NoZero | Topcoder Archive

Problem Statement

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A no-zero number system uses only the digits 1 through 9. So counting begins with 1, the first "counting number", and continues:

1,2,3,4,5,6,7,8,9,11,12,...,19,21,...,98,99,111,112,...

So, in this system 9 is the ninth counting number and 11 is the tenth counting number.

As usual, addition can be defined by reference to the counting sequence. Addition of the i-th counting number and the j-th counting number is defined to mean the (i+j)-th counting number. Thus, in this system 5 + 8 = 14, since 5 is the fifth counting number, 8 is the eighth, and 14 is the thirteenth counting number. Subtraction is the reverse of addition. Create a class NoZero that contains the method subtract that takes two no-zero numbers, big and small, and returns the no-zero value that results from calculating big - small.

Definition

Class:: NoZero
Method:: subtract
Parameters:: int, int
Returns:: int
Method signature:: int subtract(int big, int small)
(be sure your method is public)

Constraints

big and small do not contain the digit 0
big is between 1 and 999,999,999 inclusive
small is between 1 and 999,999,999 inclusive
big is greater than small

Examples

```
111
```
```
99
```
```
Returns: 1
```
This big and small are adjacent in the counting sequence. So 99 + 1 = 111 and 111 - 99 = 1.
```
19
```
```
11
```
```
Returns: 8
```
```
191
```
```
111
```
```
Returns: 79
```
```
11112
```
```
9989
```
```
Returns: 12
```

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