public void Parse(string expression)
{
this.output = new Queue();
this.ops = new Stack();
this.stringOriginalExpression = expression;
string stringBuffer = expression.ToLower();
// captures numbers. Anything like 11 or 22.34 is captured
stringBuffer = Regex.Replace(stringBuffer, @"(?<number>\d+(\.\d+)?)", " ${number} ");
// captures these symbols: + - * / ( ) ,
stringBuffer = Regex.Replace(stringBuffer, @"(?<ops>[+\-*/(),])", " ${ops} ");
// captures alphabets. Currently captures the two math constants PI and E,
// and the natural logarithm, power and square root
stringBuffer = Regex.Replace(stringBuffer, "(?<alpha>(pi|e|ln|sqrt|pow))", " ${alpha} ");
// trims up consecutive spaces and replace it with just one space
stringBuffer = Regex.Replace(stringBuffer, @"\s+", " ").Trim();
// The following chunk captures unary minus operations.
// 1) We replace every minus sign with the string "MINUS".
// 2) Then if we find a "MINUS" with a number or constant in front,
// then it's a normal minus operation.
// 3) If we find "MINUS" with a right bracket in front,
// then it's a normal minus operation.
// 4) Otherwise, it's a unary minus operation.
// Step 1.
stringBuffer = Regex.Replace(stringBuffer, "-", "MINUS");
// Step 2. Looking for pi or e or generic number \d+(\.\d+)?
stringBuffer = Regex.Replace(stringBuffer, @"(?<number>(pi|e|(\d+(\.\d+)?)))\s+MINUS", "${number} -");
// Step 3. Looking for )
stringBuffer = Regex.Replace(stringBuffer, @"(?<number>[)])\s+MINUS", "${number} -");
// Step 4. Use the tilde ~ as the unary minus operator
stringBuffer = Regex.Replace(stringBuffer, "MINUS", "~");
this.stringTransitionExpression = stringBuffer;
// tokenize it!
string[] stringParsed = stringBuffer.Split(" ".ToCharArray());
int i = 0;
double tokenValue;
bool number = false;
ReversePolishNotationToken token;
ReversePolishNotationToken opstoken;
for (i = 0; i < stringParsed.Length; ++i)
{
token = new ReversePolishNotationToken();
token.TokenValue = stringParsed[i];
token.TokenValueType = TokenType.None;
number = double.TryParse(stringParsed[i], out tokenValue);
if (number)
{
token.TokenValueType = TokenType.Number;
// If the token is a number, then add it to the output queue.
this.output.Enqueue(token);
}
else
{
switch (stringParsed[i])
{
case "+":
{
token.TokenValueType = TokenType.Plus;
if (this.ops.Count > 0)
{
opstoken = (ReversePolishNotationToken)this.ops.Peek();
// while there is an operator, o2, at the top of the stack
while (this.IsOperatorToken(opstoken.TokenValueType))
{
// pop o2 off the stack, onto the output queue;
this.output.Enqueue(this.ops.Pop());
if (this.ops.Count > 0)
{
opstoken = (ReversePolishNotationToken)this.ops.Peek();
}
else
{
break;
}
}
}
// push o1 onto the operator stack.
this.ops.Push(token);
break;
}
case "-":
{
token.TokenValueType = TokenType.Minus;
if (this.ops.Count > 0)
{
opstoken = (ReversePolishNotationToken)this.ops.Peek();
// while there is an operator, o2, at the top of the stack
while (this.IsOperatorToken(opstoken.TokenValueType))
{
// pop o2 off the stack, onto the output queue;
this.output.Enqueue(this.ops.Pop());
if (this.ops.Count > 0)
{
opstoken = (ReversePolishNotationToken)this.ops.Peek();
}
else
{
break;
}
}
}
// push o1 onto the operator stack.
this.ops.Push(token);
break;
}
case "*":
{
token.TokenValueType = TokenType.Multiply;
if (this.ops.Count > 0)
{
opstoken = (ReversePolishNotationToken)this.ops.Peek();
// while there is an operator, o2, at the top of the stack
while (this.IsOperatorToken(opstoken.TokenValueType))
{
if (opstoken.TokenValueType == TokenType.Plus || opstoken.TokenValueType == TokenType.Minus)
{
break;
}
else
{
// Once we're in here, the following algorithm condition is satisfied.
// o1 is associative or left-associative and its precedence is less than (lower precedence) or equal to that of o2, or
// o1 is right-associative and its precedence is less than (lower precedence) that of o2,
// pop o2 off the stack, onto the output queue;
this.output.Enqueue(this.ops.Pop());
if (this.ops.Count > 0)
{
opstoken = (ReversePolishNotationToken)this.ops.Peek();
}
else
{
break;
}
}
}
}
// push o1 onto the operator stack.
this.ops.Push(token);
break;
}
case "/":
{
token.TokenValueType = TokenType.Divide;
if (this.ops.Count > 0)
{
opstoken = (ReversePolishNotationToken)this.ops.Peek();
// while there is an operator, o2, at the top of the stack
while (this.IsOperatorToken(opstoken.TokenValueType))
{
if (opstoken.TokenValueType == TokenType.Plus || opstoken.TokenValueType == TokenType.Minus)
{
break;
}
else
{
// Once we're in here, the following algorithm condition is satisfied.
