123 lines
19 KiB
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123 lines
19 KiB
HTML
<!DOCTYPE html><html lang="zh-CN"><head><meta charset="utf-8"><meta name="X-UA-Compatible" content="IE=edge"><title> leetcode-he-wei-sde-lian-xu-zheng-shu-xu-lie-lcof · MarkDown</title><meta name="description" content="leetcode-he-wei-sde-lian-xu-zheng-shu-xu-lie-lcof - 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-he-wei-sde-lian-xu-zheng-shu-xu-lie-lcof</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_u989857_-_II-__u548C_u4E3As_u7684_u8FDE_u7EED_u6B63_u6570_u5E8F_u5217"><a href="#u9762_u8BD5_u989857_-_II-__u548C_u4E3As_u7684_u8FDE_u7EED_u6B63_u6570_u5E8F_u5217" class="headerlink" title="面试题57 - II. 和为s的连续正数序列"></a>面试题57 - II. 和为s的连续正数序列</h3><p><a href="https://leetcode-cn.com/problems/he-wei-sde-lian-xu-zheng-shu-xu-lie-lcof/" target="_blank" rel="noopener">题目</a></p>
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<p>又是小学奥数。由等差数列求和公式<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -1.625ex" xmlns="http://www.w3.org/2000/svg" width="20.379ex" height="4.656ex" role="img" focusable="false" viewbox="0 -1340 9007.3 2058.1" 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="mfrac"><g data-mml-node="mrow" transform="translate(220, 590) scale(0.707)"><g data-mml-node="mpadded"><g data-mml-node="mrow"/></g><g data-mml-node="mstyle" transform="scale(1.414)"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD"><g data-mml-node="mo"><use xlink:href="#MJX-TEX-N-28"/></g><g data-mml-node="mo" transform="translate(389, 0)"><text data-variant="normal" transform="matrix(1 0 0 -1 0 0)" font-size="884px" font-family="serif">首</text><text data-variant="normal" transform="translate(900, 0) matrix(1 0 0 -1 0 0)" font-size="884px" font-family="serif">项</text></g><g data-mml-node="mo" transform="translate(2466.8, 0)"><use xlink:href="#MJX-TEX-N-2B"/></g><g data-mml-node="mo" transform="translate(3522.6, 0)"><text data-variant="normal" transform="matrix(1 0 0 -1 0 0)" font-size="884px" font-family="serif">末</text><text data-variant="normal" transform="translate(900, 0) matrix(1 0 0 -1 0 0)" font-size="884px" font-family="serif">项</text></g><g data-mml-node="mo" transform="translate(5322.6, 0)"><use xlink:href="#MJX-TEX-N-29"/></g><g data-mml-node="mo" transform="translate(5711.6, 0)"><use xlink:href="#MJX-TEX-N-D7"/></g><g data-mml-node="mo" transform="translate(6767.3, 0)"><text data-variant="normal" transform="matrix(1 0 0 -1 0 0)" font-size="884px" font-family="serif">项</text><text data-variant="normal" transform="translate(900, 0) matrix(1 0 0 -1 0 0)" font-size="884px" font-family="serif">数</text></g></g></g></g><g data-mml-node="mrow" transform="translate(4253.7, -506) scale(0.707)"><g data-mml-node="mpadded"><g data-mml-node="mrow"/></g><g data-mml-node="mstyle" transform="scale(1.414)"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD"><g data-mml-node="mn"><use xlink:href="#MJX-TEX-N-32"/></g></g></g></g><rect width="8767.3" height="60" x="120" y="220"/></g></g></g></svg></mjx-container> 可知,当首项为 1 的时候项数最多,又由于是连续正整数,<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex" xmlns="http://www.w3.org/2000/svg" width="27.37ex" height="2.452ex" role="img" focusable="false" viewbox="0 -833.9 12097.6 1083.9" 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="msup"><g data-mml-node="mi"><use xlink:href="#MJX-TEX-I-6E"/></g><g data-mml-node="mn" transform="translate(600, 363) scale(0.707)"><use xlink:href="#MJX-TEX-N-32"/></g></g><g data-mml-node="mo" transform="translate(1281.3, 0)"><use xlink:href="#MJX-TEX-N-3C"/></g><g data-mml-node="mo" transform="translate(2337.1, 0)"><use xlink:href="#MJX-TEX-N-28"/></g><g data-mml-node="mn" transform="translate(2726.1, 0)"><use xlink:href="#MJX-TEX-N-31"/></g><g data-mml-node="mo" transform="translate(3448.3, 0)"><use xlink:href="#MJX-TEX-N-2B"/></g><g data-mml-node="mi" transform="translate(4448.6, 0)"><use xlink:href="#MJX-TEX-I-6E"/></g><g data-mml-node="mo" transform="translate(5048.6, 0)"><use xlink:href="#MJX-TEX-N-29"/></g><g data-mml-node="mo" transform="translate(5659.8, 0)"><use xlink:href="#MJX-TEX-N-D7"/></g><g data-mml-node="mi" transform="translate(6660, 0)"><use xlink:href="#MJX-TEX-I-6E"/></g><g data-mml-node="mo" transform="translate(7537.8, 0)"><use xlink:href="#MJX-TEX-N-3C"/></g><g