150. Evaluate Reverse Polish Notation

Description of the Problem

You are given an array of strings tokens that represents an arithmetic expression in a Reverse Polish Notation.

Evaluate the expression. Return an integer that represents the value of the expression.

Note that:

• The valid operators are '+', '-', '*', and '/'.
• Each operand may be an integer or another expression.
• The division between two integers always truncates toward zero.
• There will not be any division by zero.
• The input represents a valid arithmetic expression in a reverse polish notation.
• The answer and all the intermediate calculations can be represented in a 32-bit integer.

Example 1:

Input: tokens = ["2","1","+","3","*"]
Output: 9
Explanation: ((2 + 1) * 3) = 9

Example 2:

Input: tokens = ["4","13","5","/","+"]
Output: 6
Explanation: (4 + (13 / 5)) = 6

Example 3:

Input: tokens = ["10","6","9","3","+","-11","*","/","*","17","+","5","+"]
Output: 22
Explanation: ((10 * (6 / ((9 + 3) * -11))) + 17) + 5
= ((10 * (6 / (12 * -11))) + 17) + 5
= ((10 * (6 / -132)) + 17) + 5
= ((10 * 0) + 17) + 5
= (0 + 17) + 5
= 17 + 5
= 22

Constraints:

• 1 <= tokens.length <= 10^4
• tokens[i] is either an operator: "+", "-", "*", or "/", or an integer in the range [-200, 200].

Solution

Explanation

Simply speaking, when the token is an number, push into the stack; when the token is an operator, pop two numbers and calculate the result, push the result back to the stack.

Code (Rust)

impl Solution {
    pub fn eval_rpn(tokens: Vec<String>) -> i32 {
        let mut stack = vec![];
        for token in tokens {
            match(token.as_str()){
                "+" => {
                    let b = stack.pop().unwrap();
                    let a = stack.pop().unwrap();
                    stack.push(a + b);
                },
                "-" => {
                    let b = stack.pop().unwrap();
                    let a = stack.pop().unwrap();
                    stack.push(a - b);
                },
                "*" => {
                    let b = stack.pop().unwrap();
                    let a = stack.pop().unwrap();
                    stack.push(a * b);
                },
                "/" => {
                    let b = stack.pop().unwrap();
                    let a = stack.pop().unwrap();
                    stack.push(a / b);
                },
                _ => {
                    stack.push(token.parse::<i32>().unwrap());
                },
            }
        }

        if stack.len() != 1{
            panic!("Invalid Token");
        }else{
            return stack.pop().unwrap();
        }

    }
}

Complexity (n is the number of tokens)

Time Complexity:

• \( O(n) \)

Auxiliary Space:

• \( O(n) \)
  • The size of the stack is bound by number of tokens