SolvingEquation | Topcoder Archive

Problem Statement

You are given the following equation:

A * x + B * y + C * z = W

where x, y and z are integers greater than or equal to 0. Return the minimal possible sum x + y + z, or -1 if a solution does not exist.

Definition

Class:: SolvingEquation
Method:: solve
Parameters:: int, int, int, int
Returns:: int
Method signature:: int solve(int A, int B, int C, int W)
(be sure your method is public)

Constraints

A, B, C and W will each be between 1 and 100, inclusive.

Examples

```
1
```
```
2
```
```
3
```
```
5
```
```
Returns: 2
```
The solution that minimizes x + y + z is x = 0, y = 1 and z = 1. 1*0 + 2*1 + 3*1 = 5. The return value is x + y + z = 0 + 1 + 1 = 2.
```
1
```
```
2
```
```
3
```
```
10
```
```
Returns: 4
```
The best solution here is x = 1, y = 0 and z = 3.
```
3
```
```
3
```
```
5
```
```
7
```
```
Returns: -1
```
There is no solution for the equation 3*x + 3*y + 5*z = 7.
```
1
```
```
1
```
```
1
```
```
100
```
```
Returns: 100
```
```
1
```
```
10
```
```
20
```
```
99
```
```
Returns: 14
```
```
100
```
```
100
```
```
1
```
```
1
```
```
Returns: 1
```

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