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<?xml version="1.0" encoding="utf-8"?>
<search>
<entry>
<title>01背包问题</title>
<url>/sublog.github.io/2020/08/14/01%E8%83%8C%E5%8C%85%E9%97%AE%E9%A2%98/</url>
<content><![CDATA[<link rel="stylesheet" class="aplayer-secondary-style-marker" href="\sublog.github.io\css\APlayer.min.css"><script src="\sublog.github.io\js\APlayer.min.js" class="aplayer-secondary-script-marker"></script><script class="meting-secondary-script-marker" src="\sublog.github.io\js\Meting.min.js"></script>
<div id="aplayer-IMGcIstT" class="aplayer aplayer-tag-marker meting-tag-marker"
data-id="1383205688" data-server="netease" data-type="song" data-mode="circulation" data-autoplay="false" data-mutex="true" data-listmaxheight="340px" data-preload="auto" data-theme="#FF4081"
></div>
<p>朴素的 动规的 基本表示：</p>
<p>f[ i ] [ j ] : 表示只看前 i 个物品，总体积是 j 的情况下，总价值最大是多少</p>
<p>result = max[ f [ n ] [ 0 ~ V ] ]</p>
<p>f[i] [j] = </p>
<p>1.不选第 i 个物品： f[i] [j] = f[i - 1] [j];</p>
<p>2.选第 i个物品： f[i] [j] = f[i - 1] [j - v[i]];</p>
<p>f[i] [j] = max{1,2}</p>
<h4 id="例题"><a href="#例题" class="headerlink" title="例题"></a>例题</h4><p><img src= "/sublog.github.io/img/loading.gif" data-src="https://i.loli.net/2020/08/14/SkbKBvhHP7amWzg.png" alt="B5R6RE09MI_9_WU2_F_J_ZK.png"></p>
<p><img src= "/sublog.github.io/img/loading.gif" data-src="https://i.loli.net/2020/08/14/SED74quUPfajYOw.png" alt=""></p>
<figure class="highlight c++"><table><tr><td class="code"><pre><span class="line"><span class="comment">//板子板子</span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string"><bits/stdc++.h></span></span></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="built_in">std</span>;</span><br><span class="line"></span><br><span class="line"><span class="keyword">const</span> <span class="keyword">int</span> N = <span class="number">1010</span>;</span><br><span class="line"></span><br><span class="line"><span class="keyword">int</span> n,m;</span><br><span class="line"><span class="keyword">int</span> f[N][N];</span><br><span class="line"><span class="keyword">int</span> v[N],w[N];</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">int</span> <span class="title">main</span><span class="params">()</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="built_in">cin</span> >> n >> m;</span><br><span class="line"> <span class="comment">//小白想检验一下生成的f数组是不是全0数组</span></span><br><span class="line"> <span class="comment">// for(int j = 0;j < n;j++) cout<<f[j][4];</span></span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i = <span class="number">1</span>;i <= n;i++)</span><br><span class="line"> {</span><br><span class="line"> <span class="built_in">cin</span> >> v[i] >> w[i];</span><br><span class="line"> }</span><br><span class="line"> <span class="comment">//下面这个循环是 依次考虑 当第i个物品时，体积j依次增大，直到大于v[i]时，即当前可以装下第i个物品，即拥有了第i个物品的价值。下面进行降维优化时，j从最大体积m依次减小考虑情况。</span></span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i = <span class="number">1</span>;i <= n;i++)</span><br><span class="line"> {</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> j = <span class="number">1</span>;j <= m;j++)</span><br><span class="line"> {</span><br><span class="line"> f[i][j] = f[i - <span class="number">1</span>][j];</span><br><span class="line"> <span class="keyword">if</span>(j >= v[i])</span><br><span class="line"> {</span><br><span class="line"> f[i][j] = <span class="built_in">max</span>(f[i][j],f[i - <span class="number">1</span>][j - v[i]] + w[i]);</span><br><span class="line"> <span class="comment">//小白手动跑了一遍检验发现 f[n][m]已经是最大的价值 因为赋值时进行了选择 </span></span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="comment">// int res = 0;</span></span><br><span class="line"> <span class="comment">// for(int i = 0;i <= m;i++)</span></span><br><span class="line"> <span class="comment">// {</span></span><br><span class="line"> <span class="comment">// res = max(res,f[n][i]);</span></span><br><span class="line"> <span class="comment">// }</span></span><br><span class="line"> <span class="built_in">cout</span><<f[n][m]<<<span class="built_in">endl</span>;</span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br></pre></td></tr></table></figure>
