The Parsing A Boolean Expression problem asks you to evaluate a boolean expression string containing ! (not), & (and), | (or), t (true), and f (false). Expressions are properly parenthesized. This hard coding problem uses recursive parsing or a stack-based approach. The recursion, string, and stack interview pattern is the core.
Goldman Sachs, Microsoft, Meta, Amazon, Google, and Bloomberg ask this because it tests recursive expression evaluation — a skill directly applicable to compilers, circuit simulation, and logic processing. The ability to handle nested boolean expressions demonstrates strong recursive design.
Recursive descent or stack. Recursive: parse an expression: if 't'/'f', return true/false. If '!', parse the inner expression and negate. If '&'/'|', parse all comma-separated sub-expressions inside parentheses and apply AND/OR. Stack approach: push characters, when ')' found, collect values back to '(' and apply the operator.
"!(f)": negation of false → true. "&(t,f,t)": t AND f AND t = false. "|(f,t,f)": f OR t OR f = true. "&(|(f,t),!(t))": evaluate |(f,t)=true, !(t)=false. AND(true,false) = false.
Boolean expression parsing has two clean implementations: recursive (natural for tree structure) and stack (iterative). The stack approach: push each character; on ')', pop until '(' and collect values; apply the operator (found before '('); push result. Practice both implementations — interviewers may ask you to convert between them. This problem generalizes to any prefix-notation operator tree evaluation.
