# Evaluate Reverse Polish Notation

Evaluate the value of an arithmetic expression in[Reverse Polish Notation](http://en.wikipedia.org/wiki/Reverse_Polish_notation).

Valid operators are`+`,`-`,`*`,`/`. Each operand may be an integer or another expression.

**Note:**

* Division between two integers should truncate toward zero.
* The given RPN expression is always valid. That means the expression would always evaluate to a result and there won't be any divide by zero operation.

**Example 1:**

```
Input:
 ["2", "1", "+", "3", "*"]

Output:
 9

Explanation:
 ((2 + 1) * 3) = 9
```

**Example 2:**

```
Input:
 ["4", "13", "5", "/", "+"]

Output:
 6

Explanation:
 (4 + (13 / 5)) = 6
```

**Example 3:**

```
Input:
 ["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
```

## Analysis

此题的逻辑很简单，逆波兰表达式的计算器。使用一个辅助栈stack即可。

## Solution

Stack Implementation - (12ms)

```java
class Solution {
    public int evalRPN(String[] tokens) {
        Deque<String> stack = new ArrayDeque<>();

        for (String token : tokens) {
            if (!isOperator(token)) {
                stack.push(token);
            } else {
                int num1 = Integer.parseInt(stack.pop());
                int num2 = Integer.parseInt(stack.pop());
                int res = 0;
                switch(token) {
                    case "+":
                        res = num2 + num1;
                        break;
                    case "-":
                        res = num2 - num1;
                        break;
                    case "*":
                        res = num2 * num1;
                        break;
                    case "/":
                        res = num2 / num1;
                        break;
                }
                stack.push(String.valueOf(res));
            }
        }
        return Integer.parseInt(stack.peek());
    }

    private boolean isOperator(String token) {
        return token.equals("+") || token.equals("-") || token.equals("*") || token.equals("/");
    }
}
```

Improved without too much conversion of String / Integer - (11ms, 86.58%)

```java
class Solution {
    public int evalRPN(String[] tokens) {
        Deque<Integer> stack = new ArrayDeque<>();

        for (String token : tokens) {
            if (!isOperator(token)) {
                stack.push(Integer.valueOf(token));
            } else {
                int num1 = stack.pop(); 
                int num2 = stack.pop(); 
                int res = 0;
                switch(token) {
                    case "+":
                        res = num2 + num1;
                        break;
                    case "-":
                        res = num2 - num1;
                        break;
                    case "*":
                        res = num2 * num1;
                        break;
                    case "/":
                        res = num2 / num1;
                        break;
                }
                stack.push(res);
            }
        }
        return stack.peek();
    }

    private boolean isOperator(String token) {
        return token.equals("+") || token.equals("-") || token.equals("*") || token.equals("/");
    }
}
```

Another implementation: [https://www.jiuzhang.com/solution/evaluate-reverse-polish-notation/](https://www.jiuzhang.com/solution/evaluate-reverse-polish-notation/)

```java
public class Solution {
    public int evalRPN(String[] tokens) {
        Stack<Integer> s = new Stack<Integer>();
        String operators = "+-*/";
        for(String token : tokens){
            if(!operators.contains(token)){
                s.push(Integer.valueOf(token));
                continue;
            }

            int a = s.pop();
            int b = s.pop();
            if(token.equals("+")) {
                s.push(b + a);
            } else if(token.equals("-")) {
                s.push(b - a);
            } else if(token.equals("*")) {
                s.push(b * a);
            } else {
                s.push(b / a);
            }
        }
        return s.pop();
    }
}
```