<figure class="highlight c++"><table><tr><td class="code"><pre><span class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string"><bits/stdc++.h></span></span></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="built_in">std</span>;</span><br><span class="line"><span class="keyword">const</span> <span class="keyword">int</span> N = <span class="number">1010</span>;</span><br><span class="line"></span><br><span class="line"><span class="keyword">int</span> n,m;</span><br><span class="line"><span class="keyword">int</span> f[N]; <span class="comment">//这里进行降维优化</span></span><br><span class="line"><span class="keyword">int</span> v[N],w[N];</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">int</span> <span class="title">main</span><span class="params">()</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="built_in">cin</span> >> n >> m;</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i = <span class="number">1</span>;i <= n;i++)</span><br><span class="line"> {</span><br><span class="line"> <span class="built_in">cin</span> >> v[i] >> w[i];</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i = <span class="number">1</span>;i <= n;i++)</span><br><span class="line"> {</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> j = m;j >= v[i];j--)</span><br><span class="line"> {</span><br><span class="line"> <span class="comment">//由于此时变成了一位数组 由于比较的是和它前一位f[i-1][j-v[i]]为了更好地表示发生变化，我们应选择体积从最大的体积m依次递减</span></span><br><span class="line"> f[j] = <span class="built_in">max</span>(f[j],f[j - v[i]] + w[i]);</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> <span class="built_in">cout</span><<f[m]<<<span class="built_in">endl</span>;</span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br></pre></td></tr></table></figure>
]]></content>
<categories>
<category>ACwing</category>
</categories>
<tags>
<tag>背包</tag>
</tags>
</entry>
<entry>
<title>My first blog</title>
<url>/sublog.github.io/2020/03/13/My-first-blog/</url>
<content><![CDATA[<link rel="stylesheet" class="aplayer-secondary-style-marker" href="\sublog.github.io\css\APlayer.min.css"><script src="\sublog.github.io\js\APlayer.min.js" class="aplayer-secondary-script-marker"></script><script class="meting-secondary-script-marker" src="\sublog.github.io\js\Meting.min.js"></script>
<div id="aplayer-sZtmwqXZ" class="aplayer aplayer-tag-marker meting-tag-marker"
data-id="2919622" data-server="netease" data-type="song" data-mode="circulation" data-autoplay="false" data-mutex="true" data-listmaxheight="340px" data-preload="auto" data-theme="#FF4081"
></div>
