Problem Link - STACK07
Problem Statement
Reverse Polish Notation (RPN) is a mathematical notation where every operator follows all of its operands. For instance, to add three and four, one would write 3 4 + rather than 3 + 4. If there are multiple operations, the operator is given immediately after its second operand; so the expression written 3 − 4 + 5 would be written 3 4 − 5 + first subtract 4 from 3, then add 5 to that.
Reverse polish notations are easier to parse for computers and you don’t need parentheses to denote precedence of operations.
Transform the algebraic expression with brackets into RPN form.
Approach:
The key idea is to use a stack to maintain operators and their precedence while converting the infix expression to postfix:
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Stack for Operators: A stack stores operators and parentheses, allowing us to manage the order of operations based on their precedence.
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Traversing the Infix Expression: For each character in the infix expression:
- If it’s an operand, add it directly to the result.
- If it’s
(, push it onto the stack. - If it’s
), pop from the stack until the matching(is found.
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Handling Operators: For an operator, pop operators from the stack to the result until the top of the stack has a lower precedence, then push the current operator.
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Final Step: After processing all characters, pop any remaining operators from the stack to the result.
Time Complexity:
O(n), where n is the length of the infix expression, since we process each character once.
Space Complexity:
O(n), as the stack may need to store all operators and parentheses in the worst case.