How to Parse and Build a Tree from Arithmetic Expressions in Java?

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

Introduction

Parsing arithmetic expressions and constructing equivalent trees is an essential task in compiler design and language processing. This article will demonstrate how to parse an arithmetic expression and create a tree representation in Java.

Parsing the Expression

To parse the expression, we can use a stack-based algorithm. As we iterate through the expression:

• Push opening parentheses onto the stack.
• Push numbers and operators onto the stack.
• Encountering a closing parenthesis, evaluate the subtree by popping the stack until reaching the matching opening parenthesis, then push the result onto the stack.

Building the Tree

Once the expression is parsed, we can build the tree nodes from the stack:

• Leaf Nodes: Integers become LeafInt nodes.
• Operator Nodes: Operators become nodes with PlusOp, MinusOp, MultOp, or DivOp classes, and their children are pops from the stack.

Example

Consider the expression (5 2)*7:

<code class="java">Stack<Node> stack = new Stack<>();
stack.push(new LeafInt(5));
stack.push(new PlusOp());
stack.push(new LeafInt(2));
stack.push(new MultOp());
stack.push(new LeafInt(7));
while (stack.size() > 1) {
  Node right = stack.pop();
  Operator op = (Operator) stack.pop();
  Node left = stack.pop();
  stack.push(new OpNode(op, left, right));
}</code>

The resulting tree would have the following structure:

    *
   / \
  +   7
 / \
5   2

Handling Negative Numbers and Parentheses

To handle negative numbers, represent them as 5 (-2) instead of 5-2. Negative signs always have unary precedence. Similarly, parentheses force the order of operations.

Validation

To ensure correctness, validate the expression by checking:

• Opening parentheses have matching closing parentheses.
• Each operator has the correct number of operands.

Conclusion

Using a stack-based algorithm, it is straightforward to parse arithmetic expressions and build their equivalent tree representations. This approach provides a reliable foundation for further analysis and manipulation of arithmetic expressions in Java.

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