<h2 id="位运算"><a href="#位运算" class="headerlink" title="位运算"></a>位运算</h2><figure class="highlight c"><table><tr><td class="code"><pre><span class="line"><span class="comment">//熄灯问题</span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string"><iostream></span></span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string"><cstring></span></span></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="built_in">std</span>;</span><br><span class="line"><span class="keyword">char</span> old[<span class="number">10</span>], lights[<span class="number">10</span>], result[<span class="number">10</span>]; <span class="comment">//原数组，灯数组，结果数组</span></span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">void</span> <span class="title">SetBit</span><span class="params">(<span class="keyword">char</span> &c, <span class="keyword">int</span> i, <span class="keyword">int</span> v)</span> <span class="comment">//c代表第i行的字符，把第i行的第j位设置成v</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="keyword">if</span>(v) {</span><br><span class="line"> c = c | (<span class="number">1</span> << i);</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">else</span> </span><br><span class="line"> c = c & ~(<span class="number">1</span> << i);</span><br><span class="line">}</span><br><span class="line"><span class="comment">//v = 1</span></span><br><span class="line"><span class="comment">//如果把第3位上的设置为1</span></span><br><span class="line"><span class="comment">//0010 0101 </span></span><br><span class="line"><span class="comment">//0010 0101 | 0000 1000 = 0010 1101 按位或运算</span></span><br><span class="line"></span><br><span class="line"><span class="comment">//v = 0</span></span><br><span class="line"><span class="comment">//如果把第2位上的位设置为0</span></span><br><span class="line"><span class="comment">//0010 0101</span></span><br><span class="line"><span class="comment">//~（1 << 2）= ~(0000 0100) = (1111 1011)</span></span><br><span class="line"><span class="comment">//0010 0101 & 1111 1011 = 0010 0001</span></span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">int</span> <span class="title">GetBit</span><span class="params">(<span class="keyword">char</span> c, <span class="keyword">int</span> i)</span> <span class="comment">//取出c的第i位上的数字</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="keyword">return</span> (c >> i) & <span class="number">1</span>;</span><br><span class="line">}</span><br><span class="line"><span class="comment">//0010 0001 右移3位 0000 0100 & 0000 0001 = 0</span></span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">void</span> <span class="title">FilpBit</span><span class="params">(<span class="keyword">char</span> &c, <span class="keyword">int</span> i)</span> <span class="comment">//翻转c的第i位</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> c = c ^ (<span class="number">1</span> << i);</span><br><span class="line">}</span><br><span class="line"><span class="comment">//0010 0101</span></span><br><span class="line"><span class="comment">//翻转第3位上的数字</span></span><br><span class="line"><span class="comment">//0010 0101 ^ 0000 1000 = 0010 1101</span></span><br><span class="line"></span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">void</span> <span class="title">OutPutResult</span><span class="params">()</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i = <span class="number">0</span>; i < <span class="number">5</span>; ++i)</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> j = <span class="number">0</span>; j < <span class="number">6</span>; ++j) {</span><br><span class="line"> <span class="built_in">cout</span> << GetBit(result[i], j);</span><br><span class="line"> <span class="keyword">if</span>(j < <span class="number">5</span>) <span class="built_in">cout</span> << <span class="string">" "</span>;</span><br><span class="line"> <span class="keyword">else</span> <span class="built_in">cout</span> << <span class="built_in">endl</span>;</span><br><span class="line"> }</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">int</span> <span class="title">main</span><span class="params">()</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="keyword">int</span> kase;</span><br><span