Evaluate Reverse Polish Notation
Evaluate an arithmetic expression in Reverse Polish Notation (postfix). Valid operators: +, -, *, /. Division truncates toward zero.
Example:
2,1,+,3,*
9
- The input is processed from left to right, with the first two values
2and1being added together using the+operator, resulting in 2+1=3. - The result
3is then multiplied by3using the*operator, giving 3â‹…3=9. - The final output is 9.
Constraints:
- 1 <= len(tokens) <= 10^4
- Tokens are integers or operators
Background Knowledge
Reverse Polish Notation (RPN) is a mathematical notation where operators follow their operands. This notation is also known as postfix notation. For example, the expression 3 + 4 would be written as 3 4 + in RPN. This notation has several advantages, including the elimination of the need for parentheses to specify the order of operations.
The key concept in evaluating RPN expressions is the use of a stack data structure. A stack is a Last-In-First-Out (LIFO) data structure, meaning that the most recently added element is the first one to be removed. In the context of RPN, a stack can be used to store the operands, and when an operator is encountered, the top two operands are popped from the stack, the operation is performed, and the result is pushed back onto the stack.
Understanding the order of operations is also crucial when evaluating RPN expressions. Since the operators follow their operands, the order of operations is implicit in the notation. However, when implementing the evaluation algorithm, it's essential to consider the order in which the operators are applied to ensure correct results. For example, in the expression **3 4 + 2 ***, the addition operation is performed first, and then the result is multiplied by 2.
Algorithm/Approach
The general approach to solving this problem involves using a stack-based algorithm to evaluate the RPN expression. The algorithm iterates through the tokens in the expression, and for each token, it checks if it's an operand or an operator. If it's an operand, it's pushed onto the stack. If it's an operator, the top two operands are popped from the stack, the operation is performed, and the result is pushed back onto the stack.
Step-by-Step Strategy
To implement the solution, follow these steps:
- Initialize an empty stack to store the operands.
- Iterate through the tokens in the RPN expression.
- For each token, check if it's an operand or an operator.
- If it's an operand, convert it to a number and push it onto the stack.
- If it's an operator, pop the top two operands from the stack, perform the operation, and push the result back onto the stack.
- After iterating through all the tokens, the final result should be the only element left on the stack.
Common Pitfalls
When implementing the solution, watch out for the following common pitfalls:
- Forgetting to handle the case where there are not enough operands on the stack for an operator.
- Not checking for division by zero.
- Not handling the case where the input expression is invalid (e.g., contains unknown operators or operands).
Time & Space Complexity
The expected time complexity for this problem is O(n), where n is the number of tokens in the RPN expression, since we're iterating through the tokens once. The expected space complexity is also O(n), since in the worst case, we might need to store all the tokens on the stack.