BooksNumbering | Topcoder Archive

Problem Statement

A new library was founded in our city. The books were labeled 1, 2, 3, 4, etc., with no leading zeroes. A total of usedDigits digits were used to create the labels. Return the total number of books in the library, or -1 if usedDigits does not correspond to a valid solution.

Definition

Class:: BooksNumbering
Method:: numberOfBooks
Parameters:: int
Returns:: int
Method signature:: int numberOfBooks(int usedDigits)
(be sure your method is public)

Constraints

usedDigits will be between 1 and 2 * 109, inclusive.

Examples

```
11
```
```
Returns: 10
```
Each of the first 9 numbers (1-9) contain one digit. Number 10 contains 2 digits. Therefore, there's a total of 11 digits.
```
10
```
```
Returns: -1
```
There is no possible solution. It takes 9 digits to label 9 books, and 11 digits to label 10 books.
```
189
```
```
Returns: 99
```
```
192
```
```
Returns: 100
```
```
7
```
```
Returns: 7
```
```
1863927342
```
```
Returns: 219448716
```
```
1863927343
```
```
Returns: -1
```

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