Parsing Arithmetic Expressions into Tree Structures in Java

Creating custom trees from arithmetic expressions can be a challenging task, particularly when ensuring the tree structure accurately reflects the expression's operations and precedence.

To achieve this, one effective approach involves using a stack. Here's a step-by-step description of the process:

1. Initialization: Start with an empty stack.

2. Processing Tokens: Iterate through each token in the expression:

   • If the token is an opening parenthesis, push it onto the stack.
   • If the token is an integer, create a new leaf node containing the integer and push it onto the stack.

   • If the token is an operator, check its precedence:

     • If the operator's precedence is higher than the current precedence on the stack (initially 0), push it onto the stack.
     • If the operator's precedence is lower or equal to the current precedence, evaluate the expression until the operator's precedence becomes higher than the current precedence.
3. Evaluation: When the operator's precedence is higher, perform the operation on the top two nodes on the stack, creating a new node with the result. Push the new node onto the stack.
4. Parenthesis Handling: If a closing parenthesis is encountered, pop nodes from the stack until the corresponding opening parenthesis is found. Perform any pending operations before continuing.
5. Final Result: When all tokens have been processed, evaluate any remaining nodes on the stack. The resulting node will represent the root of the expression tree.

By following these steps, you can construct an expression tree that accurately reflects the given arithmetic expression, including support for negative numbers represented as "5 + (-2)". The stack-based approach allows for efficient handling of operator precedence and parentheses, resulting in a correct tree structure.