How to solve a Tree Traversal Algorithm?

Question

The following algorithm describes a postorder tree traversal

Postorder(tree)

If left subtree exists then Postorder(left subtree)

If right subtree exists then Postorder(right subtree)

Print root

end

 

Can you apply that to the following  tree

 

 

                                            +

                                        /       \

                                       /         \

                                       *            -

                                      /  \       /     \

                                     2   3    *       +

                                              /  \     /  \

                                             4   2  1   5

What is the result of the executing the algorithm?  what kind of algorithm are we considering here?

Answer 1

Start at left subtree: operands 2, 3; operator is multiply (*), result=2*3=6.

Right subtree: 4*2=8 and 1+5=6; next level up: 8-6=2. Where the operands are derived from the operations at the previous level.

Root: operands 6, 2 operator + gives 6+2=8. Root=8.

Algorithm is (2*3)+(4*2)-(1+5)=8, an arithmetic problem.

The binary operation at each branch appears to be an arithmetic operation (at the root) between two operands (children of the root).