class="line"> <span class="built_in">cin</span>>>kase;</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i = <span class="number">1</span>;i <= kase ;i++)</span><br><span class="line"> {</span><br><span class="line"> <span class="keyword">int</span> v, switchs;</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i = <span class="number">0</span>; i < <span class="number">5</span>; ++i)</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> j = <span class="number">0</span>; j < <span class="number">6</span>; ++j) {</span><br><span class="line"> <span class="built_in">cin</span> >> v;</span><br><span class="line"> SetBit(old[i], j, v);</span><br><span class="line"> }</span><br><span class="line"> </span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> n = <span class="number">0</span>; n < <span class="number">1</span> << <span class="number">6</span>; ++n) { <span class="comment">//6个开关，2的6次方种情况， (1 << 6 == 2^6)</span></span><br><span class="line"> <span class="built_in">memcpy</span>(lights, old, <span class="keyword">sizeof</span>(old)); <span class="comment">//还原lights数组</span></span><br><span class="line"> switchs = n;</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i = <span class="number">0</span>; i < <span class="number">5</span>; ++i) {</span><br><span class="line"> result[i] = switchs; <span class="comment">// 0 0 1 0 1 0</span></span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> j = <span class="number">0</span>; j < <span class="number">6</span>; ++j) {</span><br><span class="line"> <span class="keyword">if</span>(GetBit(switchs, j)) {</span><br><span class="line"> <span class="keyword">if</span>(j > <span class="number">0</span>) FilpBit(lights[i], j - <span class="number">1</span>); <span class="comment">//翻转左边</span></span><br><span class="line"> FilpBit(lights[i], j); <span class="comment">//翻转本身</span></span><br><span class="line"> <span class="keyword">if</span>(j < <span class="number">5</span>) FilpBit(lights[i], j + <span class="number">1</span>); <span class="comment">//翻转右边</span></span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">if</span>(i < <span class="number">4</span>) lights[i + <span class="number">1</span>] ^= switchs;</span><br><span class="line"> switchs = lights[i];</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">if</span>(lights[<span class="number">4</span>] == <span class="number">0</span>) {</span><br><span class="line"> <span class="built_in">printf</span>(<span class="string">"PUZZLE #%d\n"</span>,i);</span><br><span class="line"> OutPutResult();</span><br><span class="line"> <span class="keyword">break</span>;</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br></pre></td></tr></table></figure>
]]></content>
</entry>
<entry>
<title>Hello World</title>
<url>/sublog.github.io/2020/03/13/hello-world/</url>
<content><![CDATA[<link rel="stylesheet" class="aplayer-secondary-style-marker" href="\sublog.github.io\css\APlayer.min.css"><script src="\sublog.github.io\js\APlayer.min.js" class="aplayer-secondary-script-marker"></script><script class="meting-secondary-script-marker" src="\sublog.github.io\js\Meting.min.js"></script><p>Welcome to <a href="https://hexo.io/" target="_blank" rel="noopener">Hexo</a>! This is your very first post. Check <a href="https://hexo.io/docs/" target="_blank" rel="noopener">documentation</a> for more info. If you get any problems when using Hexo, you can find the answer in <a href="https://hexo.io/docs/troubleshooting.html" target="_blank" rel="noopener">troubleshooting</a> or you can ask me on <a href="https://github.com/hexojs/hexo/issues" target="_blank" rel="noopener">GitHub</a>.</p>
