Programming Project: Expression Trees
This project is adapted from Project 1 of Chapter 9 of the textbook. It deals with a simple kind of expression trees, in which there are two kinds of nodes:
(a) Leaf nodes, which contain a real number as their clement; and
(b) Non-leaf nodes, which have exactly two children and contain one of these characters as their element: +, -, * and /. These characters represent arithmetic operations and have usual interpretations.
Implement a class for expression trees with these operations:
(a) A constructor that builds an expression tree. It accepts a String that represents a grammatically correct expression as its sole input. Hint: refer to a previous assignment on evaluating expressions.
(b) A recursive method named eval that evaluates a non-empty expression tree using these rules:
i. If the tree has only one node (which must be a leaf), then eval returns the real number that is the node's clement;
ii. If the tree has more than one node and the root contains op where op is one of +, -, * and /, then eval first evaluates the sub-trees of the root and returns the real number obtained by performing operation op on the results from evaluating the sub-trees.
(c) A recursive method named infix that output the expression represented by a non-empty expression tree to a String in infix format.
(d) A recursive method named postfix that outputs the expression represented by a non-empty expression tree in postfix format.
You also need to write another class that applies the operations of the above class.
Please submit
1. Analysis: test data;
2. Design:
- A class invariant for each class;
- Pre/Post conditions for required operations;
- Algorithms for required operations.
3. Code;
4. Screen snapshots of test runs.