LeetCode (Others) Evaluate Reverse Polish Notation

2018-07-12

Evaluate Reverse Polish Notation

Evaluate the value of an arithmetic expression in 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:

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2
3

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

Example 2:

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2
3

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

思路：首先我们需要搞清楚什么是逆波兰(Reverse Polish Notation)表达式。逆波兰表示法（Reverse Polish notation，RPN，或逆波兰记法），是一种是由波兰数学家扬·武卡谢维奇1920年引入的数学表达式方式，在逆波兰记法中，所有操作符置于操作数的后面，因此也被称为后缀表示法。逆波兰记法不需要括号来标识操作符的优先级。

　　逆波兰表达式的运算规则：从左到右遍历表达式的每个数字和符号，遇到是数字就进栈，遇到是符号，就将处于栈顶的两个数字出栈，进行运算，运算结果进栈，一直到最终获得结果。结果就是栈只剩下一个数字，弹出这个数字即可。

代码如下：

class Solution {
    public int evalRPN(String[] tokens) {
        int a, b;
        Stack<Integer> stack = new Stack<Integer>();
        for (String s : tokens) {
            if (s.equals("+")) {
                a = stack.pop();
                b = stack.pop();
                stack.push(a + b);
            } else if (s.equals("-")) {
                a = stack.pop();
                b = stack.pop();
                stack.push(b - a);
            } else if (s.equals("*")) {
                stack.push(stack.pop() * stack.pop());
            } else if (s.equals("/")) {
                a = stack.pop();
                b = stack.pop();
                stack.push(b / a);
            } else {
                stack.push(Integer.valueOf(s));
            }
        }
        return stack.pop();
    }
}