<h2 id="Quick-Start"><a href="#Quick-Start" class="headerlink" title="Quick Start"></a>Quick Start</h2><h3 id="Create-a-new-post"><a href="#Create-a-new-post" class="headerlink" title="Create a new post"></a>Create a new post</h3><figure class="highlight bash"><table><tr><td class="code"><pre><span class="line">$ hexo new <span class="string">"My New Post"</span></span><br></pre></td></tr></table></figure>
<p>More info: <a href="https://hexo.io/docs/writing.html" target="_blank" rel="noopener">Writing</a></p>
<h3 id="Run-server"><a href="#Run-server" class="headerlink" title="Run server"></a>Run server</h3><figure class="highlight bash"><table><tr><td class="code"><pre><span class="line">$ hexo server</span><br></pre></td></tr></table></figure>
<p>More info: <a href="https://hexo.io/docs/server.html" target="_blank" rel="noopener">Server</a></p>
<h3 id="Generate-static-files"><a href="#Generate-static-files" class="headerlink" title="Generate static files"></a>Generate static files</h3><figure class="highlight bash"><table><tr><td class="code"><pre><span class="line">$ hexo generate</span><br></pre></td></tr></table></figure>
<p>More info: <a href="https://hexo.io/docs/generating.html" target="_blank" rel="noopener">Generating</a></p>
<h3 id="Deploy-to-remote-sites"><a href="#Deploy-to-remote-sites" class="headerlink" title="Deploy to remote sites"></a>Deploy to remote sites</h3><figure class="highlight bash"><table><tr><td class="code"><pre><span class="line">$ hexo deploy</span><br></pre></td></tr></table></figure>
<p>More info: <a href="https://hexo.io/docs/one-command-deployment.html" target="_blank" rel="noopener">Deployment</a></p>
]]></content>
<categories>
<category>note</category>
</categories>
<tags>
<tag>tip</tag>
</tags>
</entry>
<entry>
<title>os --第一章 操作系统引论</title>
<url>/sublog.github.io/2020/07/11/os%E7%AC%AC%E4%B8%80%E7%AB%A0/</url>
<content><![CDATA[<link rel="stylesheet" class="aplayer-secondary-style-marker" href="\sublog.github.io\css\APlayer.min.css"><script src="\sublog.github.io\js\APlayer.min.js" class="aplayer-secondary-script-marker"></script><script class="meting-secondary-script-marker" src="\sublog.github.io\js\Meting.min.js"></script><h4 id="操作系统的目标和作用"><a href="#操作系统的目标和作用" class="headerlink" title="操作系统的目标和作用"></a>操作系统的目标和作用</h4><p> 定义： ==os==是直接控制和管理计算机硬件、软件资源，合理地对各类作业进行调度，以方便用户使用的==程序集合==</p>
<p> 地位：系统硬件之上，所有其他软件之下</p>
<p> 目标：</p>
<ul>
<li>方便性 （如果没有os，c语言程序无法运行）</li>
<li>有效性</li>
<li>可扩充性</li>
</ul>
<h5 id="发展过程"><a href="#发展过程" class="headerlink" title="发展过程"></a>发展过程</h5>]]></content>
<categories>
<category>复习</category>
</categories>
<tags>
<tag>操作系统</tag>
</tags>
</entry>
<entry>
<title>python review--01</title>
<url>/sublog.github.io/2020/08/26/python-review-01/</url>
<content><![CDATA[<link rel="stylesheet" class="aplayer-secondary-style-marker" href="\sublog.github.io\css\APlayer.min.css"><script src="\sublog.github.io\js\APlayer.min.js" class="aplayer-secondary-script-marker"></script><script class="meting-secondary-script-marker" src="\sublog.github.io\js\Meting.min.js"></script><h4 id="对象和变量"><a href="#对象和变量" class="headerlink" title="对象和变量"></a>对象和变量</h4><h5 id="1-一切都是对象"><a href="#1-一切都是对象" class="headerlink" title="1.一切都是对象"></a>1.一切都是对象</h5><p>所有的对象都具有三个特征：</p>
<ul>
<li><p>身份</p>
<p>每一个对象唯一身份标识，可以使用内建函数id( )查看，所得到的值也可以认为是该对象的内存地址。</p>
<figure class="highlight bash"><table><tr><td class="code"><pre><span class="line">a = b = 34</span><br><span class="line">id(x) = id(y)</span><br></pre></td></tr></table></figure>
<p>引用计数</p>
</li>
<li><p>类型</p>
