }

The very last cell visited in this cube.

```
4
```
```
32
```
```
Returns: {0, 2, 3 }
```

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