public async Task <SearchResultCollection> SearchAsync(SearchQuery query, CancellationToken ct)
{
string latex;
string infix;
double?evaluated;
try
{
// simplify
var expression = Infix.ParseOrThrow(query.QueryString);
latex = LaTeX.Format(expression);
infix = Infix.Format(expression);
// try to calculate
var symbols = new Dictionary <string, FloatingPoint>();
try
{
evaluated = Evaluate.Evaluate(symbols, expression).RealValue;
}
catch (Exception ex)
{
// expression valid, but can't be calculated
return(null);
}
}
catch (Exception ex)
{
// expression error
return(null);
}
var results = new SearchResultCollection
{
Title = "Math evaluation",
Relevance = evaluated != null ? SearchResultRelevance.ONTOP : SearchResultRelevance.DEFAULT,
FontAwesomeIcon = "Calculator"
};
results.Results = new ObservableCollection <SearchResult>
{
new MathSearchResult
{
Title = infix,
LaTeXExpression = latex,
LaTeXEvaluated = evaluated != null ? "= " + evaluated : "",
ParentCollection = results
}
};
return(results);
}
internal SolveChallenge(int answerCount = 4, int minNum = STD_MIN_NUM, int maxNum = STD_MAX_NUM, bool dummy = false)
{
QuestionNodeHeight = 340f;
NodeHeight = 320f;
CreateAnswerArrays(answerCount);
if (dummy)
{
return;
}
// prepare the RNG
var rng = new Random();
// choose the variables
string[] signs = new string[3];
string[] variables = new string[3];
for (int i = 0; i < variables.Length; i++)
{
if (rng.NextBoolean())
{
// choose a letter
switch (rng.Next(9))
{
case 0: variables[i] = "a"; break;
case 1: variables[i] = "b"; break;
case 2: variables[i] = "c"; break;
case 3: variables[i] = "y"; break;
case 4: variables[i] = "t"; break;
case 5: variables[i] = "k"; break;
case 6: variables[i] = "i"; break;
case 7: variables[i] = "s"; break;
case 8: variables[i] = "p"; break;
case 9: variables[i] = "r"; break;
}
}
else
{
// choose a number
if (rng.NextBoolean())
{
variables[i] = rng.Next(minNum, maxNum).ToString();
}
else
{
variables[i] = 1.ToString();
}
}
if (rng.Next(4) == 0)
{
signs[i] = "-";
}
else
{
signs[i] = "";
}
}
// create the challenge
const string LA_MUL = @"\cdot";
var challengeType = rng.Next(5);
string side1Infix = "";
string side1LaTeX = "";
string side2Infix = "";
string side2LaTeX = "";
bool NegStr(string str)
{
return(str.StartsWith("-"));
}
string SignedVar(int i)
{
return(signs[i] + variables[i]);
}
string MulFromLeft(int i)
{
return(variables[i].Equals("1") ? signs[i] : SignedVar(i) + " " + LA_MUL + " ");
}
string MulStrFromLeft(string str)
{
return(str.Equals("1") ? "" : (str.Equals("-1") ? "-" : str + " " + LA_MUL + " "));
}
string AddFromRight(string str)
{
return((NegStr(str) ? "" : " + ") + str);
}
string SubFromRight(string str)
{
return(NegStr(str) ? " + " + str.Substring(1) : str);
}
switch (challengeType)
{
case 0:
{
side1Infix = SignedVar(0);
side1LaTeX = SignedVar(0);
side2Infix = "x * " + SignedVar(1) + " + x * " + SignedVar(2);
side2LaTeX = MulFromLeft(1) + "x" + AddFromRight(MulFromLeft(2) + "x");
}
break;
case 1:
{
side1Infix = SignedVar(0) + " * x";
side1LaTeX = MulFromLeft(0) + "x";
side2Infix = SignedVar(1) + " + " + SignedVar(2) + " * x";
side2LaTeX = SignedVar(1) + AddFromRight(MulFromLeft(2) + "x");
}
break;
case 2:
{
side1Infix = "(" + SignedVar(0) + " + " + SignedVar(1) + ") / x";
side1LaTeX = @"\frac{" + SignedVar(0) + AddFromRight(SignedVar(1)) + "}{ x }";
side2Infix = SignedVar(2);
side2LaTeX = SignedVar(2);
}
break;
case 3:
{
