126 lines
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126 lines
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HTML
<!DOCTYPE html><html lang="zh-CN"><head><meta charset="utf-8"><meta name="X-UA-Compatible" content="IE=edge"><title> leetcode-the-masseuse-lcci · MarkDown</title><meta name="description" content="leetcode-the-masseuse-lcci - Ching"><meta name="viewport" content="width=device-width, initial-scale=1"><link rel="short icon" href="/favicon.png"><link rel="stylesheet" href="/css/apollo.css"><link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Source+Sans+Pro:400,600" type="text/css"><style><!-- hexo-inject:begin --><!-- hexo-inject:end -->mjx-container[jax="SVG"] {
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</style><!-- hexo-inject:begin --><!-- hexo-inject:end --></head><body><header><a href="/" class="logo-link"><img src="/logo.png"></a><ul class="nav nav-list"><li class="nav-list-item"><a href="/" target="_self" class="nav-list-link">ALL</a></li><li class="nav-list-item"><a href="/categories/leetcode/" target="_self" class="nav-list-link">LEETCODE</a></li><li class="nav-list-item"><a href="https://bearmiebear.blogspot.com" target="_blank" class="nav-list-link">BEAR</a></li><li class="nav-list-item"><a href="/atom.xml" target="_self" class="nav-list-link">RSS</a></li></ul></header><section class="container"><div class="post"><article class="post-block"><h1 class="post-title">leetcode-the-masseuse-lcci</h1><div class="post-meta"><div class="post-time">2020年4月9日</div></div><div class="post-content"><h3 id="u9762_u8BD5_u9898_17-16-__u6309_u6469_u5E08"><a href="#u9762_u8BD5_u9898_17-16-__u6309_u6469_u5E08" class="headerlink" title="面试题 17.16. 按摩师"></a>面试题 17.16. 按摩师</h3><p><a href="https://leetcode-cn.com/problems/the-masseuse-lcci/" target="_blank" rel="noopener">题目</a></p>
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<p>一开始以为是用递归，想了半天没想出来，偷看了一下答案。答案的思路跟递归类似，假设在当前 <mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.025ex" xmlns="http://www.w3.org/2000/svg" width="0.781ex" height="1.52ex" role="img" focusable="false" viewbox="0 -661 345 672" xmlns:xlink="http://www.w3.org/1999/xlink"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g data-mml-node="math"><g data-mml-node="mi"><use xlink:href="#MJX-TEX-I-69"/></g></g></g></svg></mjx-container> 时刻，<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex" xmlns="http://www.w3.org/2000/svg" width="6.742ex" height="2.262ex" role="img" focusable="false" viewbox="0 -750 2980 1000" xmlns:xlink="http://www.w3.org/1999/xlink"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g data-mml-node="math"><g data-mml-node="mi"><use xlink:href="#MJX-TEX-I-64"/></g><g data-mml-node="mi" transform="translate(520, 0)"><use xlink:href="#MJX-TEX-I-70"/></g><g data-mml-node="mo" transform="translate(1023, 0)"><use xlink:href="#MJX-TEX-N-5B"/></g><g data-mml-node="mi" transform="translate(1301, 0)"><use xlink:href="#MJX-TEX-I-69"/></g><g data-mml-node="mo" transform="translate(1646, 0)"><use xlink:href="#MJX-TEX-N-5D"/></g><g data-mml-node="mo" transform="translate(1924, 0)"><use xlink:href="#MJX-TEX-N-5B"/></g><g data-mml-node="mn" transform="translate(2202, 0)"><use xlink:href="#MJX-TEX-N-30"/></g><g data-mml-node="mo" transform="translate(2702, 0)"><use xlink:href="#MJX-TEX-N-5D"/></g></g></g></svg></mjx-container> 为当前预约不接的情况下最长预约时间，<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex" xmlns="http://www.w3.org/2000/svg" width="6.742ex" height="2.262ex" role="img" focusable="false" viewbox="0 -750 2980 1000" xmlns:xlink="http://www.w3.org/1999/xlink"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g