How to Parse an Arithmetic Expression and Construct a Tree Representation in Java?

Parsing an Arithmetic Expression and Building a Tree from It in Java

In this article, we'll delve into the intricacies of parsing an arithmetic expression and constructing a tree representation of it in Java.

Introduction

To begin with, we'll assume that the input expression is supplied as a string and complies with the following rules:

• Negative numbers must be enclosed in parentheses.
• Parentheses must balance consistently.

Building the Tree

At its core, constructing a tree from an arithmetic expression involves utilizing a stack. As we parse the expression character by character, we push operators and numerical values onto the stack. Operators have an associated precedence, allowing us to evaluate and combine sub-expressions as we encounter them.

Approach

1. Initialize the Stack: Start with an empty stack.
2. Parse the Expression: Visit each character in the expression string.
3. Handle Parentheses: If a parenthesis is encountered, either push it onto the stack or evaluate the sub-expression within parentheses.
4. Handle Operators: On encountering an operator, compare its precedence to the current "highest precedence" in the stack. If current is lower than the new operator's precedence, push the new operator onto the stack. Otherwise, evaluate the operators on the stack until the new operator's precedence is higher or equal.
5. Handle Numerical Values: Push numerical values directly onto the stack.
6. Evaluate the Stack: Once all characters are processed, evaluate the remaining operators on the stack from top to bottom.

Example

Consider the expression:

(5+2)*7

We would parse it as follows:

Character	Action	Stack
(	Push (	(
5	Push 5	(, 5
	Push	(, 5,
2	Push 2	(, 5, , 2
)	Evaluate to 7, push 7	(, 7
*	Push *	(, 7, *
7	Push 7	7, *, 7

The resulting tree would be:

(5+2)*7

Conclusion

Parsing an arithmetic expression and building a tree is a fundamental operation in computer science. This article provided a step-by-step approach using a stack, highlighting the importance of precedence rules and parenthetical balance. Implementing this algorithm in Java will enable you to create powerful applications that can process and manipulate arithmetic expressions effectively.

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