side1Infix = SignedVar(0) + " + " + SignedVar(1);
side1LaTeX = SignedVar(0) + AddFromRight(SignedVar(1));
side2Infix = "x / " + SignedVar(2);
side2LaTeX = @"\frac{ x }{" + SignedVar(2) + "}";
}
break;
case 4:
{
side1Infix = SignedVar(0) + " / " + SignedVar(1);
side1LaTeX = @"\frac{" + SignedVar(0) + "}{" + SignedVar(1) + "}";
side2Infix = SignedVar(2) + " / x";
side2LaTeX = @"\frac{" + SignedVar(2) + "}{ x }";
}
break;
}
// shuffle the sides
if (rng.NextBoolean())
{
ChallengeInfix = side1Infix + " = " + side2Infix;
ChallengeLaTeX = side1LaTeX + " = " + side2LaTeX;
}
else
{
ChallengeInfix = side2Infix + " = " + side1Infix;
ChallengeLaTeX = side2LaTeX + " = " + side1LaTeX;
}
// create the solution
switch (challengeType)
{
case 0:
{
SolutionInfix = SignedVar(0) + " / (" + SignedVar(1) + " + " + SignedVar(2) + ")";
// the following SolutionLaTeX-commands are commented out, because it's simply better (more beautiful/ easier to read) to use Latex.Format
//SolutionLaTeX = @"x = \frac{" + SignedVar(0) + "}{" + SignedVar(1) + AddFromRight(SignedVar(2)) + "}";
}
break;
case 1:
{
SolutionInfix = SignedVar(1) + " / (" + SignedVar(0) + " - " + SignedVar(2) + ")";
//SolutionLaTeX = @"x = \frac{" + SignedVar(1) + "}{" + SignedVar(0) + SubFromRight(SignedVar(2)) + "}";
}
break;
case 2:
{
SolutionInfix = "(" + SignedVar(0) + " + " + SignedVar(1) + ") / " + SignedVar(2);
//SolutionLaTeX = @"x = \frac{" + SignedVar(0) + AddFromRight(SignedVar(1)) + "}{" + SignedVar(2) + "}";
}
break;
case 3:
{
SolutionInfix = "(" + SignedVar(0) + " + " + SignedVar(1) + ") * " + SignedVar(2);
//SolutionLaTeX = "x = " + MulStrFromLeft("(" + SignedVar(0) + AddFromRight(SignedVar(1)) + ")") + SignedVar(2);
}
break;
case 4:
{
SolutionInfix = "(" + SignedVar(2) + " * " + SignedVar(1) + ") / " + SignedVar(0);
//SolutionLaTeX = @"x = \frac{" + MulFromLeft(2) + SignedVar(1) + "}{" + SignedVar(0) + "}";
}
break;
}
SolutionLaTeX = "x = " + LaTeX.Format(Infix.ParseOrThrow(SolutionInfix));
// map it to a random answer
int solutionIndex = rng.Next(answerCount);
AnswersInfix[solutionIndex] = SolutionInfix;
AnswersLaTeX[solutionIndex] = SolutionLaTeX;
// generate the false answers
for (int i = 0; i < answerCount; i++)
{
// don't overwrite the solution
if (i == solutionIndex)
{
continue;
}
// choose a random algorithm to create the next answer
bool[] alreadyTried = new bool[7];
string infix = Infix.ParseOrThrow(SolutionInfix).Equals(0) ? "1" : "0";
int method = -1;
bool ok = false;
for (int tries = 0; tries < 30 && !ok; tries++)
{
var whileTries = 0;
switch (challengeType)
{
case 0:
{
do
{
whileTries++;
if (method != -1)
{
alreadyTried[method] = true;
}
method = rng.Next(7);
switch (method)
{
case 0:
{
infix = "(" + SignedVar(0) + " - " + SignedVar(2) + ") / " + SignedVar(1);
}
break;
case 1:
{
infix = SignedVar(0) + " - " + SignedVar(1) + " - " + SignedVar(2);
}
break;
case 2:
{
infix = SignedVar(0) + " - (" + SignedVar(1) + " + " + SignedVar(2) + ")";
}
break;
case 3:
{
infix = SignedVar(0) + " / (" + SignedVar(1) + " * " + SignedVar(2) + ")";
}
break;
case 4:
{
infix = SignedVar(1) + " + " + SignedVar(2);
}
break;
case 5:
{
infix = SignedVar(1) + " / (" + SignedVar(0) + " + " + SignedVar(2) + ")";
}
break;
case 6:
{
infix = SignedVar(2) + " / (" + SignedVar(0) + " + " + SignedVar(1) + ")";
}
break;
}
}while (alreadyTried[method] && whileTries < 14);
}
break;
case 1:
{
do
{
whileTries++;
if (method != -1)
{
alreadyTried[method] = true;