// o1 is associative or left-associative and its precedence is less than (lower precedence) or equal to that of o2, or
// o1 is right-associative and its precedence is less than (lower precedence) that of o2,
// pop o2 off the stack, onto the output queue;
this.output.Enqueue(this.ops.Pop());
if (this.ops.Count > 0)
{
opstoken = (ReversePolishNotationToken)this.ops.Peek();
}
else
{
break;
}
}
}
}
// push o1 onto the operator stack.
this.ops.Push(token);
break;
}
case "~":
{
token.TokenValueType = TokenType.UnaryMinus;
// push o1 onto the operator stack.
this.ops.Push(token);
break;
}
case ",":
{
token.TokenValueType = TokenType.Coma;
// Until the topmost element of the stack is a left parenthesis,
// pop the element onto the output queue.
if (this.ops.Count > 0)
{
opstoken = (ReversePolishNotationToken)this.ops.Peek();
// Until the token at the top of the stack is a left parenthesis
while (opstoken.TokenValueType != TokenType.LeftParenthesis)
{
// pop operators off the stack onto the output queue
this.output.Enqueue(this.ops.Pop());
if (this.ops.Count > 0)
{
opstoken = (ReversePolishNotationToken)this.ops.Peek();
}
else
{
// If the stack runs out without finding a left parenthesis,
// then there are mismatched parentheses.
throw new Exception("Unbalanced parenthesis!");
}
}
}
break;
}
case "(":
{
token.TokenValueType = TokenType.LeftParenthesis;
// If the token is a left parenthesis, then push it onto the stack.
this.ops.Push(token);
break;
}
case ")":
{
token.TokenValueType = TokenType.RightParenthesis;
if (this.ops.Count > 0)
{
opstoken = (ReversePolishNotationToken)this.ops.Peek();
// Until the token at the top of the stack is a left parenthesis
while (opstoken.TokenValueType != TokenType.LeftParenthesis)
{
// pop operators off the stack onto the output queue
this.output.Enqueue(this.ops.Pop());
if (this.ops.Count > 0)
{
opstoken = (ReversePolishNotationToken)this.ops.Peek();
}
else
{
// If the stack runs out without finding a left parenthesis,
// then there are mismatched parentheses.
throw new Exception("Unbalanced parenthesis!");
}
}
// Pop the left parenthesis from the stack, but not onto the output queue.
this.ops.Pop();
}
if (this.ops.Count > 0)
{
opstoken = (ReversePolishNotationToken)this.ops.Peek();
// If the token at the top of the stack is a function token
if (this.IsFunctionToken(opstoken.TokenValueType))
{
// pop it and onto the output queue.
this.output.Enqueue(this.ops.Pop());
}
}
break;
}
case "pi":
{
token.TokenValueType = TokenType.Constant;
// If the token is a number, then add it to the output queue.
this.output.Enqueue(token);
break;
}
case "e":
{
token.TokenValueType = TokenType.Constant;
// If the token is a number, then add it to the output queue.
this.output.Enqueue(token);
break;
}
case "ln":
{
token.TokenValueType = TokenType.NaturalLogarithm;
// If the token is a function token, then push it onto the stack.
this.ops.Push(token);
break;
}
case "sqrt":
{
token.TokenValueType = TokenType.SquareRoot;
// If the token is a function token, then push it onto the stack.
this.ops.Push(token);
break;
}
case "pow":
{
token.TokenValueType = TokenType.Power;
// push o1 onto the operator stack.
this.ops.Push(token);
break;
}
}
}
}
// When there are no more tokens to read:
// While there are still operator tokens in the stack:
while (this.ops.Count != 0)
{
opstoken = (ReversePolishNotationToken)this.ops.Pop();
// If the operator token on the top of the stack is a parenthesis
if (opstoken.TokenValueType == TokenType.LeftParenthesis)
{
// then there are mismatched parenthesis.
throw new Exception("Unbalanced parenthesis!");
}
else
{
// Pop the operator onto the output queue.
this.output.Enqueue(opstoken);
}
}
this.stringPostfixExpression = string.Empty;
foreach (object obj in this.output)
{
opstoken = (ReversePolishNotationToken)obj;
this.stringPostfixExpression += string.Format("{0} ", opstoken.TokenValue);
}
}
public double Evaluate()
{
Stack result = new Stack();
double oper1 = 0.0;
double oper2 = 0.0;
ReversePolishNotationToken token = new ReversePolishNotationToken();
// While there are input tokens left
foreach (object obj in this.output)
{
// Read the next token from input.
token = (ReversePolishNotationToken)obj;
switch (token.TokenValueType)
{
case TokenType.Number:
// If the token is a value
// Push it onto the stack.