data-mml-node="math"><g data-mml-node="mi"><use xlink:href="#MJX-TEX-I-64"/></g><g data-mml-node="mi" transform="translate(520, 0)"><use xlink:href="#MJX-TEX-I-70"/></g><g data-mml-node="mo" transform="translate(1023, 0)"><use xlink:href="#MJX-TEX-N-5B"/></g><g data-mml-node="mi" transform="translate(1301, 0)"><use xlink:href="#MJX-TEX-I-69"/></g><g data-mml-node="mo" transform="translate(1646, 0)"><use xlink:href="#MJX-TEX-N-5D"/></g><g data-mml-node="mo" transform="translate(1924, 0)"><use xlink:href="#MJX-TEX-N-5B"/></g><g data-mml-node="mn" transform="translate(2202, 0)"><use xlink:href="#MJX-TEX-N-31"/></g><g data-mml-node="mo" transform="translate(2702, 0)"><use xlink:href="#MJX-TEX-N-5D"/></g></g></g></svg></mjx-container> 则为接受当前预约的最长预约时间。</p>
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<p>那很显然，由于不能接受相邻两个预约，<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex" xmlns="http://www.w3.org/2000/svg" width="29.528ex" height="2.262ex" role="img" focusable="false" viewbox="0 -750 13051.4 1000" xmlns:xlink="http://www.w3.org/1999/xlink"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g data-mml-node="math"><g data-mml-node="mi"><use xlink:href="#MJX-TEX-I-64"/></g><g data-mml-node="mi" transform="translate(520, 0)"><use xlink:href="#MJX-TEX-I-70"/></g><g data-mml-node="mo" transform="translate(1023, 0)"><use xlink:href="#MJX-TEX-N-5B"/></g><g data-mml-node="mi" transform="translate(1301, 0)"><use xlink:href="#MJX-TEX-I-69"/></g><g data-mml-node="mo" transform="translate(1646, 0)"><use xlink:href="#MJX-TEX-N-5D"/></g><g data-mml-node="mo" transform="translate(1924, 0)"><use xlink:href="#MJX-TEX-N-5B"/></g><g data-mml-node="mn" transform="translate(2202, 0)"><use xlink:href="#MJX-TEX-N-31"/></g><g data-mml-node="mo" transform="translate(2702, 0)"><use xlink:href="#MJX-TEX-N-5D"/></g><g data-mml-node="mo" transform="translate(3257.8, 0)"><use xlink:href="#MJX-TEX-N-3D"/></g><g data-mml-node="mi" transform="translate(4313.6, 0)"><use xlink:href="#MJX-TEX-I-64"/></g><g data-mml-node="mi" transform="translate(4833.6, 0)"><use xlink:href="#MJX-TEX-I-70"/></g><g data-mml-node="mo" transform="translate(5336.6, 0)"><use xlink:href="#MJX-TEX-N-5B"/></g><g data-mml-node="mi" transform="translate(5614.6, 0)"><use xlink:href="#MJX-TEX-I-69"/></g><g data-mml-node="mo" transform="translate(6181.8, 0)"><use xlink:href="#MJX-TEX-N-2212"/></g><g data-mml-node="mn" transform="translate(7182, 0)"><use xlink:href="#MJX-TEX-N-31"/></g><g data-mml-node="mo" transform="translate(7682, 0)"><use xlink:href="#MJX-TEX-N-5D"/></g><g data-mml-node="mo" transform="translate(7960, 0)"><use xlink:href="#MJX-TEX-N-5B"/></g><g data-mml-node="mn" transform="translate(8238, 0)"><use xlink:href="#MJX-TEX-N-30"/></g><g data-mml-node="mo" transform="translate(8738, 0)"><use xlink:href="#MJX-TEX-N-5D"/></g><g data-mml-node="mo" transform="translate(9238.2, 0)"><use xlink:href="#MJX-TEX-N-2B"/></g><g data-mml-node="mi" transform="translate(10238.4, 0)"><use xlink:href="#MJX-TEX-I-6E"/></g><g data-mml-node="mi" transform="translate(10838.4, 0)"><use xlink:href="#MJX-TEX-I-75"/></g><g data-mml-node="mi" transform="translate(11410.4, 0)"><use xlink:href="#MJX-TEX-I-6D"/></g><g data-mml-node="msub" transform="translate(12288.4, 0)"><g data-mml-node="mi"><use xlink:href="#MJX-TEX-I-73"/></g><g data-mml-node="mi" transform="translate(469, -150) scale(0.707)"><use xlink:href="#MJX-TEX-I-69"/></g></g></g></g></svg></mjx-container></p>
