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# Title: Evaluate mathematical expressions with code in C#

This program shows how you can use C# code to evaluate mathematical expressions. The program starts with the following code.

// Stores user-entered primitives like X = 10. private Dictionary<string, string> Primatives; private enum Precedence { None = 11, Unary = 10, // Not actually used. Power = 9, // We use ^ to mean exponentiation. Times = 8, Div = 7, Modulus = 6, Plus = 5, }

This code declares a Dictionary that it will later use to hold variables. (For example, if the user wants A = 10, B = 3, and Pi = 3.14159265.)

It then defines a Precedence enumeration to represent operator precedence. For example, multiplication has higher precedence than addition.

When you click the Evaluate button, the program copies any primatives you entered into the Primatives Dictionary and then calls the EvaluateExpression method, which does all of the interesting work. That method is long, so I'll describe it in pieces.

// Evaluate the expression. private double EvaluateExpression(string expression) { int best_pos = 0; int parens = 0; // Remove all spaces. string expr = expression.Replace(" ", ""); int expr_len = expr.Length; if (expr_len == 0) return 0; // If we find + or - now, then it's a unary operator. bool is_unary = true; // So far we have nothing. Precedence best_prec = Precedence.None; // Find the operator with the lowest precedence. // Look for places where there are no open // parentheses. for (int pos = 0; pos < expr_len; pos++) { // Examine the next character. string ch = expr.Substring(pos, 1); // Assume we will not find an operator. In // that case, the next operator will not // be unary. bool next_unary = false; if (ch == " ") { // Just skip spaces. We keep them here // to make the error messages easier to } else if (ch == "(") { // Increase the open parentheses count. parens += 1; // A + or - after "(" is unary. next_unary = true; } else if (ch == ")") { // Decrease the open parentheses count. parens -= 1; // An operator after ")" is not unary. next_unary = false; // if parens < 0, too many )'s. if (parens < 0) throw new FormatException( "Too many close parentheses in '" + expression + "'"); } else if (parens == 0) { // See if this is an operator. if ((ch == "^") || (ch == "*") || (ch == "/") || (ch == "\\") || (ch == "%") || (ch == "+") || (ch == "-")) { // An operator after an operator // is unary. next_unary = true; // See if this operator has higher // precedence than the current one. switch (ch) { case "^": if (best_prec >= Precedence.Power) { best_prec = Precedence.Power; best_pos = pos; } break; case "*": case "/": if (best_prec >= Precedence.Times) { best_prec = Precedence.Times; best_pos = pos; } break; case "%": if (best_prec >= Precedence.Modulus) { best_prec = Precedence.Modulus; best_pos = pos; } break; case "+": case "-": // Ignore unary operators // for now. if ((!is_unary) && best_prec >= Precedence.Plus) { best_prec = Precedence.Plus; best_pos = pos; } break; } // End switch (ch) } // End if this is an operator. } // else if (parens == 0) is_unary = next_unary; } // for (int pos = 0; pos < expr_len; pos++)

This part of the method finds the operator in the expression that has the lowest precedence. To do that, it simply loops through the expression examining its operator characters and determining whether they have lower precedence than the previously found operator.

The following piece of code shows the next step.

// If the parentheses count is not zero, // there's a ) missing. if (parens != 0) { throw new FormatException( "Missing close parenthesis in '" + expression + "'"); } // Hopefully we have the operator. if (best_prec < Precedence.None) { string lexpr = expr.Substring(0, best_pos); string rexpr = expr.Substring(best_pos + 1); switch (expr.Substring(best_pos, 1)) { case "^": return Math.Pow( EvaluateExpression(lexpr), EvaluateExpression(rexpr)); case "*": return EvaluateExpression(lexpr) * EvaluateExpression(rexpr); case "/": return EvaluateExpression(lexpr) / EvaluateExpression(rexpr); case "%": return EvaluateExpression(lexpr) % EvaluateExpression(rexpr); case "+": return EvaluateExpression(lexpr) + EvaluateExpression(rexpr); case "-": return EvaluateExpression(lexpr) - EvaluateExpression(rexpr); } }

If there is an unclosed parenthesis, the method throws an exception. Otherwise it breaks the expression into pieces using the operator with lowest precedence as the dividing point. It then calls itself recursively to evaluate the sub-expressions, using the appropriate operation to combine the results.

For example, suppose the expression is 2 * 3 + 4 * 5. Then the operator with the lowest precedence is +. The function breaks the expression into 2 * 3 and 4 * 5, calls itself recursively to evaluate these sub-expressions (getting 6 and 20), and then combines the results using addition (to get 26).

The following code shows how the method handles function calls.

// if we do not yet have an operator, there // are several possibilities: // // 1. expr is (expr2) for some expr2. // 2. expr is -expr2 or +expr2 for some expr2. // 3. expr is Fun(expr2) for a function Fun. // 4. expr is a primitive. // 5. It's a literal like "3.14159". // Look for (expr2). if (expr.StartsWith("(") & expr.EndsWith(")")) { // Remove the parentheses. return EvaluateExpression(expr.Substring(1, expr_len - 2)); } // Look for -expr2. if (expr.StartsWith("-")) { return -EvaluateExpression(expr.Substring(1)); } // Look for +expr2. if (expr.StartsWith("+")) { return EvaluateExpression(expr.Substring(1)); } // Look for Fun(expr2). if (expr_len > 5 & expr.EndsWith(")")) { // Find the first (. int paren_pos = expr.IndexOf("("); if (paren_pos > 0) { // See what the function is. string lexpr = expr.Substring(0, paren_pos); string rexpr = expr.Substring(paren_pos + 1, expr_len - paren_pos - 2); switch (lexpr.ToLower()) { case "sin": return Math.Sin(EvaluateExpression(rexpr)); case "cos": return Math.Cos(EvaluateExpression(rexpr)); case "tan": return Math.Tan(EvaluateExpression(rexpr)); case "sqrt": return Math.Sqrt(EvaluateExpression(rexpr)); case "factorial": return Factorial(EvaluateExpression(rexpr)); // Add other functions (including // program-defined functions) here. } } }

This code checks whether the expression begins with ( and ends with ). If so, it removes those parenthesis and evaluates the rest of the expression.

Next the code determines whether the expression begins with the unary + or - operators. If it does, the program evaluates the expression without the operator and negates the result if the operator is -.

The code then looks for functions such as Sin, Cos, and Factorial. If it finds one, it calls that function and returns the result. (Download the example to se the Factorial function.) You can add other functions similarly.

The following code shows the rest of the method.

// See if it's a primitive. if (Primatives.ContainsKey(expr)) { // Return the corresponding value, // converted into a Double. try { // Try to convert the expression into a value. return double.Parse(Primatives[expr]); } catch (Exception) { throw new FormatException( "Primative '" + expr + "' has value '" + Primatives[expr] + "' which is not a Double."); } } // It must be a literal like "2.71828". try { // Try to convert the expression into a Double. return double.Parse(expr); } catch (Exception) { throw new FormatException( "Error evaluating '" + expression + "' as a constant."); } }

If the expression still have not been evaulated, it must be a primative value you entered into the text boxes or a numeric value. The code checks the Primatives Dictionary to see if the expression is present. If the value is in the Dictionary, the code gets its value, converts it into a double, and returns the result.

If the expression is not in the Dictionary, then it must be a numeric constant. The program tries to parse the expression and return the result.

If the expression is not a numeric constant, the method throws an exception.