The shunting-yard algorithm, developed by computer science pioneer Edsger Dijkstra in the early 1960s, converts mathematical expressions from standard infix notation (like "5+4+3") into postfix notation (Reverse Polish Notation). A new interactive visualization now brings this foundational computer science concept to life through animation, showing step-by-step how the algorithm processes tokens, manages an operator stack, and produces the final output.

The algorithm reads tokens sequentially from left to right. Numbers and variables go directly to the output queue, while operators are placed on a stack and released based on precedence rules. When encountering parentheses, the algorithm handles them by discarding the brackets and releasing any operators trapped between them. This ensures that expressions like "5+(2×3)" correctly become "5 2 3 × +" rather than "5 2 3 + ×".

The visualization demonstrates why the shunting-yard algorithm remains essential in modern compilers and calculators. Understanding this algorithm helps developers grasp how programming languages parse mathematical expressions, making it valuable knowledge for anyone building interpreters or expression evaluators.