PyramidOfCubes | Topcoder Archive

Problem Statement

Consider a N-level pyramid built of unit cubes. An example for N=3 can be seen in the image below.

Formally, a pyramid of size N has N levels, where the i-th level (counting from the top) contains an i by i grid of unit cubes.

You have K cubes. First, you select a suitable pyramid size as follows: If K is exactly the number of cubes necessary to build a pyramid of size N for some N, you pick that size. Otherwise, you pick the smallest pyramid size you can not build.

Now you start building the pyramid in a systematic bottom-up way. First you build the complete bottom level, then you build the level above that, etc. When building a level, also proceed in a systematic way, starting the next row only when the previous one is full.

For example, for 21 cubes you should get the following incomplete pyramid:

Given an int K specifying the number of cubes you have, return the surface area of the possibly incomplete pyramid you will build according to the instructions above.

Definition

Class:: PyramidOfCubes
Method:: surface
Parameters:: int
Returns:: double
Method signature:: double surface(int K)
(be sure your method is public)

Notes

The returned value must be accurate to within a relative or absolute value of 1E-9.
The bottom sides of the cubes on the bottommost level are a part of the surface.

Constraints

K will be between 1 and 1,000,000,000, inclusive.

Examples

```
14
```
```
Returns: 42.0
```
The first example from the problem statement.
```
21
```
```
Returns: 58.0
```
The second example from the problem statement.
```
1
```
```
Returns: 6.0
```
A single cube.
```
2
```
```
Returns: 10.0
```
Two cubes next to each other.
```
451234
```
```
Returns: 47498.0
```
Quite a lot of cubes.

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