Nisoku | Topcoder Archive

Problem Statement

Taro and Hanako are playing a game called Nisoku, which is played as follows. Initially, there is a pile of cards. Each card contains a real number between 1.5 and 10.0, inclusive. You are given a double[] cards, the i-th element of which is the number written on the i-th card.

Repeat the following step until there is only one card left in the pile: Remove any two cards from the pile, and add one new card to the pile. Write either a+b or a*b on the new card, where a and b are the numbers written on the two cards that were removed.

Return the maximal possible number written on the final card in the pile.

Definition

Class:: Nisoku
Method:: theMax
Parameters:: double[]
Returns:: double
Method signature:: double theMax(double[] cards)
(be sure your method is public)

Notes

Your return value must have an absolute or relative error less than 1e-9.

Constraints

cards will contain between 2 and 50 elements, inclusive.
Each element of cards will be between 1.5 and 10.0, inclusive.

Examples

```
{5, 8}
```
```
Returns: 40.0
```
5 * 8 = 40.
```
{1.5, 1.8}
```
```
Returns: 3.3
```
1.5 + 1.8 = 3.3.

{8.26, 7.54, 3.2567}

Returns: 202.82857868

{1.5, 1.7, 1.6, 1.5}

Returns: 9.920000000000002

{10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 
10, 10, 10, 10, 10, 10, 10, 10, 10, 10}

Returns: 1.0E50

The answer can be extremely big.

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