FillBox | Topcoder Archive

Problem Statement

You have a length x width x height box, and you want to fill it with cubes. The cubes have sides that are powers of 2 (1x1x1, 2x2x2, 4x4x4, 8x8x8, etc.). You are given a int[] cubes, the i-th element of which is the number of 2^i x 2^i x 2^i cubes you have (i is a 0-based index). Return the minimum number of cubes necessary to fill the box, or -1 if it is impossible to do so.

Definition

Class:: FillBox
Method:: minCubes
Parameters:: int, int, int, int[]
Returns:: int
Method signature:: int minCubes(int length, int width, int height, int[] cubes)
(be sure your method is public)

Constraints

length, width and height will each be between 1 and 10^6, inclusive.
cubes will contain between 1 and 20 elements, inclusive.
Each element of cubes will be between 0 and 10^6, inclusive.

Examples

```
4
```
```
4
```
```
8
```
```
{10,10,10}
```
```
Returns: 2
```
In order to cover the 4x4x8 box we need two 4x4x4 cubes.
```
4
```
```
4
```
```
8
```
```
{10,10,1}
```
```
Returns: 9
```
Same case as before but we have only one 4x4x4 cube so we will use eight 2x2x2 cubes
```
10
```
```
10
```
```
11
```
```
{2000}
```
```
Returns: 1100
```
We have only 1x1x1 cubes. We will need 1100 of those cubes to cover the whole box.
```
10
```
```
10
```
```
11
```
```
{1099}
```
```
Returns: -1
```
We don't have enough 1x1x1 cubes.

{143821,14382,1438,143,14,1}

Returns: 5061

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