<p><img src= "/sublog.github.io/img/loading.gif" data-src="https://i.loli.net/2020/08/26/GTIvx7t9y8ZCHej.png" alt="image-20200826104012089"></p>
<p>b继承a</p>
<p>类型可以通过type( )方法来查看类型，</p>
<figure class="highlight"><table><tr><td class="code"><pre><span class="line"><span class="comment">#以字符串形式输出它的类型名字</span></span><br><span class="line">type('a') -->str</span><br><span class="line">type(str).__name__ -->'type'</span><br></pre></td></tr></table></figure>
<p>使用 isinstance ( )方法来验证类型</p>
<figure class="highlight"><table><tr><td class="code"><pre><span class="line">isinstance(object,classinfo)</span><br><span class="line"><span class="comment">#参数</span></span><br><span class="line">object --实例对象</span><br><span class="line">classinfo --可以直接或间接类名，基本类型或者由它们组成的元组</span><br><span class="line"></span><br><span class="line">isinstance(3,int) --> True</span><br><span class="line">isinstance(3.7,(str,float,int)) -->True</span><br></pre></td></tr></table></figure>
</li>
<li><p>值 操作符：< > <= >= == != <> 返回值：布尔值</p>
</li>
</ul>
<h5 id="2-变量"><a href="#2-变量" class="headerlink" title="2.变量"></a>2.变量</h5><p>变量，是在程序中为了方便引用内存中的值而为它所取的名字。</p>
<figure class="highlight python"><table><tr><td class="code"><pre><span class="line"><span class="comment"># 增量赋值，与C语言中的算数自反赋值运算一样</span></span><br><span class="line">int_example *= <span class="number">3</span></span><br><span class="line">string_example += <span class="string">'Try it!'</span></span><br><span class="line"></span><br><span class="line"><span class="comment"># 多重赋值</span></span><br><span class="line">x = y = z = <span class="number">1</span></span><br><span class="line"></span><br><span class="line"><span class="comment"># 多元赋值，很有用，用起来效率很高，括号是可选的，但保留可以增强代码可读性</span></span><br><span class="line">(x, y, z) = (<span class="number">1</span>, <span class="number">2</span>, <span class="string">'a string'</span>)</span><br><span class="line"></span><br><span class="line">(x, y) = (y, x) <span class="comment"># 对x, y的值做交换，不需要第三个辅助变量了</span></span><br></pre></td></tr></table></figure>
<p>变量名 标识符</p>
<p>1.命名规则：只能包含 小写字母，大写字母，下划线，数字，且不能以数字开头，<strong>python以下划线开头的名字有特殊含义。</strong></p>
<p>2.关键字</p>
<p>3.builtins 进入解释器时，builtins模块自动导入，一般情况下，定义的标识符不要冲突。</p>
<figure class="highlight python"><table><tr><td class="code"><pre><span class="line"><span class="keyword">import</span> builtins</span><br><span class="line">dir(builtins) <span class="comment">#参数为对象、变量、类型 返回模块的属性列表</span></span><br><span class="line"></span><br><span class="line">dir() <span class="comment">#返回当前模块属性列表</span></span><br><span class="line">dir( [ ]) <span class="comment">#查看列表的方法</span></span><br></pre></td></tr></table></figure>
<figure class="highlight"><table><tr><td class="code"><pre><span class="line">a = <span class="number">90</span></span><br><span class="line">b = <span class="number">90</span></span><br><span class="line">a <span class="keyword">is</span> b</span><br><span class="line">-->True #连等就是True，不连等就是False 整数小于256都是True</span><br></pre></td></tr></table></figure>
<h4 id="数字"><a href="#数字" class="headerlink" title="数字"></a>数字</h4><p>注意：</p>
<p> 浮点数除法：/ 两个整数进行运算时，还会得到浮点型结果</p>
<p> 整数除法： //</p>
<p>数字可以直接访问，是不可更改并且不可分割的原子类型。 不可更改意味着变更数字值的实质是新对象的创建。</p>
<h5 id="更新数字对象：创建了新的对象，然后让变量指向新的对象"><a href="#更新数字对象：创建了新的对象，然后让变量指向新的对象" class="headerlink" title="更新数字对象：创建了新的对象，然后让变量指向新的对象"></a>更新数字对象：创建了新的对象，然后让变量指向新的对象</h5><h5 id="删除数字对象：-del-变量名"><a href="#删除数字对象：-del-变量名" class="headerlink" title="删除数字对象： del 变量名"></a>删除数字对象： del 变量名</h5><p>注意：注意引用计数与对象之间</p>
<h4 id="布尔值"><a href="#布尔值" class="headerlink" title="布尔值"></a>布尔值</h4><p>事实上，布尔型是整型的子类，对应整型1和0</p>
