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Title Evaluate mathematical expressions using code in VB .NET This example shows how to evaluate mathematical expressions using code in VB .NET. mathematical expression, expression, evaluate, VB.NET Algorithms, Strings

Find the higher precedence operator in the expression. Break the expression into the operator's operands (for example, in 1 + 3 the operator is + and the operands are 1 and 3). Recursively call the EvaluateExpression function to evaluate the operands and combine the results using the correct Visual Basic operator.

A couple details require some thought. First, keep track of the number of open parentheses. If an operator is inside open parentheses, it does not have the highest precedence.

Second, the code needs to watch for unary operators as in +12 and 13 + -6. Where the function encounters a + or - determines whether it is unary. For example, in 13 + -6 the - is unary but the + is not. Read the code to see how the function handles this.

Note how the program handles the code-defined function Factorial. You can add other functions similarly.

```' Evaluate the expression.
Private Function EvaluateExpression(ByVal expression As _
String) As Double
Dim expr As String
Dim is_unary As Boolean
Dim next_unary As Boolean
Dim parens As Integer
Dim expr_len As Integer
Dim ch As String
Dim lexpr As String
Dim rexpr As String
Dim status As Long
Dim best_pos As Integer
Dim best_prec As Precedence

' Remove all spaces.
expr = expression.Replace(" ", "")
expr_len = Len(expr)
If expr_len = 0 Then Return 0

' If we find + or - now, it is a unary operator.
is_unary = True

' So far we have nothing.
best_prec = Precedence.None

' Find the operator with the lowest precedence.
' Look for places where there are no open
' parentheses.
For pos As Integer = 0 To expr_len - 1
' Examine the next character.
ch = expr.Substring(pos, 1)

' Assume we will not find an operator. In
' that case, the next operator will not
' be unary.
next_unary = False

If ch = " " Then
' Just skip spaces. We keep them here
' to make the error messages easier to
ElseIf ch = "(" Then
' Increase the open parentheses count.
parens += 1

' A + or - after "(" is unary.
next_unary = True
ElseIf ch = ")" Then
' 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 Then
Throw New FormatException( _
"Too many close parentheses in '" & _
expression & "'")
End If
ElseIf parens = 0 Then
' See if this is an operator.
If ch = "^" Or ch = "*" Or _
ch = "/" Or ch = "\" Or _
ch = "%" Or ch = "+" Or _
ch = "-" _
Then
' An operator after an operator
' is unary.
next_unary = True

' See if this operator has higher
' precedence than the current one.
Select Case ch
Case "^"
If best_prec >= Precedence.Power _
Then
best_prec = Precedence.Power
best_pos = pos
End If

Case "*", "/"
If best_prec >= Precedence.Times _
Then
best_prec = Precedence.Times
best_pos = pos
End If

Case "\"
If best_prec >= Precedence.IntDiv _
Then
best_prec = Precedence.IntDiv
best_pos = pos
End If

Case "%"
If best_prec >= Precedence.Modulus _
Then
best_prec = Precedence.Modulus
best_pos = pos
End If

Case "+", "-"
' Ignore unary operators
' for now.
If (Not is_unary) And _
best_prec >= Precedence.Plus _
Then
best_prec = Precedence.Plus
best_pos = pos
End If
End Select
End If
End If
is_unary = next_unary
Next pos

' If the parentheses count is not zero,
' there's a ')' missing.
If parens <> 0 Then
Throw New FormatException( _
"Missing close parenthesis in '" & _
expression & "'")
End If

' Hopefully we have the operator.
If best_prec < Precedence.None Then
lexpr = expr.Substring(0, best_pos)
rexpr = expr.Substring(best_pos + 1)
Select Case expr.Substring(best_pos, 1)
Case "^"
Return _
EvaluateExpression(lexpr) ^ _
EvaluateExpression(rexpr)
Case "*"
Return _
EvaluateExpression(lexpr) * _
EvaluateExpression(rexpr)
Case "/"
Return _
EvaluateExpression(lexpr) / _
EvaluateExpression(rexpr)
Case "\"
Return _
CLng(EvaluateExpression(lexpr)) \ _
CLng(EvaluateExpression(rexpr))
Case "%"
Return _
EvaluateExpression(lexpr) Mod _
EvaluateExpression(rexpr)
Case "+"
Return _
EvaluateExpression(lexpr) + _
EvaluateExpression(rexpr)
Case "-"
Return _
EvaluateExpression(lexpr) - _
EvaluateExpression(rexpr)
End Select
End If

' 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("(") And expr.EndsWith(")") Then
' Remove the parentheses.
Return EvaluateExpression(expr.Substring(1, _
expr_len - 2))
Exit Function
End If

' Look for -expr2.
If expr.StartsWith("-") Then
Return -EvaluateExpression(expr.Substring(1))
End If

' Look for +expr2.
If expr.StartsWith("+") Then
Return EvaluateExpression(expr.Substring(2))
End If

' Look for Fun(expr2).
If expr_len > 5 And expr.EndsWith(")") Then
' Find the first (.
Dim paren_pos As Integer = expr.IndexOf("(")
If paren_pos > 0 Then
' See what the function is.
lexpr = expr.Substring(0, paren_pos)
rexpr = expr.Substring(paren_pos + 1, expr_len _
- paren_pos - 2)
Select Case 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))
' program-defined functions) here.
End Select
End If
End If

' See if it's a primitive.
If m_Primatives.Contains(expr) Then
' Return the corresponding value,
' converted into a Double.
Try
' Try to convert the expression into a value.
Dim value As Double = _
Double.Parse(m_Primatives.Item(expr).ToString)
Return value
Catch ex As Exception
Throw New FormatException( _
"Primative '" & expr & _
"' has value '" & _
m_Primatives.Item(expr).ToString & _
"' which is not a Double.")
End Try
End If

' It must be a literal like "2.71828".
Try
' Try to convert the expression into a Double.
Dim value As Double = Double.Parse(expr)
Return value
Catch ex As Exception
Throw New FormatException( _
"Error evaluating '" & expression & _
"' as a constant.")
End Try
End Function

' Return the factorial of the expression.
Private Function Factorial(ByVal value As Double) As Double
Dim result As Double

' Make sure the value is an integer.
If CLng(value) <> value Then
Throw New ArgumentException( _
"Parameter to Factorial function must be an " & _
"integer in Factorial(" & _
Format\$(value) & ")")
End If

result = 1
Do While value > 1
result = result * value
value = value - 1
Loop
Return result
End Function```

For more information on a variety of algorithms, see my book Visual Basic Algorithms.