Given the Infix, Prefix, or Postfix notation of an expression, write the code to compute the final result.

The final result of an expression given in Infix, Prefix, or Postfix notation can be computed using stack-based algorithms, with Infix requiring an intermediate conversion step. This problem tests understanding of fundamental data structures and parsing logic crucial for compilers and interpreters.

Mechanics

Postfix (Reverse Polish Notation): Evaluate expressions by iterating from left to right. When a number is encountered, push it onto a stack. When an operator (+, -, , /) is encountered, pop the top two operands from the stack, apply the operator (second popped operand first, then first popped operand), and push the result back onto the stack. The final result is the single value remaining on the stack. * Prefix (Polish Notation): Similar to Postfix, but iterate from right to left. When a number is encountered, push it onto a stack. When an operator is encountered, pop the top two operands, apply the operator (first popped operand first, then second popped operand), and push the result. * Infix (Standard Notation): This requires a two-step process, typically using the Shunting Yard algorithm, to convert it into Postfix notation first. This algorithm uses an operator stack and an output queue, handling operator precedence (e.g., multiplication before addition) and associativity (left-to-right or right-to-left) to correctly order operations. Once converted to Postfix, it can be evaluated as described above. Alternatively, recursive descent parsers can directly evaluate Infix expressions by breaking them down based on grammar rules.

Example: Postfix Evaluation

def evaluate_postfix(expression):
    stack = []
    for char in expression.split():
        if char.isdigit() or (char[0] == '-' and char[1:].isdigit()): # Handle negative numbers
            stack.append(int(char))
        else:
            operand2 = stack.pop()
            operand1 = stack.pop()
            if char == '+': stack.append(operand1 + operand2)
            elif char == '-': stack.append(operand1 - operand2)
            elif char == '': stack.append(operand1  operand2)
            elif char == '/': stack.append(operand1 // operand2) # Integer division
    return stack.pop()
# Example: 3 4 + 2  (should be (3+4)2 = 14)
# print(evaluate_postfix("3 4 + 2 *"))

Why and Production Considerations

This problem is a foundational exercise in parsing and compiler design. In real-world data engineering, understanding expression evaluation is critical for systems like SQL query optimizers (e.g., Spark's Catalyst optimizer), which parse user-defined expressions, convert them into an internal representation (often a syntax tree or a form of postfix), and then optimize and execute them. Production-grade solutions must handle operator precedence, associativity, different data types (integers, floats, booleans), error handling for invalid expressions, and potentially user-defined functions.

In the interview, also mention…

The importance of operator precedence and associativity in Infix evaluation, and how these concepts are fundamental to how programming languages and query engines interpret code.