data-mml-node="mo" transform="translate(8593.6, 0)"><use xlink:href="#MJX-TEX-N-28"/></g><g data-mml-node="mi" transform="translate(8982.6, 0)"><use xlink:href="#MJX-TEX-I-6E"/></g><g data-mml-node="mo" transform="translate(9804.8, 0)"><use xlink:href="#MJX-TEX-N-2B"/></g><g data-mml-node="mn" transform="translate(10805, 0)"><use xlink:href="#MJX-TEX-N-31"/></g><g data-mml-node="msup" transform="translate(11305, 0)"><g data-mml-node="mo"><use xlink:href="#MJX-TEX-N-29"/></g><g data-mml-node="mn" transform="translate(389, 363) scale(0.707)"><use xlink:href="#MJX-TEX-N-32"/></g></g></g></g></svg></mjx-container>,那最大的 <mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.025ex" xmlns="http://www.w3.org/2000/svg" width="1.357ex" height="1.025ex" role="img" focusable="false" viewbox="0 -442 600 453" 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-6E"/></g></g></g></svg></mjx-container> 就不大于 <mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.683ex" xmlns="http://www.w3.org/2000/svg" width="16.086ex" height="2.851ex" role="img" focusable="false" viewbox="0 -958 7109.9 1260" 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="msqrt"><g transform="translate(1020, 0)"><g data-mml-node="mn"><use xlink:href="#MJX-TEX-N-32"/></g><g data-mml-node="mo" transform="translate(722.2, 0)"><use xlink:href="#MJX-TEX-N-D7"/></g><g data-mml-node="mi" transform="translate(1722.4, 0)"><use xlink:href="#MJX-TEX-I-74"/></g><g data-mml-node="mi" transform="translate(2083.4, 0)"><use xlink:href="#MJX-TEX-I-61"/></g><g data-mml-node="mi" transform="translate(2612.4, 0)"><use xlink:href="#MJX-TEX-I-72"/></g><g data-mml-node="mi" transform="translate(3063.4, 0)"><use xlink:href="#MJX-TEX-I-67"/></g><g data-mml-node="mi" transform="translate(3540.4, 0)"><use xlink:href="#MJX-TEX-I-65"/></g><g data-mml-node="mi" transform="translate(4006.4, 0)"><use xlink:href="#MJX-TEX-I-74"/></g></g><g data-mml-node="mo" transform="translate(0, 48)"><use xlink:href="#MJX-TEX-SO-221A"/></g><rect width="4367.4" height="60" x="1020" y="838"/></g><g data-mml-node="mo" transform="translate(5609.7, 0)"><use xlink:href="#MJX-TEX-N-2B"/></g><g data-mml-node="mn" transform="translate(6609.9, 0)"><use xlink:href="#MJX-TEX-N-31"/></g></g></g></svg></mjx-container>。</p>
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<p>由小到大遍历 <mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.025ex" xmlns="http://www.w3.org/2000/svg" width="1.357ex" height="1.025ex" role="img" focusable="false" viewbox="0 -442 600 453" 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-6E"/></g></g></g></svg></mjx-container>,可以求得首项。</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><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">import</span> math</span><br><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">findContinuousSequence</span><span class="params">(self, target: int)</span>:</span></span><br><span class="line"> n = int(math.sqrt(<span class="number">2</span> * target) + <span class="number">1</span>)</span><br><span class="line"> <span class="keyword">if</span> n < <span class="number">2</span>:</span><br><span class="line"> <span class="keyword">return</span> []</span><br><span class="line"> sum_list = []</span><br><span class="line"> a = <span class="number">0</span></span><br><span class="line"> <span class="keyword">for</span> i <span class="keyword">in</span> range(<span class="number">2</span>, n+<span class="number">1</span>):</span><br><span class="line"> a = ((<span class="number">2</span> * target) / i + <span class="number">1</span> - i) / <span class="number">2</span></span><br><span class="line"> <span class="keyword">if</span> a <span class="keyword">and</span> <span class="keyword">not</span> a % <span class="number">1</span>:</span><br><span class="line"> a = int(a)</span><br><span class="line"> s_ = []</span><br><span class="line"> <span class="keyword">for</span> j <span class="keyword">in</span> range(<span class="number">0</span>, i):</span><br><span class="line"> s_.append(a + j)</span><br><span class="line"> sum_list.append(s_)</span><br><span class="line"> <span class="keyword">return</span> sorted(sum_list)</span><br><span class="line"> <span class="comment"># 60 ms 13.7 MB</span></span><br></pre></td></tr></table></figure>
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