8000 【栈】150.逆波兰表达式求值 · Issue #10 · attack-on-backend/algorithm · GitHub
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【栈】150.逆波兰表达式求值 #10

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lyonyang opened this issue Aug 7, 2021 · 1 comment
Open

【栈】150.逆波兰表达式求值 #10

lyonyang opened this issue Aug 7, 2021 · 1 comment

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@lyonyang
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lyonyang commented Aug 7, 2021

根据 逆波兰表示法,求表达式的值。

有效的算符包括 +-*/ 。每个运算对象可以是整数,也可以是另一个逆波兰表达式。

说明:

  • 整数除法只保留整数部分。
  • 给定逆波兰表达式总是有效的。换句话说,表达式总会得出有效数值且不存在除数为 0 的情况。

示例 1:

输入:tokens = ["2","1","+","3","*"]
输出:9
解释:该算式转化为常见的中缀算术表达式为:((2 + 1) * 3) = 9

示例 2:

输入:tokens = ["4","13","5","/","+"]
输出:6
解释:该算式转化为常见的中缀算术表达式为:(4 + (13 / 5)) = 6

示例 3:

输入:tokens = ["10","6","9","3","+","-11","*","/","*","17","+","5","+"]
输出:22
解释:
该算式转化为常见的中缀算术表达式为:
  ((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

提示:

  • 1 <= tokens.length <= 104
  • tokens[i] 要么是一个算符("+""-""*""/"),要么是一个在范围 [-200, 200] 内的整数

逆波兰表达式:

逆波兰表达式是一种后缀表达式,所谓后缀就是指算符写在后面。

平常使用的算式则是一种中缀表达式,如 ( 1 + 2 ) * ( 3 + 4 )
该算式的逆波兰表达式写法为 ( ( 1 2 + ) ( 3 4 + ) * )
逆波兰表达式主要有以下两个优点:

去掉括号后表达式无歧义,上式即便写成 1 2 + 3 4 + * 也可以依据次序计算出正确结果。
适合用栈操作运算:遇到数字则入栈;遇到算符则取出栈顶两个数字进行计算,并将结果压入栈中。

来源:力扣(LeetCode)
链接:https://leetcode-cn.com/problems/evaluate-reverse-polish-notation
著作权归领扣网络所有。商业转载请联系官方授权,非商业转载请注明出处。

@lyonyang
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思路一 - 栈

将数字推入栈中 , 遇到运算符就 pop 两次进行计算 , 将计算结果重新推入栈中 , 循环处理

class Solution:
    def evalRPN(self, tokens: List[str]) -> int:
        import operator
        _stack = []
        opt_map = {'+': operator.add, '-': operator.sub, '*': operator.mul, '/':operator.truediv}
        for t in range(len(tokens)):
            if tokens[t] in opt_map:
                r, l = _stack.pop(), _stack.pop()
                _stack.append(int(opt_map[tokens[t]](l, r)))
            else:
                _stack.append(int(tokens[t]))
        return _stack.pop()

时间复杂度:$O(N)$ , N 为数组长度

空间复杂度:$O(N)$

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