VariableSolve | Topcoder Archive

Problem Statement

You will be given an equation of the form <side>=<side> where <side> is a list of <term>s separated by <op>s. Each <op> is either + or -, and each <term> is a positive length string of uppercase letters. Each letter denotes a variable taking on real values. No letter will occur in a <term> more than twice.

The <term>s are products of variables. As you would expect, the + and - operators take lower precedence than the multiplications within the <term>s. For example,

	ABC+ADF=PQ-PQ

is a properly formatted equation. Sometimes, by fixing a single variable at a particular value, we can force the entire equation to always be true. Return a String[] containing all such variables that satisfy this requirement. If a variable can be set to n distinct values all of which satisfy this requirement, then that variable should occur n times in the return. If a variable can be set to an infinite number of distinct values that satisfy this requirement, it should not be returned. The return should be sorted in alphabetical order.

Definition

Class:: VariableSolve
Method:: getSolutions
Parameters:: String
Returns:: String[]
Method signature:: String[] getSolutions(String equation)
(be sure your method is public)

Constraints

equation will contain between 3 and 50 characters inclusive.
equation will be formatted as described in the problem statement.

Examples

```
"P=NP"
```
```
Returns: {"N", "P" }
```
Simpler than it looks: let N = 1 or P = 0.
```
"RED+BLUE=PURPLE"
```
```
Returns: {"E" }
```
Only E = 0 guarantees the equation holds.
```
"ABCD+ABCD-ABCD=ABCD"
```
```
Returns: { }
```
Each variable has an infinite number of values causing the equation to hold.
```
"BAA+BA+B=P-P"
```
```
Returns: {"B" }
```
We cannot consider the complex solutions for A.
```
"ABB-AB-AB+A=BCB-C"
```
```
Returns: {"B" }
```

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