<h5 id="布尔运算：-优先级由高到低：not-，and-，-or"><a href="#布尔运算：-优先级由高到低：not-，and-，-or" class="headerlink" title="布尔运算： 优先级由高到低：not ，and ， or"></a>布尔运算： 优先级由高到低：not ，and ， or</h5><p>要善于运用括号避免问题</p>
<h4 id="复数"><a href="#复数" class="headerlink" title="复数"></a>复数</h4><p>real + imag j 注意：虚数部分结尾是j 或 J</p>
<p>real 实数部分，imag虚数部分，还有一个方法，conjugate（ ），用来获取共轭复数。</p>
<figure class="highlight"><table><tr><td class="code"><pre><span class="line">a_complex = <span class="number">3.5</span> + <span class="number">2.9</span> j</span><br><span class="line">a_complex.real --> 3.5</span><br><span class="line">a_complex.imag --> 2.9</span><br><span class="line">a_complex.conjugate() --> (3.5-2.9j)</span><br></pre></td></tr></table></figure>
<h4 id="基数"><a href="#基数" class="headerlink" title="基数"></a>基数</h4><p>0b 或者 0B表示二进制 0b10 —>2</p>
<p>0o 或者 0O表示八进制 0o10 —>8</p>
<p>0x 或者 0X表示十六进制 0x10 —>16</p>
<h5 id="类型转换：转换失败会产生ValueError异常。"><a href="#类型转换：转换失败会产生ValueError异常。" class="headerlink" title="类型转换：转换失败会产生ValueError异常。"></a>类型转换：转换失败会产生<code>ValueError</code>异常。</h5><p>基本规则：整型转换为浮点型，非复数转换为复数。总之，简单类型向复杂类型转换，不精确向更精确类型转换。</p>
<ul>
<li><code>int()</code></li>
<li><code>float()</code></li>
<li><code>complex()</code></li>
<li><code>bool()</code></li>
</ul>
<h5 id="功能函数："><a href="#功能函数：" class="headerlink" title="功能函数："></a>功能函数：</h5><p>abs( ) : 返回绝对值，如果参数是整型，返回整型，如果是浮点型，返回浮点类型， 同样也可用于复数绝对值的计算，即返回实部和虚部平方和的二次方根。</p>
<figure class="highlight"><table><tr><td class="code"><pre><span class="line">abs(3 +4j) --> 5.0</span><br><span class="line">abs(4.5) --> 4.5</span><br><span class="line">abs(-3) --> 3</span><br></pre></td></tr></table></figure>
<p>divmod ( ) : 此函数将除法和求余结合起来，返回一个包含商和余数的元组.</p>
<figure class="highlight"><table><tr><td class="code"><pre><span class="line">divmod(2.5,10) --> (0.0,2.5)</span><br><span class="line">divmod(10,3) --> (3,1)</span><br></pre></td></tr></table></figure>
<p>pow ( ) : 幂运算 传两个参数</p>
<p>round ( ) : 做真正的四舍五入！可以用第二个参数指定精确到小数点后第几位：</p>
<figure class="highlight"><table><tr><td class="code"><pre><span class="line">round(4.499) -> 4</span><br><span class="line">round(4.6) -> 5</span><br><span class="line">round(4.51) -> 5</span><br><span class="line">round(4.492,2)-> 4.49</span><br><span class="line">round(4.499,2)-> 4.5</span><br></pre></td></tr></table></figure>
<h4 id="字符串"><a href="#字符串" class="headerlink" title="字符串"></a>字符串</h4><p>字符串由一系列Unicode码位组成的不可变序列</p>
<p>使用内建函数<code>len（）</code>可以获得字符串长度</p>
<p>不可变指无法对字符串本身进行更改操作</p>
<figure class="highlight python"><table><tr><td class="code"><pre><span class="line">s = <span class="string">'a'</span><span class="string">'b'</span></span><br><span class="line">s</span><br><span class="line">---> 'ab'</span><br><span class="line"></span><br><span class="line"><span class="comment">#常见的转义符：`\n`（换行符）、`\t`（Tab制表符）、`\'`（单引号）、`\"`（双引号）、`\\`（反斜线）</span></span><br></pre></td></tr></table></figure>
<h5 id="内建函数"><a href="#内建函数" class="headerlink" title="内建函数"></a>内建函数</h5><figure class="highlight python"><table><tr><td class="code"><pre><span class="line">input( ) <span class="comment">#获取用户输入，返回字符串</span></span><br><span class="line">chr( ) <span class="comment">#接收一个整数，返回对应的Unicode字符</span></span><br><span class="line">ord( ) <span class="comment">#功能与chr( )相反</span></span><br></pre></td></tr></table></figure>
]]></content>
<tags>
<tag>python</tag>
</tags>
</entry>
<entry>
<title>page</title>
<url>/sublog.github.io/2020/06/03/page/</url>
<content><![CDATA[<link rel="stylesheet" class="aplayer-secondary-style-marker" href="\sublog.github.io\css\APlayer.min.css"><script src="\sublog.github.io\js\APlayer.min.js" class="aplayer-secondary-script-marker"></script><script class="meting-secondary-script-marker" src="\sublog.github.io\js\Meting.min.js"></script>]]></content>
