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Competition Arena > VariableSolve
TCO05 Sponsor Rd 1 · 2005-08-16 · by AdminBrett · Math
Class Name: VariableSolve
Return Type: String[]
Method Name: getSolutions
Arg Types: (string)
Problem Statement

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.

Constraints

  • equation will contain between 3 and 50 characters inclusive.
  • equation will be formatted as described in the problem statement.
Examples
0)
"ABCD+ABCD-ABCD=ABCD"
Returns: { }
1)
"ABA+BA+B=P-P"
Returns: {"B" }
2)
"ABA+BA+B=P-P+B"
Returns: {"A", "A", "B" }
3)
"ABA+BA+B=P-P+B+B"
Returns: {"A", "A", "B" }
4)
"P=NP"
Returns: {"N", "P" }

Simpler than it looks: let N = 1 or P = 0.

5)
"RED+BLUE=PURPLE"
Returns: {"E" }

Only E = 0 guarantees the equation holds.

6)
"ABCD+ABCD-ABCD=ABCD"
Returns: { }

Each variable has an infinite number of values causing the equation to hold.

7)
"BAA+BA+B=P-P"
Returns: {"B" }

We cannot consider the complex solutions for A.

Submissions are judged against all 104 archived test cases, of which 8 are shown here. Case numbers match the judge’s.

Coding Area

Language: C++17 · define a public class VariableSolve with a public method vector<string> getSolutions(string equation) · 104 test cases · 2 s / 256 MB per case

Submitting as anonymous