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datetime="2024-04-05T12:49:52.000Z" title="更新于 2024-04-05 20:49:52">2024-04-05</time></header><h1>1.什么式波兰表达式</h1>
<p> 波兰表达式（<mark class="hl-label orange">又称逆波兰表达式</mark> ）是一种数学和逻辑表达式的表示方法。在波兰表达式中，操作符放在它们所操作的数之前，而不是在它们之间，这样可以消除括号的需求。波兰表达式通过一种前缀或后缀的方式来表示，分别称为前缀波兰表达式和后缀波兰表达式。</p>
<h1>2.为什么会有这种表达式</h1>
<p> 在计算机中，要本着能简化就简化的原则来设计，对于一个正常的数学运算表达式，除了有加减乘除之外，还有一些括号来标识运算的优先级，那么对于计算机而言，能不能不写括号就能正常运算这个表达式呢，那么波兰表达式就产生了。</p>
<h1>3.直接上🌰</h1>
<p>下面的表达式就是一个比较简单的例子，我们也叫它<mark class="hl-label orange">中缀表达式</mark> </p>
<p>a + b * (c - d) + e/f</p>
<p>有了<mark class="hl-label orange">中缀表达式</mark> ，那肯定也有<mark class="hl-label orange">前缀表达式</mark> 和<mark class="hl-label orange">后缀表达式</mark> </p>
<h2 id="中缀表达式转换">中缀表达式转换</h2>
<p>首先根据中缀表达式构造一个二叉树</p>
<pre><code> + +
/ \ / \
a + + /
/ \ / \ / \
* / 或者 a * e f
/ \ / \ / \
b - e f b -
/ \ / \
c d c d
</code></pre>
<div class="note info no-icon flat"><p>前缀表达式 = 前序遍历 （波兰式）<br>
中缀表达式 = 中序遍历<br>
后缀表达式 = 后序遍历 （逆波兰式）</p>
</div>
<p>所以根据上面的二叉树我们可以知道<br>
前缀表达式 = <mark class="hl-label green">+ a + * b - c d / e f</mark> 或 <mark class="hl-label green">+ + a * b - c d / e f</mark> <br>
后缀表达式 = <mark class="hl-label green">a b c d - * e f / + +</mark> 或 <mark class="hl-label green">a b c d - * + e f / +</mark> </p>
<div class="note warning no-icon flat"><p> 通过树基础知识我们知道，树的三种遍历方式中，如果告诉我们任意一种遍历，我们式无法确切的推出另外两种遍历方式的，也就是说我们无法确定这一棵树的形态，所以波兰式也是一样的，一个表达式可能对应多个波兰式</p>
</div>
<h1>在计算机中的计算方式</h1>
<div class="note success no-icon flat"><p> 在计算机中，表达式的计算通常是按照逆波兰式（后缀表达式）进行的。逆波兰式具有很好的计算机解析性质，可以直接通过栈数据结构进行求解</p>
</div>
<p>首先将转换后的表达式想象成一个队列，</p>
<ol>
<li>从左往右依次出队，</li>
<li>然后进行入栈，当遇到符号时，将前两个操作数取出，进行运算</li>
<li>将上一步运算的结果继续入栈</li>
<li>直到队列中没有操作数，表达式计算完毕</li>
</ol>
<hr>
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class="toc-number">1.</span> <span class="toc-text">1.什么式波兰表达式</span></a></li><li class="toc-item toc-level-1"><a class="toc-link"><span class="toc-number">2.</span> <span class="toc-text">2.为什么会有这种表达式</span></a></li><li class="toc-item toc-level-1"><a class="toc-link"><span class="toc-number">3.</span> <span class="toc-text">3.直接上🌰</span></a><ol class="toc-child"><li class="toc-item toc-level-2"><a class="toc-link" href="#%E4%B8%AD%E7%BC%80%E8%A1%A8%E8%BE%BE%E5%BC%8F%E8%BD%AC%E6%8D%A2"><span class="toc-number">3.1.</span> <span class="toc-text">中缀表达式转换</span></a></li></ol></li><li class="toc-item toc-level-1"><a class="toc-link"><span class="toc-number">4.</span> <span class="toc-text">在计算机中的计算方式</span></a></li></ol></div></div><div class="card-widget card-recent-post"><div class="item-headline"><i class="anzhiyufont anzhiyu-icon-history"></i><span>最近发布</span></div><div class="aside-list"><div class="aside-list-item"><a class="thumbnail" href="/8a0c.html" 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reply: '回复TA，开启一场对话吧！',
cancelReply: '等等，我话还没说完，取消回复！',
comment: '来，说说你的看法，让评论区热闹起来！',
refresh: '刷新一下，看看有啥新动态！',
more: '哇塞，还有更多精彩内容等你来加载！',
preview: '先睹为快，预览一下你的大作吧！',
emoji: '来，加点表情，让你的评论更生动！',
uploadImage: '上传你的美照，让大家一起欣赏！',
seconds: '刚刚才发的，新鲜出炉！',
minutes: '几分钟前，还热乎着呢！',
hours: '几小时前，热度还在哦！',
days: '几天前，但依旧值得一看！',
now: '哇塞，刚刚发的，快抢沙发！',
uploading: '稍等片刻，你的图片正在飞奔而来！',
login: '登录一下，解锁更多功能！',
logout: '拜拜了您嘞，下次再见！',
admin: '博主大人在此，谁敢造次！',
sticky: '置顶一下，让更多人看到你的精彩内容！',
word: '字',
wordHint: '评论字数要在0到1字之间哦！\n现在你已经写了$2个字了，加油！',
anonymous: '神秘人出没，猜猜是谁？',
level0: '潜水员，深藏不露！',
level1: '冒泡小能手，偶尔露个头！',
level2: '吐槽大师，一针见血！',
level3: '活跃分子，无处不在！',
level4: '话痨达人，说个不停！',
level5: '传说级大神，膜拜一下！',
gif: '动态表情包，让你的评论更有趣！',
gifSearchPlaceholder: '快来搜索你喜欢的表情包，让评论更生动！',
profile: '看看我的个人资料，了解一下我吧！',
approved: '审核通过，可以展示啦！',
waiting: '正在等待审核，别急哦！',
spam: '垃圾内容，走开走开！',
unsticky: '换个位置看看！',
oldest: '看看最早的评论！',
latest: '看看最新的动态！',
hottest: '看看哪条评论最火！',
reactionTitle: '快来对这篇文章发表你的看法吧，让博主知道你的想法！😜'
};
const initWaline = () => {
const waline = Waline.init(Object.assign({
el: '#waline-wrap',
serverURL: 'https://bc.ctext.top/',