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<p>不接受当前预约的话，上一个预约接不接受都可以，<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex" xmlns="http://www.w3.org/2000/svg" width="38.281ex" height="2.262ex" role="img" focusable="false" viewbox="0 -750 16920.1 1000" xmlns:xlink="http://www.w3.org/1999/xlink"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g data-mml-node="math"><g data-mml-node="mi"><use xlink:href="#MJX-TEX-I-64"/></g><g data-mml-node="mi" transform="translate(520, 0)"><use xlink:href="#MJX-TEX-I-70"/></g><g data-mml-node="mo" transform="translate(1023, 0)"><use xlink:href="#MJX-TEX-N-5B"/></g><g data-mml-node="mi" transform="translate(1301, 0)"><use xlink:href="#MJX-TEX-I-69"/></g><g data-mml-node="mo" transform="translate(1646, 0)"><use xlink:href="#MJX-TEX-N-5D"/></g><g data-mml-node="mo" transform="translate(1924, 0)"><use xlink:href="#MJX-TEX-N-5B"/></g><g data-mml-node="mn" transform="translate(2202, 0)"><use xlink:href="#MJX-TEX-N-30"/></g><g data-mml-node="mo" transform="translate(2702, 0)"><use xlink:href="#MJX-TEX-N-5D"/></g><g data-mml-node="mo" transform="translate(3257.8, 0)"><use xlink:href="#MJX-TEX-N-3D"/></g><g data-mml-node="mi" transform="translate(4313.6, 0)"><use xlink:href="#MJX-TEX-I-6D"/></g><g data-mml-node="mi" transform="translate(5191.6, 0)"><use xlink:href="#MJX-TEX-I-61"/></g><g data-mml-node="mi" transform="translate(5720.6, 0)"><use xlink:href="#MJX-TEX-I-78"/></g><g data-mml-node="mo" transform="translate(6292.6, 0)"><use xlink:href="#MJX-TEX-N-28"/></g><g data-mml-node="mi" transform="translate(6681.6, 0)"><use xlink:href="#MJX-TEX-I-64"/></g><g data-mml-node="mi" transform="translate(7201.6, 0)"><use xlink:href="#MJX-TEX-I-70"/></g><g data-mml-node="mo" transform="translate(7704.6, 0)"><use xlink:href="#MJX-TEX-N-5B"/></g><g data-mml-node="mi" transform="translate(7982.6, 0)"><use xlink:href="#MJX-TEX-I-69"/></g><g data-mml-node="mo" transform="translate(8549.8, 0)"><use xlink:href="#MJX-TEX-N-2212"/></g><g data-mml-node="mn" transform="translate(9550, 0)"><use xlink:href="#MJX-TEX-N-31"/></g><g data-mml-node="mo" transform="translate(10050, 0)"><use xlink:href="#MJX-TEX-N-5D"/></g><g data-mml-node="mo" transform="translate(10328, 0)"><use xlink:href="#MJX-TEX-N-5B"/></g><g data-mml-node="mn" transform="translate(10606, 0)"><use xlink:href="#MJX-TEX-N-30"/></g><g data-mml-node="mo" transform="translate(11106, 0)"><use xlink:href="#MJX-TEX-N-5D"/></g><g data-mml-node="mo" transform="translate(11384, 0)"><use xlink:href="#MJX-TEX-N-2C"/></g><g data-mml-node="mi" transform="translate(11828.7, 0)"><use xlink:href="#MJX-TEX-I-64"/></g><g data-mml-node="mi" transform="translate(12348.7, 0)"><use xlink:href="#MJX-TEX-I-70"/></g><g data-mml-node="mo" transform="translate(12851.7, 0)"><use xlink:href="#MJX-TEX-N-5B"/></g><g data-mml-node="mi" transform="translate(13129.7, 0)"><use xlink:href="#MJX-TEX-I-69"/></g><g data-mml-node="mo" transform="translate(13696.9, 0)"><use xlink:href="#MJX-TEX-N-2212"/></g><g data-mml-node="mn" transform="translate(14697.1, 0)"><use xlink:href="#MJX-TEX-N-31"/></g><g data-mml-node="mo" transform="translate(15197.1, 0)"><use xlink:href="#MJX-TEX-N-5D"/></g><g data-mml-node="mo" transform="translate(15475.1, 0)"><use xlink:href="#MJX-TEX-N-5B"/></g><g data-mml-node="mn" transform="translate(15753.1, 0)"><use xlink:href="#MJX-TEX-N-31"/></g><g data-mml-node="mo" transform="translate(16253.1, 0)"><use xlink:href="#MJX-TEX-N-5D"/></g><g data-mml-node="mo" transform="translate(16531.1, 0)"><use xlink:href="#MJX-TEX-N-29"/></g></g></g></svg></mjx-container></p>
