ChessTourney | Topcoder Archive

Problem Statement

John is a chess player and is going to compete in the upcoming tournament. When a player loses a game, he immediately leaves the tournament. Only the player who can win all his games will become the winner.

During the tournament John may win some prizes given in a int[] winnings. Element 0 of winnings represents the prize John gets for just entering the tournament, and element i of winnings (for i > 0) represents the amount John gets for winning his game in the i-th round. For example, if John wins the first two games and loses the third one, he'll get winnings[0] for entering the tournament, winnings[1] for winning his game in the first round (which grants him a spot in round 2) and winnings[2] for winning his second game and advancing to round 3. Losing in round 3 will give him nothing.

You've analyzed the play-off tree and now you know John's chances of advancing through each of the rounds, given in a int[] odds. Element i of odds represents the probability (as a percentage) that John will win his game in round (i + 1). Return John's expected winnings in the tournament.

Definition

Class:: ChessTourney
Method:: expectedWinning
Parameters:: int[], int[]
Returns:: double
Method signature:: double expectedWinning(int[] winnings, int[] odds)
(be sure your method is public)

Notes

The returned value must be accurate to within a relative or absolute value of 1E-9.

Constraints

winnings will contain between 2 and 50 elements, inclusive.
odds will contain exactly n - 1 elements, where n is the number of elements in winnings.
Each element of winnings will be between 0 and 1000, inclusive.
Each element of odds will be between 0 and 100, inclusive.

Examples

```
{10, 100}
```
```
{100}
```
```
Returns: 110.0
```
John is very good - he definitely wins the only round of the tournament and takes home both prizes.
```
{10, 10, 10, 10}
```
```
{50, 50, 50}
```
```
Returns: 18.75
```
John gets the participation prize of 10 dollars with a probability of 100%, the prize for the first round win with a probability of 50%, the second round prize with a probability of 25% and the final prize with a probability of 12.5%.

{100, 100, 200, 200}

{100, 0, 100}

Returns: 200.0

{100, 100, 200, 400, 800, 1000}

{100, 50, 25, 10, 5}

Returns: 360.625

Each next round is harder.

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