}
method = rng.Next(6);
switch (method)
{
case 0:
{
infix = SignedVar(1) + " / (" + SignedVar(2) + " - " + SignedVar(0) + ")";
}
break;
case 1:
{
infix = SignedVar(0) + " / (" + SignedVar(1) + " + " + SignedVar(2) + ")";
}
break;
case 2:
{
infix = "(" + SignedVar(0) + " + " + SignedVar(1) + ") / " + SignedVar(2);
}
break;
case 3:
{
infix = "(" + SignedVar(2) + " * " + SignedVar(1) + ") /" + SignedVar(0);
}
break;
case 4:
{
infix = "(" + SignedVar(0) + " + " + SignedVar(1) + ") *" + SignedVar(2);
}
break;
case 5:
{
infix = "(" + SignedVar(0) + " + " + SignedVar(2) + ") /" + SignedVar(1);
}
break;
}
}while (alreadyTried[method] && whileTries < 14);
}
break;
case 2:
{
do
{
whileTries++;
if (method != -1)
{
alreadyTried[method] = true;
}
method = rng.Next(6);
switch (method)
{
case 0:
{
infix = SignedVar(0) + " / (" + SignedVar(1) + " + " + SignedVar(2) + ")";
}
break;
case 1:
{
infix = SignedVar(1) + " / (" + SignedVar(0) + " - " + SignedVar(2) + ")";
}
break;
case 2:
{
infix = "1 / (" + SignedVar(2) + " - " + SignedVar(0) + " - " + SignedVar(1) + ")";
}
break;
case 3:
{
infix = "(" + SignedVar(0) + " + " + SignedVar(2) + ") /" + SignedVar(1);
}
break;
case 4:
{
infix = "(" + SignedVar(1) + " + " + SignedVar(2) + ") /" + SignedVar(0);
}
break;
case 5:
{
infix = "(" + SignedVar(1) + " - " + SignedVar(0) + ") /" + SignedVar(2);
}
break;
}
}while (alreadyTried[method] && whileTries < 14);
}
break;
case 3:
{
do
{
whileTries++;
if (method != -1)
{
alreadyTried[method] = true;
}
method = rng.Next(6);
switch (method)
{
case 0:
{
infix = "(" + SignedVar(0) + " + " + SignedVar(1) + ") /" + SignedVar(2);
}
break;
case 1:
{
infix = SignedVar(0) + " / (" + SignedVar(1) + " + " + SignedVar(2) + ")";
}
break;
case 2:
{
infix = SignedVar(1) + " / (" + SignedVar(0) + " - " + SignedVar(2) + ")";
}
break;
case 3:
{
infix = "(" + SignedVar(0) + " + " + SignedVar(2) + ") *" + SignedVar(1);
}
break;
case 4:
{
infix = "(" + SignedVar(1) + " + " + SignedVar(2) + ") *" + SignedVar(0);
}
break;
case 5:
{
infix = "(" + SignedVar(2) + " - " + SignedVar(1) + ") *" + SignedVar(0);
}
break;
}
}while (alreadyTried[method] && whileTries < 14);
}
break;
case 4:
{
do
{
whileTries++;
if (method != -1)
{
alreadyTried[method] = true;
}
method = rng.Next(6);
switch (method)
{
case 0:
{
infix = SignedVar(0) + " / (" + SignedVar(1) + " + " + SignedVar(2) + ")";
}
break;
case 1:
{
infix = SignedVar(1) + " / (" + SignedVar(0) + " - " + SignedVar(2) + ")";
}
break;
case 2:
{
infix = "(" + SignedVar(0) + " * " + SignedVar(1) + ") /" + SignedVar(2);
}
break;
case 3:
{
infix = "(" + SignedVar(0) + " * " + SignedVar(2) + ") /" + SignedVar(1);
}
break;
case 4:
{
infix = SignedVar(2) + " / (" + SignedVar(0) + " * " + SignedVar(1) + ")";
}
break;
case 5:
{
infix = SignedVar(0) + " / (" + SignedVar(2) + " * " + SignedVar(1) + ")";
}
break;
}
}while (alreadyTried[method] && whileTries < 14);
}
break;
}
// check if the answer is ok
ok = true;
// check if the answer is identical to another
foreach (string answer in AnswersInfix)
{
// if it is, begin anew
if (answer != null && answer.Equals(infix))
{
ok = false;
}
}
// check if the answer is actually a solution
if (IsSolution(infix))
{
ok = false;
tries--;
}
}
AnswersInfix[i] = infix;
AnswersLaTeX[i] = "x = " + LaTeX.Format(Infix.ParseOrThrow(AnswersInfix[i]));
}
}
internal static string InfixToLatex(string infix)
{
return(LaTeX.Format(Infix.ParseOrUndefined(infix)));
}