Basic Calculator III

Basic Calculator III

What is this problem about?

The "Basic Calculator III interview question" is the ultimate evolution of the expression evaluation series. It combines the challenges of its predecessors: it includes non-negative integers, the four basic operators (+, -, *, /), and parentheses ( and ). Your task is to evaluate the entire expression while strictly following the order of operations (PEMDAS/BODMAS).

Why is this asked in interviews?

Top-tier companies like Meta, Google, and Amazon use the "Basic Calculator III coding problem" to identify candidates with exceptional logical structured thinking. This problem requires a perfect blend of recursion and stack-based management. It tests your ability to break a complex problem into nested, solvable sub-problems, mirroring how real-world compilers and interpreters function.

Algorithmic pattern used

This problem is best solved using a combination of the Stack and Recursion patterns.

1. Recursive Function: Define a function that processes an expression. When it encounters (, it calls itself recursively to solve the sub-expression. When it hits ), it returns the result of the current scope.
2. Precedence Management: Within each recursive call, use a stack to manage the values. Just like in Basic Calculator II, multiply and divide as you go, and push addition/subtraction results to the stack to be summed at the end.
3. Index Tracking: Use a shared index or a queue to ensure all recursive calls consume characters from the same global string position.

Example explanation

Expression: 2 * (5 + 5 / 2)

1. Start at 2. last_op = '*'.
2. Hit (. Recursive call for 5 + 5 / 2.
   • 5. last_op = '+'.
   • +. Push 5. last_op = '+'.
   • 5. last_op = '/'.
   • /. Push 5. last_op = '/'.
   • 2. last_op was /, pop 5, divide by 2, push 2 (integer division).
   • Return $5 + 2 = 7$.
3. Back in main call: last_op was *, multiply 2 by returned 7.
4. Final Result: 14.

Common mistakes candidates make

• Not sharing the pointer: Failing to update the current position in the string across recursive calls, leading to redundant or skipped processing.
• Complexity Overload: Trying to handle parentheses and precedence in a single iterative loop without recursion, which usually results in unreadable and bug-prone code.
• Handling Multi-digit numbers: Just like in the earlier versions, forgetting that digits need to be accumulated into a full integer.

Interview preparation tip

If you can solve "Basic Calculator III," you have mastered the "Stack interview pattern." Focus on writing modular code—have a clear section for number parsing, operator handling, and recursive calls. This makes your logic much easier to communicate to an interviewer.