LinearCombinations | Topcoder Archive

Problem Statement

You will be given a formula in the following form:

	aw+bx=cy+dz,

where a, b, c and d are positive integers between 1 and 9 inclusive. You will also be given positive values for 3 of w, x, y, and z. The remaining value will be -1, denoting a blank. Return what value the blank must have (possibly 0 or negative) in order to satisfy the given formula.

Definition

Class:: LinearCombinations
Method:: computeValue
Parameters:: String, int, int, int, int
Returns:: double
Method signature:: double computeValue(String formula, int w, int x, int y, int z)
(be sure your method is public)

Notes

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

Constraints

formula will contain exactly 11 characters.
formula will have the form (quotes for clarity) "aw+bx=cy+dz" where a,b,c,d are positive digits ('1'-'9').
Exactly three of w, x, y, and z will be between 1 and 10000 inclusive.
Exactly one of w, x, y, and z will be -1.

Examples

```
"2w+3x=4y+5z"
```
```
-1
```
```
1
```
```
2
```
```
3
```
```
Returns: 10.0
```
2w+3(1)=4(2)+5(3) so 2w + 3 = 23.
```
"1w+1x=1y+1z"
```
```
1
```
```
1
```
```
1
```
```
-1
```
```
Returns: 1.0
```
1(1) + 1(1) = 1(1) + 1z so 2 = 1 + z.

"9w+9x=8y+8z"

-1

Returns: 22491.375

"9w+8x=1y+9z"

-1

Returns: 4369.777777777777

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