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

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

This article delves into the task of parsing an arithmetic expression and constructing a corresponding tree data structure in Java. The objective is to process an expression like "(5 2)*7" into a tree resembling the expression's structure.

Approach: Using a Stack

To parse the expression, a stack can be utilized. The approach involves iteratively processing tokens from the expression:

• If an opening parenthesis "(" is encountered, it is pushed onto the stack.
• If a number (operand) is encountered, it is stored as a leaf node and pushed onto the stack.

• If an operator ( , -, *, /) is encountered:

  • Its precedence is compared to the top operator on the stack.
  • If the precedence is lower or equal, the expression is evaluated up to the previous "(" or the beginning of the expression.
  • The result of the evaluation is pushed onto the stack.

Example: Parsing "(5 2)*7"

Consider parsing the expression "(5 2)*7":

• "(" is pushed onto the stack.
• "5" is pushed onto the stack as a leaf node.
• " " is pushed onto the stack.
• "2" is pushed onto the stack as a leaf node.

• ")" is encountered, so the expression "5 2" is evaluated:

  • The leaf nodes "5" and "2" are popped from the stack.
  • A new addition node " " is created, with the two leaf nodes as its children.
  • The addition node is pushed onto the stack.
• "*" is pushed onto the stack.
• "7" is pushed onto the stack as a leaf node.

• "eof" (end of expression) is encountered, so the expression "(node) 7" is evaluated:

  • The multiplication node "(*node)" and the leaf node "7" are popped from the stack.
  • A new multiplication node "*" is created and pushed onto the stack.

The final tree structure retrieved from the stack will align with the original expression:

    *
   / \
  +   7
 / \
5   2

Conclusion

Using a stack to parse arithmetic expressions allows for efficient construction of tree data structures representing those expressions. This approach enables further operations and analysis to be performed on the parsed trees.

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