It is possible to represent arithmetic, parenthesized expressions using a
tree. If a node is an operator, such as a plus or a division sign, then
each of the two children must be either a number or an expression which
will evaluate to a number. In other words, the two children of an operator
will be its operands.
Figure 1.5: Simple Arithmetic Tree
The above represents
(3 + 4).
Problem 1.1:
Convert the following expression into such a tree:
((3 + 4)*5)/6
[Solution]
Problem 1.2:
Convert the following expression into such a tree:
3 + 4*(5/6)
[Solution]
Problem 1.3:
How could you use this tree representation to devise a scheme to represent
the expressions without using any parentheses. Hint: Consider a the
different sorts of traversals. See the
recursion
SparkNote
for information on
tree traversals.
[Solution]
