ImprovingStatistics | Topcoder Archive

Problem Statement

Several years ago I was playing Spider Solitaire on my computer all the time. Sometimes I won, sometimes I lost. Then I stopped playing Spider Solitaire and started participating in programming competitions. After a few years I happened to start my old solitaire program again. I was pleased to discover that with the skill I gained during the years I am now able to win each and every game of Spider Solitaire. However, the program still remembers some of my previous games and thus the statistics don't necessarily reflect my current perfect skills.

The program displays the statistics in the following way:
Games played: X
Games won: Y (Z %)

The number Z is the percentage of games I won, rounded down to the nearest integer. For example, if X=53 and Y=47, then Z=88.
(The value Y/X is roughly equal to 0.8868, which means that I won roughly 88.68% of the games I played. 88.68% rounded down to an integer is 88%.)

You will be given two ints played and won - the number of games I played so far, and the number of games I won so far. Return the smallest positive integer G such that if I now win G games in a row the displayed value of Z will increase. If this is impossible, return -1 instead.

Definition

Class:: ImprovingStatistics
Method:: howManyGames
Parameters:: int, int
Returns:: int
Method signature:: int howManyGames(int played, int won)
(be sure your method is public)

Notes

You may assume that the return value will always be less than 2,000,000,000.

Constraints

played will be between 1 and 1,000,000,000, inclusive.
won will be between 0 and played, inclusive.

Examples

```
10
```
```
8
```
```
Returns: 1
```
So far I won 8 games out of 10, and thus the displayed success percentage is 80%. After I win the next game the percentage will increase to 81%.
```
100
```
```
80
```
```
Returns: 6
```
Again, the currently displayed value is 80%. However, now I need to win at least 6 more games to bring it to 81%.
```
47
```
```
47
```
```
Returns: -1
```
Nothing left to improve.
```
99000
```
```
0
```
```
Returns: 1000
```
```
1000000000
```
```
470000000
```
```
Returns: 19230770
```

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