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leetcode-problemset/leetcode-cn/problem (Chinese)/逆波兰表达式求值 [evaluate-reverse-polish-notation].html
2022-03-29 12:43:11 +08:00

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<p>根据<a href="https://baike.baidu.com/item/%E9%80%86%E6%B3%A2%E5%85%B0%E5%BC%8F/128437" target="_blank"> 逆波兰表示法</a>,求表达式的值。</p>
<p>有效的算符包括&nbsp;<code>+</code><code>-</code><code>*</code><code>/</code>&nbsp;。每个运算对象可以是整数,也可以是另一个逆波兰表达式。</p>
<p><b>注意&nbsp;</b>两个整数之间的除法只保留整数部分。</p>
<p>可以保证给定的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。</p>
<p>&nbsp;</p>
<p><strong>示例&nbsp;1</strong></p>
<pre>
<strong>输入:</strong>tokens = ["2","1","+","3","*"]
<strong>输出:</strong>9
<strong>解释:</strong>该算式转化为常见的中缀算术表达式为:((2 + 1) * 3) = 9
</pre>
<p><strong>示例&nbsp;2</strong></p>
<pre>
<strong>输入:</strong>tokens = ["4","13","5","/","+"]
<strong>输出:</strong>6
<strong>解释:</strong>该算式转化为常见的中缀算术表达式为:(4 + (13 / 5)) = 6
</pre>
<p><strong>示例&nbsp;3</strong></p>
<pre>
<strong>输入:</strong>tokens = ["10","6","9","3","+","-11","*","/","*","17","+","5","+"]
<strong>输出:</strong>22
<strong>解释:</strong>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</pre>
<p>&nbsp;</p>
<p><strong>提示:</strong></p>
<ul>
<li><code>1 &lt;= tokens.length &lt;= 10<sup>4</sup></code></li>
<li><code>tokens[i]</code>&nbsp;是一个算符(<code>"+"</code><code>"-"</code><code>"*"</code><code>"/"</code>),或是在范围 <code>[-200, 200]</code> 内的一个整数</li>
</ul>
<p>&nbsp;</p>
<p><strong>逆波兰表达式:</strong></p>
<p>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。</p>
<ul>
<li>平常使用的算式则是一种中缀表达式,如 <code>( 1 + 2 ) * ( 3 + 4 )</code></li>
<li>该算式的逆波兰表达式写法为 <code>( ( 1 2 + ) ( 3 4 + ) * )</code></li>
</ul>
<p>逆波兰表达式主要有以下两个优点:</p>
<ul>
<li>去掉括号后表达式无歧义,上式即便写成 <code>1 2 + 3 4 + * </code>也可以依据次序计算出正确结果。</li>
<li>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</li>
</ul>