Reverse Polish Notation (RPN) is a mathematical notation in which every operator follows all of its operands. It is especially useful in computer science and stack-based calculations because it eliminates the need for parentheses to dictate operation order. When evaluating an RPN expression, operands are pushed onto a stack, and when an operator is encountered, it is applied to the operands at the top of the stack. This process continues until the entire expression has been evaluated.
- Define an Interface for Operations: Create an Apply interface that has a method apply(int a, int b) to handle different arithmetic operations dynamically.
- Determine the Operation Function: Use a switch statement to return the corresponding operation for each
arithmetic operator (
+,-,*,/). This allows the operations to be applied in a clean and concise manner. - Initialize a Stack: Use a
Deque<Integer>(double-ended queue) to implement the stack where integers are stored as they are encountered in the tokens array. - Iterate through Tokens: For each token:
- If the token is an operator, pop the top two elements from the stack, apply the operation, and push the result back onto the stack.
- Else, parse the token to an integer and push it onto the stack.
- Return the Final Result: After processing all tokens, the final result will be the last remaining element in the stack.
- Time Complexity:
O(N):Each token is processed exactly once, making the time complexity linear with respect to the number of tokens. - Space Complexity:
O(N):The space complexity is linear as well because, in the worst case, all tokens could be numbers, requiring storage for all of them in the stack.