# Problems building expression tree from postfix notation

algorithm expression-trees language-agnostic postfix-notation ### Question

I'm currently writing an impreter for simple mathematical expressions (constants and simple arithmetic).

The problem I'm having is with building an expression tree from a postfix formatted expression. What I've done works fine in most scenarios, but not with this example from Wikipedia.

If I evaluate the expression `3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3`, I get the result `3,0001220703125` even though the result should be `3,001953125`. The reason for this seems to be that the expression tree looks like `3+((4*2)/((1-5)^(2^3)))` instead of `(3+((4*2)/(((1-5)^2)^3)))`.

The postfix notation of the original expression looks like `3 4 2 * 1 5 âˆ’ 2 3 ^ ^ / +`

Any suggestions how to get the expression tree as I want it to be?
Below is the postfix to expression tree code and some tests which is in C# but should be pretty self-explanatory.

``````public MathExpression Parse()
{
var tokens = this.ToPostFix(_tokens);
var stack = new Stack<MathExpression>();
foreach(token in tokens)
{
if(token.IsOperand())
{
// Push the operand on the stack.
stack.Push(new ConstantExpression(token.Value));
}
else
{
Debug.Assert(token.Type == TokenType.Operator, "Expected operator.");
var op = (Operator)token.Value;
var right = stack.Pop();
var left = stack.Pop();
var expression = new ArithmeticExpression(op, left, right);
stack.Push(expression);
}
}
Debug.Assert(stack.Count == 1, "More than one expression on stack.");
return stack.Pop();
}
``````

And some tests:

``````[Test]
public void Wikipedia_Example_Can_Be_Evaluated()
{
var expected = 3+4*2/(1-5)^2^3; // 3,001953125
var actual = MathExpression.Parse("3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3")
.Evaluate(); // 3,0001220703125
Assert.AreEqual(expected, actual); // Not equal :(
}

[Test]
public void Can_Convert_To_Prefix()
{
string expected = "3 4 2 * 1 5 âˆ’ 2 3 ^ ^ / +"
string actual = MathExpression.ToPostFix("3+4*2/(1-5)^2^3")
Assert.AreEqual(expected, actual); // Works as expected
}
``````
1
0
7/4/2012 11:49:05 AM

#### Fastest Entity Framework Extensions

`^` is evaluated right-to-left

I don't see your code taking that into account, `^` is treated the same as the other operators, as left-associative.

That means that your interpretation might be wrong:

`x ^ 2 ^ 3` => `x^(2^3)` => `x 2 3 ^ ^`

5
7/5/2012 4:10:16 PM

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