MHB Is this Tree of Algebraic Expression Correct?

[Brian82784]

Hello I just wanted to see if I did this right. I've come up with two trees and I'm pretty sure one of them is correct, I'm just not sure.

Construct the Tree of the algebraic expression:
((x - 2) + 3) / ((2 - (3 + y)) x (w - 8))

 

[evinda]

Hello I just wanted to see if I did this right. I've come up with two trees and I'm pretty sure one of them is correct, I'm just not sure.

Construct the Tree of the algebraic expression:
((x - 2) + 3) / ((2 - (3 + y)) x (w - 8))

Hi! :) I think that both of them are right,but it would be better to include also the parentheses of the algebraic expression at the trees,that you constructed.

 

[Brian82784]

Okay thank you. I also had to do this with one of the trees. So I picked the first tree. Does this look correct?

1) Show the results of performing a preorder search.
× ÷ + - X 2 3 - - 2 3 Y - W 82) Show the results of performing an inorder search.
X – 2 + 3 ÷ 2 – 3 – Y × W - 8 3) Show the results of performing a postorder search.
X 2 - 3 + 2 3 - y - ÷ W 8 - ×

 

[evinda]

Okay thank you. I also had to do this with one of the trees. So I picked the first tree. Does this look correct?

1) Show the results of performing a preorder search.
× ÷ + - X 2 3 - - 2 3 Y - W 82) Show the results of performing an inorder search.
X – 2 + 3 ÷ 2 – 3 – Y × W - 8 3) Show the results of performing a postorder search.
X 2 - 3 + 2 3 - y - ÷ W 8 - ×

I also tried it,and found the same result as yours!It should be right! (Nod) (Yes)

 

[Ackbach]

The one on the right is correct, the one on the left is incorrect. The one on the left is evaluating the expression $\dfrac{(x-2)+3}{(2-3)-y}(w-8),$ whereas the one on the right is evaluating the expression $\dfrac{(x+2)-3}{(2-(3+y)) \cdot (w-8)}$. You can see that in the left version, $w-8$ is in the numerator, whereas in the right version, $w-8$ is in the denominator.

 

[Brian82784]

So the one I did starting with Division is actually correct

 

[evinda]

The one on the right is correct, the one on the left is incorrect. The one on the left is evaluating the expression $\dfrac{(x-2)+3}{(2-3)-y}(w-8),$ whereas the one on the right is evaluating the expression $\dfrac{(x+2)-3}{(2-(3+y)) \cdot (w-8)}$. You can see that in the left version, $w-8$ is in the numerator, whereas in the right version, $w-8$ is in the denominator.

Oh,yes you are right! Sorry for assuming that the left tree is also right.. (Sadface)

 

[Ackbach]

So the one I did starting with Division is actually correct

Right - the "biggest" mathematical operator is the last one you'd evaluate.

By the way, the only reason I can answer this question is that http://mathhelpboards.com/mathematics-software-calculator-discussion-29/hp-50g-1953.html?highlight=calculator, with Reverse Polish Notation (postfix notation) and a stack. That's a very nice combination, because it let's you play with calculations as you go.

 

[Brian82784]

So then would this be correct for the tree on the right?

1) Show the results of performing a preorder search.
÷ + - X 2 3 × - 2 + 3 Y- W 82) Show the results of performing an inorder search.
X – 2 + 3 ÷ 2 – 3 +Y × W - 8 3) Show the results of performing a postorder search.
X 2 - 3 + 2 3 y +- W 8 - ×÷

 

[Evgeny.Makarov]

So then would this be correct for the tree on the right?

Yes, they seem correct.