# Introduction to Trees

### Problems

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 %: Simple Arithmetic Tree
The above represents (3 + 4) .

Problem : Convert the following expression into such a tree: ((3 + 4)*5)/6

Problem : Convert the following expression into such a tree: 3 + 4*(5/6)

Problem : 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.

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