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<p>最后只要比较两种情况即可 <mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex" xmlns="http://www.w3.org/2000/svg" width="20.728ex" height="2.262ex" role="img" focusable="false" viewbox="0 -750 9161.7 1000" xmlns:xlink="http://www.w3.org/1999/xlink"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g data-mml-node="math"><g data-mml-node="mi"><use xlink:href="#MJX-TEX-I-6D"/></g><g data-mml-node="mi" transform="translate(878, 0)"><use xlink:href="#MJX-TEX-I-61"/></g><g data-mml-node="mi" transform="translate(1407, 0)"><use xlink:href="#MJX-TEX-I-78"/></g><g data-mml-node="mo" transform="translate(1979, 0)"><use xlink:href="#MJX-TEX-N-28"/></g><g data-mml-node="mi" transform="translate(2368, 0)"><use xlink:href="#MJX-TEX-I-64"/></g><g data-mml-node="mi" transform="translate(2888, 0)"><use xlink:href="#MJX-TEX-I-70"/></g><g data-mml-node="mo" transform="translate(3391, 0)"><use xlink:href="#MJX-TEX-N-5B"/></g><g data-mml-node="mi" transform="translate(3669, 0)"><use xlink:href="#MJX-TEX-I-69"/></g><g data-mml-node="mo" transform="translate(4014, 0)"><use xlink:href="#MJX-TEX-N-5D"/></g><g data-mml-node="mo" transform="translate(4292, 0)"><use xlink:href="#MJX-TEX-N-5B"/></g><g data-mml-node="mn" transform="translate(4570, 0)"><use xlink:href="#MJX-TEX-N-30"/></g><g data-mml-node="mo" transform="translate(5070, 0)"><use xlink:href="#MJX-TEX-N-5D"/></g><g data-mml-node="mo" transform="translate(5348, 0)"><use xlink:href="#MJX-TEX-N-2C"/></g><g data-mml-node="mi" transform="translate(5792.7, 0)"><use xlink:href="#MJX-TEX-I-64"/></g><g data-mml-node="mi" transform="translate(6312.7, 0)"><use xlink:href="#MJX-TEX-I-70"/></g><g data-mml-node="mo" transform="translate(6815.7, 0)"><use xlink:href="#MJX-TEX-N-5B"/></g><g data-mml-node="mi" transform="translate(7093.7, 0)"><use xlink:href="#MJX-TEX-I-69"/></g><g data-mml-node="mo" transform="translate(7438.7, 0)"><use xlink:href="#MJX-TEX-N-5D"/></g><g data-mml-node="mo" transform="translate(7716.7, 0)"><use xlink:href="#MJX-TEX-N-5B"/></g><g data-mml-node="mn" transform="translate(7994.7, 0)"><use xlink:href="#MJX-TEX-N-31"/></g><g data-mml-node="mo" transform="translate(8494.7, 0)"><use xlink:href="#MJX-TEX-N-5D"/></g><g data-mml-node="mo" transform="translate(8772.7, 0)"><use xlink:href="#MJX-TEX-N-29"/></g></g></g></svg></mjx-container></p>
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<figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br></pre></td><td class="code"><pre><span class="line"><span class="class"><span class="keyword">class</span> <span class="title">Solution</span>:</span></span><br><span class="line"> <span class="function"><span class="keyword">def</span> <span class="title">massage</span><span class="params">(self, nums)</span> -> int:</span></span><br><span class="line"> <span class="keyword">if</span> <span class="keyword">not</span> nums:</span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span></span><br><span class="line"> n = len(nums)</span><br><span class="line"> not_choose = <span class="number">0</span></span><br><span class="line"> choose = <span class="number">0</span></span><br><span class="line"> <span class="keyword">for</span> n <span class="keyword">in</span> nums:</span><br><span class="line"> not_choose, choose = max(not_choose, choose), not_choose+n</span><br><span class="line"> <span class="keyword">return</span> max(not_choose, choose)</span><br><span class="line"> <span class="comment"># 52 ms 13.6 MB</span></span><br></pre></td></tr></table></figure>
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<p>这种问题原来有个名字叫<a href="https://zh.wikipedia.org/wiki/动态规划" target="_blank" rel="noopener">动态规划</a>，上面推导的方程叫<a href="https://baike.baidu.com/item/状态转移方程" target="_blank" rel="noopener">状态转移方程</a>，可以找找资料来看一下。</p>
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