10 lines
5.1 KiB
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10 lines
5.1 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"><meta name="generator" content="Hexo 6.0.0"><link rel="alternate" href="/atom.xml" title="MarkDown" type="application/atom+xml">
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</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="/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="面试题57-II-和为s的连续正数序列"><a href="#面试题57-II-和为s的连续正数序列" 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 target="_blank" rel="noopener" href="https://leetcode-cn.com/problems/he-wei-sde-lian-xu-zheng-shu-xu-lie-lcof/">题目</a></p>
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<p>又是小学奥数。由等差数列求和公式$\cfrac{(首项 + 末项)×项数}{2}$ 可知，当首项为 1 的时候项数最多，又由于是连续正整数，$n^2 < (1+n)×n < (n+1)^2 $，那最大的 $n$ 就不大于 $\sqrt{2×target} + 1$。</p>
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<p>由小到大遍历 $n$，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: <span class="built_in">int</span></span>):</span></span><br><span class="line"> n = <span class="built_in">int</span>(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> <span class="built_in">range</span>(<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 = <span class="built_in">int</span>(a)</span><br><span class="line"> s_ = []</span><br><span class="line"> <span class="keyword">for</span> j <span class="keyword">in</span> <span class="built_in">range</span>(<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> <span class="built_in">sorted</span>(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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