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.