Example 02 - More About Algebraic Tree

In previous example we demonstrated how to build an algebraic tree for a simple addition expression. In this chapter we will walk through building arbitrarily complicated algebraic tree.

General Rules of Building Algebraic Tree

The following is a three step rule to build an algebraic tree.

1. Write down the algebraic expression in the way we usually do
   For example:
   ((a * b + c * d) / e + (f * g + h * i) / 2) / 12
2. Use parenthesis to group the "operators" based on the precedence of evaluation
   For example, for the expression above, we have:
   ((((a * b) + (c * d)) / e) + (((f * g) + (h * i)) / 2)) / 12
   In order to make it clear we use color code to show different group of parenthesis.
3. Build the expression from "outer" parenthesis groups to "deeper" parenthesis groups
   The "deeper" the expression in the parenthesis grouping, the deeper tree node it belongs to in the expression tree. Deeper tree nodes should be added later than the "shallower" nodes.

Example 2.1: The Expression Tree of the Above Expression

The following screen shot shows the expression tree of the expression: ((a * b + c * d) / e + (f * g + h * i) / 2) / 12

Tips: User can add comments to expression tree node by writing text in the upper right panel. The lower panel displays the pseudo-code of the expression.

Example 2.2: Another Expression Tree Example

The follow is the tree of a Boolean expression: (a AND b) OR (c AND d)