Problem Statement
Convert a simple infix expression (e.g., A+B) to postfix notation (e.g., AB+). In postfix notation, operators follow their operands, which allows for simpler evaluation without needing parentheses.
Example Usage
Additional Examples:
- Input:
"A+B*C"
- Input:
"A*B+C"
- Input:
"A*(B+C)"
JavaScript Stack - Using Custom Stack Class
We’ll use the following custom Stack class to handle operators during the conversion. This class includes methods like push, pop, peek, isEmpty, size, and clear.
Dry Run
For the input "A+B*C":
- Process
A: Operand, add to postfix → postfix = "A"
- Process
+: Operator, push to stack → stack = ["+"]
- Process
B: Operand, add to postfix → postfix = "AB"
- Process
*: Higher precedence than +, push to stack → stack = ["+", "*"]
- Process
C: Operand, add to postfix → postfix = "ABC"
- Pop remaining operators: Pop
* and then + → postfix = "ABC*+"
Complexity Analysis
Custom Defined Stack Methods
- Time Complexity: Each character is processed once, so the solution is O(n) for
n characters in the expression.
- Space Complexity: O(n) for storing operators in the stack.
Conclusion
Using a stack to convert infix expressions to postfix notation simplifies the handling of operator precedence and parentheses. This method provides an efficient solution, especially for evaluating mathematical expressions.