How to Parse Arithmetic Expressions and Create Tree Representations in Java?

Parsing Arithmetic Expressions into Tree Structures in Java

In this article, we tackle the challenge of parsing arithmetic expressions and constructing corresponding tree structures. Given an expression like "(5 2)*7," the goal is to create a tree representation reflecting the expression's structure.

To achieve this, we leverage a stack data structure. The parsing process unfolds as follows:

• Push parentheses '(' onto the stack.
• Push operands (e.g., "5") and operators (e.g., " ") onto the stack.
• When an opening parenthesis is encountered, push it onto the stack.
• When a closing parenthesis is encountered, evaluate the contents of the stack until reaching the matching opening parenthesis.
• Push a node representing the evaluated expression onto the stack.
• Repeat steps until all characters in the expression have been processed.

In situations where the expression contains multiple operators, the order of precedence must be considered. To handle this, a "highest current precedence" variable is maintained, which assigns priorities to operators ( /-), (* or /), and "^." If the precedence of a newly encountered operator is lower or equal to the current precedence, evaluation is performed.

For instance, in the expression "5 2 7," the stack would contain "5," " ," "2," and "" before encountering the " ." As "" has higher precedence, it is pushed onto the stack. When evaluating the stack, the top three elements ("5," "2," and "") are combined into a "*" node. This process continues until the entire expression has been processed, resulting in the desired tree structure.

By employing a stack-based approach, we can efficiently parse arithmetic expressions and construct corresponding tree structures, enabling further operations or analysis based on the expression's structure.

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