Guided Project 3: Arithmetic Expression Evaluator & Shunting-Yard Engine

01Project Architecture & Shunting-Yard Algorithm

In this third guided project, we engineer a full mathematical expression parser and evaluator from scratch. Mathematical notation written by humans (like 3 + 4 * (2 - 1)) is Infix Notation: operators sit between operands, and evaluation order depends on operator precedence and parentheses.

Edsger Dijkstra invented the Shunting-Yard Algorithm to transform infix expressions into Postfix Notation (Reverse Polish Notation or RPN: 3 4 2 1 - * +). In RPN, operators follow their operands, and parentheses are completely eliminated, making evaluation trivial with a single stack.

02The Shunting-Yard Algorithm Implementation

The algorithm uses an operator stack and an output queue. As tokens are scanned:

1. Numbers go directly to the output queue. 2. Left parenthesis '(' is pushed to the operator stack. 3. Right parenthesis ')' pops operators from the stack to the output queue until matching '(' is reached. 4. Operator Op1: while stack top is an operator Op2 with higher (or equal left-associative) precedence, pop Op2 to output. Then push Op1.

03Evaluating Reverse Polish Notation (RPN)

Evaluating RPN is linear O(N) time and O(N) space. We iterate through the RPN tokens: if the token is a number, we push it onto the operand stack. If the token is an operator, we pop the top two numbers, apply the operation, and push the result back onto the stack.

When token processing finishes, the single value remaining on the stack is the final result of the expression.

04Why This Matters in Production

Expression parsing engines power database SQL WHERE-clause evaluators, spreadsheet formula calculations (Excel/Google Sheets), configuration rule engines, and programming language compilers.

By separating lexical tokenization, AST shunting-yard conversion, and RPN stack evaluation, you build an extensible calculation engine that supports custom functions (sin, cos, max) without modifying core evaluation logic.

05Production Architecture & Engineering Trade-Offs

Building an industrial-grade production project requires rigorous engineering beyond passing unit test suites. Real-world systems must handle partial network failures, malformed input streams, concurrency race conditions, and graceful shutdown sequences without data corruption or memory leaks.

When developing this project, ensure that domain boundaries are clearly defined, errors are modeled with typed exceptions or sealed result types rather than generic runtime errors, and performance critical paths are profiled to verify zero unnecessary heap allocations and predictable latency profiles.

Furthermore, real-world deployments mandate structured observability: instrument latency percentiles (p50, p95, p99) using Micrometer metrics, log contextual correlation identifiers across asynchronous thread boundaries, and implement health-check readiness probes for Kubernetes container orchestration.

Finally, validate defensive resource cleanup: all file descriptors, network sockets, and database connections must be managed via try-with-resources blocks to guarantee deterministic reclamation even when unhandled exceptions occur during critical processing loops.