pageview: false,
dark: 'html[data-theme="dark"]',
path: window.location.pathname,
turnstileKey: '0x4AAAAAAAexA2vW2PBFT3wv',
comment: false,
copyright: false,
reaction: true,
locale
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if (typeof Waline === 'object') initWaline()
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await getCSS('https://cdn.cbd.int/@waline/client@3.1.3/dist/waline.css')
await getScript('https://cdn.cbd.int/@waline/client@3.1.3/dist/waline.js')
initWaline()
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const changeContent = content => {
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content = content.replace(/<a[^>]+?href=["']?([^"']+)["']?[^>]*>([^<]+)<\/a>/gi, '[链接]') // replace url
content = content.replace(/<pre><code>.*?<\/pre>/gi, '[代码]') // replace code
content = content.replace(/<[^>]+>/g,"") // remove html tag
if (content.length > 150) {
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}
return content
}
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let result = ''
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result += '<div class=\'aside-list-item\'>'
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const name = 'data-lazy-src'
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$dom && ($dom.innerHTML= result)
window.lazyLoadInstance && window.lazyLoadInstance.update()
window.pjax && window.pjax.refresh($dom)
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try {
const res = await fetch('https://bc.ctext.top/api/comment?type=recent&count=6', { method: 'GET' })
const result = await res.json()
const walineArray = result.data.map(e => {
return {
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'avatar': e.avatar,
'nick': e.nick,
'url': e.url + '#' + e.objectId,
'date': e.time || e.insertedAt
}
})
saveToLocal.set('waline-newest-comments', JSON.stringify(walineArray), 10/(60*24))
generateHtml(walineArray)
} catch (err) {
console.error(err)
const $dom = document.querySelector('#card-newest-comments .aside-list')
$dom.textContent= "无法获取评论，请确认相关配置是否正确"
}
}
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if (document.querySelector('#card-newest-comments .aside-list')) {
const data = saveToLocal.get('waline-newest-comments')
if (data) {
generateHtml(JSON.parse(data))
} else {
getComment()
}
}
}
newestCommentInit()
document.addEventListener('pjax:complete', newestCommentInit)
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selectors: pjaxSelectors,
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anzhiyu.removeGlobalFnEvent('pjax')
anzhiyu.removeGlobalFnEvent('themeChange')
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typeof typed === 'object' && typed.destroy()
//reset readmode
const $bodyClassList = document.body.classList
$bodyClassList.contains('read-mode') && $bodyClassList.remove('read-mode')
})
document.addEventListener('pjax:complete', function () {
window.refreshFn()
document.querySelectorAll('script[data-pjax]').forEach(item => {
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const content = item.text || item.textContent || item.innerHTML || ""
Array.from(item.attributes).forEach(attr => newScript.setAttribute(attr.name, attr.value))
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item.parentNode.replaceChild(newScript, item)
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GLOBAL_CONFIG.islazyload && window.lazyLoadInstance.update()
typeof panguInit === 'function' && panguInit()
// google analytics
typeof gtag === 'function' && gtag('config', '', {'page_path': window.location.pathname});
// baidu analytics
typeof _hmt === 'object' && _hmt.push(['_trackPageview',window.location.pathname]);
typeof loadMeting === 'function' && document.getElementsByClassName('aplayer').length && loadMeting()
// prismjs
typeof Prism === 'object' && Prism.highlightAll()
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