TVShow | Topcoder Archive

Problem Statement

You are on a TV game show where two players try to maximize their earnings. Initially, your opponent has X0 dollars and you have Y0 dollars. Before the game starts, your opponent chooses a number A and you choose a number B (A > 0, B > 0).

The game consists of n rounds. Each round of the game proceeds as follows. Let X be the amount of money your opponent has at the beginning of the round, and let Y be the amount of money you have. Your opponent will choose between two options. He can either turn his money into X+A dollars and turn your money into Y*B dollars, or he can turn his money into X*B dollars and turn your money into Y+A dollars. All operations are done with real numbers. The amount of money each player has at the end of n rounds is that player's final earnings.

Your opponent will play in such a way that maximizes his final earnings. If, during a round, both of his options would lead to the same final earnings for himself, he will choose the first option (turn his money into X+A dollars and turn your money into Y*B dollars).

Your only choice in the game is the value of B. Return the maximum possible final earnings you can achieve.

Definition

Class:: TVShow
Method:: maximalWin
Parameters:: int, double, double, double
Returns:: double
Method signature:: double maximalWin(int n, double X0, double Y0, double A)
(be sure your method is public)

Notes

The returned value must have an absolute or relative error less than 1e-9.

Constraints

n will be between 1 and 100, inclusive.
X0 will be between 1 and 1000, inclusive.
Y0 will be between 1 and 1000, inclusive.
A will be between 1 and 1000, inclusive.

Examples

```
1
```
```
100
```
```
100
```
```
30
```
```
Returns: 130.0
```
In this case, whatever B you select, your opponent will have the advantage. If you choose B > 1.3, you will get Y+A = 130, and if you choose B <= 1.3, you will get Y*B <= 130. Your maximum possible earnings is therefore 130.0.
```
1
```
```
100
```
```
200
```
```
30
```
```
Returns: 260.0
```
In this case, if you choose B = 1.3, your opponent will choose to turn his money into X+A, so you will get Y*B = 260.0.
```
3
```
```
100
```
```
140
```
```
35
```
```
Returns: 259.0
```
The optimal value for B here is 1.35.
```
10
```
```
100
```
```
200
```
```
30
```
```
Returns: 544.912109375
```

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