{
result.Push(double.Parse(token.TokenValue));
break;
}
case TokenType.Constant:
// If the token is a value
// Push it onto the stack.
{
result.Push(this.EvaluateConstant(token.TokenValue));
break;
}
case TokenType.Plus:
// NOTE: n is 2 in this case
// If there are fewer than n values on the stack
{
if (result.Count >= 2)
{
// So, pop the top n values from the stack.
oper2 = (double)result.Pop();
oper1 = (double)result.Pop();
// Evaluate the function, with the values as arguments.
// Push the returned results, if any, back onto the stack.
result.Push(oper1 + oper2);
}
else
{
// (Error) The user has not input sufficient values in the expression.
throw new Exception("Evaluation error!");
}
break;
}
case TokenType.Minus:
// NOTE: n is 2 in this case
// If there are fewer than n values on the stack
{
if (result.Count >= 2)
{
// So, pop the top n values from the stack.
oper2 = (double)result.Pop();
oper1 = (double)result.Pop();
// Evaluate the function, with the values as arguments.
// Push the returned results, if any, back onto the stack.
result.Push(oper1 - oper2);
}
else
{
// (Error) The user has not input sufficient values in the expression.
throw new Exception("Evaluation error!");
}
break;
}
case TokenType.Multiply:
// NOTE: n is 2 in this case
// If there are fewer than n values on the stack
{
if (result.Count >= 2)
{
// So, pop the top n values from the stack.
oper2 = (double)result.Pop();
oper1 = (double)result.Pop();
// Evaluate the function, with the values as arguments.
// Push the returned results, if any, back onto the stack.
result.Push(oper1 * oper2);
}
else
{
// (Error) The user has not input sufficient values in the expression.
throw new Exception("Evaluation error!");
}
break;
}
case TokenType.Divide:
// NOTE: n is 2 in this case
// If there are fewer than n values on the stack
{
if (result.Count >= 2)
{
// So, pop the top n values from the stack.
oper2 = (double)result.Pop();
oper1 = (double)result.Pop();
// Evaluate the function, with the values as arguments.
// Push the returned results, if any, back onto the stack.
result.Push(oper1 / oper2);
}
else
{
// (Error) The user has not input sufficient values in the expression.
throw new Exception("Evaluation error!");
}
break;
}
case TokenType.Power:
// NOTE: n is 2 in this case
// If there are fewer than n values on the stack
{
if (result.Count >= 2)
{
// So, pop the top n values from the stack.
oper2 = (double)result.Pop();
oper1 = (double)result.Pop();
// Evaluate the function, with the values as arguments.
// Push the returned results, if any, back onto the stack.
result.Push(Math.Pow(oper1, oper2));
}
else
{
// (Error) The user has not input sufficient values in the expression.
throw new Exception("Evaluation error!");
}
break;
}
case TokenType.UnaryMinus:
// NOTE: n is 1 in this case
// If there are fewer than n values on the stack
{
if (result.Count >= 1)
{
// So, pop the top n values from the stack.
oper1 = (double)result.Pop();
// Evaluate the function, with the values as arguments.
// Push the returned results, if any, back onto the stack.
result.Push(-oper1);
}
else
{
// (Error) The user has not input sufficient values in the expression.
throw new Exception("Evaluation error!");
}
break;
}
case TokenType.NaturalLogarithm:
// NOTE: n is 1 in this case
// If there are fewer than n values on the stack
{
if (result.Count >= 1)
{
// So, pop the top n values from the stack.
oper1 = (double)result.Pop();
// Evaluate the function, with the values as arguments.
// Push the returned results, if any, back onto the stack.
result.Push(Math.Log(oper1));
}
else
{
// (Error) The user has not input sufficient values in the expression.
throw new Exception("Evaluation error!");
}
break;
}
case TokenType.SquareRoot:
// NOTE: n is 1 in this case
// If there are fewer than n values on the stack
{
if (result.Count >= 1)
{
// So, pop the top n values from the stack.
oper1 = (double)result.Pop();
// Evaluate the function, with the values as arguments.
// Push the returned results, if any, back onto the stack.
result.Push(Math.Sqrt(oper1));
}
else
{
// (Error) The user has not input sufficient values in the expression.
throw new Exception("Evaluation error!");
}
break;
}
}
}
// If there is only one value in the stack
if (result.Count == 1)
{
// That value is the result of the calculation.
return((double)result.Pop());
}
else
{
// If there are more values in the stack
// (Error) The user input too many values.
throw new Exception("Evaluation error!");
}
}
