The Order of Operations Bug That Plagues Every Online Calculator

Type 2 + 3 * 4 into a calculator. If it returns 14, it understands order of operations (PEMDAS/BODMAS). If it returns 20, it's evaluating left-to-right. You'd be surprised how many online calculators get this wrong. The parsing problem Building a calculator that handles 2 + 3 * 4 = 14 requires an expression parser that understands operator precedence. The naive approach, evaluating left-to-right as the user types, gives the wrong answer. The correct approach uses one of two algorithms: Shunting-yard algorithm (Dijkstra, 1961): Converts infix notation (the way humans write expressions) to reverse Polish notation (RPN), which can be evaluated on a stack without worrying about precedence. The algorithm uses an operator stack to handle precedence and associativity. Recursive descent parser: Builds a parse tree where higher-precedence operators are deeper in the tree. Evaluating the tree bottom-up naturally gives the correct precedence. The shunting-yard algorithm is more common in calculat