private static Tuple <string, TokenTypes, int> GetNextToken(string expression)
{
// Try to get a number first
var number = ExpressionRegex.GetNextNumber(expression);
// Try function next
var function = ExpressionRegex.GetNextMathFunction(expression);
// Operand last
var operand = ExpressionRegex.GetNextOperand(expression);
// Find the min index. This will indicate what the next token is
var minIndex = Math.Min(Math.Min(number.Item2, function.Item2), operand.Item2);
if (minIndex == number.Item2)
{
return(new Tuple <string, TokenTypes, int>(number.Item1, TokenTypes.Number, number.Item2));
}
if (minIndex == function.Item2)
{
return(new Tuple <string, TokenTypes, int>(function.Item1, TokenTypes.Function, function.Item2));
}
if (minIndex == operand.Item2)
{
return(new Tuple <string, TokenTypes, int>(operand.Item1, TokenTypes.Operand, operand.Item2));
}
return(new Tuple <string, TokenTypes, int>(string.Empty, TokenTypes.None, int.MinValue));
}
public static double Calculate(string expression)
{
var calcStack = new Stack <string>();
var rpnNotation = Parser.ConvertToRPN(expression);
while (rpnNotation.Count > 0)
{
var rpnToken = rpnNotation.Pop();
if (ExpressionRegex.IsFunction(rpnToken))
{
var argumentCount = ExpressionRegex.FunctionArgumentCount[rpnToken];
if (calcStack.Count >= argumentCount)
{
var argList = new List <double>();
for (var i = 0; i < argumentCount; i++)
{
argList.Add(double.Parse(calcStack.Pop()));
}
var calculateFunctionResult = CalculateFunction(rpnToken, argList.ToArray()).ToString();
calcStack.Push(calculateFunctionResult);
}
else
{
throw new ArgumentException($"Unable to find {argumentCount} arguments for {rpnToken}");
}
}
else if (ExpressionRegex.IsOperand(rpnToken))
{
if (calcStack.Count < 2)
{
throw new ArgumentException($"Unable to find 2 arguments for {rpnToken}");
}
else
{
var arg1 = double.Parse(calcStack.Pop());
var arg2 = double.Parse(calcStack.Pop());
var calculateOperandResult = CalculateOperand(rpnToken, arg2, arg1).ToString();
calcStack.Push(calculateOperandResult);
}
}
else // Number TokenType
{
calcStack.Push(rpnToken);
}
}
// There should be only 1 item left on the stack at this stage
return(double.Parse(calcStack.Pop()));
}
/// <summary>
/// Implementation of the Shunting-yard algorithm which is a method for parsing mathematical expressions
/// specified in infix notation to postfix notation string, also known as Reverse Polish notation
/// </summary>
/// <param name="expression">expression to convert from infix notation to postif notation</param>
/// <returns>expression in Reverse Polish notation</returns>
public static Stack <string> ConvertToRPN(string inputExpression)
{
var returnValue = new Stack <string>();
var index = 0;
var functionsAndOperands = new List <TokenTypes> {
TokenTypes.Function, TokenTypes.Operand
};
var operatorPrecedence = new Dictionary <string, int> {
{ "(", 5 }, { ")", 5 }, { "^", 4 }, { "*", 3 }, { "/", 3 }, { "+", 2 }, { "-", 2 }
};
var brackets = new[] { "(", ")" };
var rpnSb = new List <string>();
var stack = new Stack <string>();
var expression = ExpressionRegex.RemoveAllWhiteSpaces(inputExpression);
while (index < expression.Length)
{
var token = GetNextToken(expression.Substring(index));
if (token.Item2 == TokenTypes.None)
{
break;
}
if (token.Item2 == TokenTypes.Number)
{
rpnSb.Add(token.Item1);
index += token.Item3 + token.Item1.Length;
}
else if (functionsAndOperands.Contains(token.Item2))
{
string stackPeek = stack.Count > 0 ? stack.Peek() : string.Empty;
if (token.Item1 == ")")
{
while (stack.Any())
{
var stackPop = stack.Pop();
if (stackPop == "(")
{
break;
}
rpnSb.Add(stackPop);
}
}
// Check if the top and of the Stack and the current operand are of the same precedence
// Note: Same rule applies when we're processing an operand and we have function (not one of the brackets!) on top of the stack
else if (operatorPrecedence.ContainsKey(token.Item1) && operatorPrecedence.ContainsKey(stackPeek) &&
operatorPrecedence[token.Item1] == operatorPrecedence[stackPeek] && token.Item1 != "^" ||
token.Item2 == TokenTypes.Operand && !brackets.Contains(token.Item1) && ExpressionRegex.IsFunction(stackPeek))
{
rpnSb.Add(stack.Pop());
stack.Push(token.Item1);
}
else
{
stack.Push(token.Item1);
}
index += token.Item3 + token.Item1.Length;
}
}
while (stack.Count > 0)
{
rpnSb.Add(stack.Pop());
}
rpnSb.Reverse();
rpnSb.ForEach(p => returnValue.Push(p));
return(returnValue);
}