</entry>
<entry>
<title>leetcode03.数组中重复的数字-1</title>
<url>/sublog.github.io/2020/07/22/leetcode03-%E6%95%B0%E7%BB%84%E4%B8%AD%E9%87%8D%E5%A4%8D%E7%9A%84%E6%95%B0%E5%AD%97/</url>
<content><![CDATA[<link rel="stylesheet" class="aplayer-secondary-style-marker" href="\sublog.github.io\css\APlayer.min.css"><script src="\sublog.github.io\js\APlayer.min.js" class="aplayer-secondary-script-marker"></script><script class="meting-secondary-script-marker" src="\sublog.github.io\js\Meting.min.js"></script>
<div id="aplayer-cUgtjviA" class="aplayer aplayer-tag-marker meting-tag-marker"
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></div>
<h4 id="题目描述："><a href="#题目描述：" class="headerlink" title="题目描述："></a>题目描述：</h4><p>找出数组中重复的数字。</p>
<p>在一个长度为 n 的数组 nums 里的所有数字都在 0～n-1 的范围内。数组中某些数字是重复的，但不知道有几个数字重复了，也不知道每个数字重复了几次。请找出数组中任意一个重复的数字。</p>
<h5 id="示例"><a href="#示例" class="headerlink" title="示例"></a>示例</h5><figure class="highlight bash"><table><tr><td class="code"><pre><span class="line">输入：</span><br><span class="line">[2, 3, 1, 0, 2, 5, 3]</span><br><span class="line">输出：2 或 3</span><br></pre></td></tr></table></figure>
<h5 id="限制：2-lt-n-lt-100000"><a href="#限制：2-lt-n-lt-100000" class="headerlink" title="限制：2 <= n <= 100000"></a>限制：2 <= n <= 100000</h5><h4 id="思路："><a href="#思路：" class="headerlink" title="思路："></a>思路：</h4><p>==方法一：遍历数组==</p>
<p> 遍历整个数组，找到任意一个重复的数字，即返回。且当为了判断一个数字是否重复遇到，使用集合存储已经遇到的数字，如果遇到的数字已经在集合中，则当前的数字是重复数字。</p>
<ul>
<li><p>时间复杂度：O(n)。</p>
<pre><code>遍历数组一遍。使用哈希集合（HashSet），添加元素的时间复杂度为 O(1)，故总的时间复杂度是 O(n)。
</code></pre></li>
<li><p>空间复杂度：O(n)。</p>
<p> 不重复的每个元素都可能存入集合，因此占用 O(n) 额外空间。</p>
</li>
</ul>
<h4 id="Java语言版本"><a href="#Java语言版本" class="headerlink" title="Java语言版本"></a>Java语言版本</h4><figure class="highlight java"><table><tr><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">public</span> <span class="keyword">int</span> <span class="title">findRepeatNumber</span><span class="params">(<span class="keyword">int</span>[] nums)</span> </span>{</span><br><span class="line"> Set<Integer> set = <span class="keyword">new</span> HashSet<Integer>(); </span><br><span class="line"> <span class="comment">//数组中已遍历的要存入的集合</span></span><br><span class="line"> <span class="keyword">int</span> repeat = -<span class="number">1</span>; <span class="comment">//如果找到重复的返回值</span></span><br><span class="line"> <span class="keyword">for</span> (<span class="keyword">int</span> num : nums) { </span><br><span class="line"> <span class="keyword">if</span> (!set.add(num)) { <span class="comment">//如果放入集合失败，则查找到重复的</span></span><br><span class="line"> repeat = num;</span><br><span class="line"> <span class="keyword">break</span>;</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> repeat;</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure>
<p>==方法二：哈希表冲突（修改数组）==</p>
<p> 由题意可以看出：<strong><em>数组 nums 里的所有数字都在 0～n-1 的范围内</em></strong></p>
<p> 那么可以，将下标与数组中的值一一对应。即看到数值，就知道它应该在下标对应的位置，即数字num[i]应该放在 i 的位置上，这就像数据结构中人为编写的哈希函数。而重复的数即哈希冲突。</p>
<p>算法流程:</p>
<ul>
<li>遍历数组 nums ，设索引初始值为 i = 0:<br>若 nums[i] == i ： 说明此数字已在对应索引位置，无需交换，因此执行 i += 1 与 continue ；<pre><code> 若 nums[nums[i]] == nums[i] ： 说明索引 nums[i] 处的元素值也为 nums[i]，即找到一组相同值，返回此值 nums[i]；
否则： 当前数字是第一次遇到，因此交换索引为 i 和 nums[i] 的元素值，将此数字交换至对应索引位置。
</code></pre></li>
<li>若遍历完毕尚未返回，则返回 -1，代表数组中无相同值。</li>
</ul>
<p>复杂度分析：</p>
<ul>
<li>时间复杂度：O(N)，这里 N 是数组的长度。虽然 for 循环里面套了 while，但是每一个数来到它应该在的位置以后，位置就不会再变化。这里用到的是均摊复杂度分析的方法：如果在某一个位置 while 循环体执行的次数较多，那么一定在后面的几个位置，根本不会执行 while 循环体内的代码，也就是说最坏的情况不会一直出现。也就是说最坏复杂度的情况不会一直出现。</li>
<li>空间复杂度：O(1)。</li>
</ul>
<h4 id="Python语言版本"><a href="#Python语言版本" class="headerlink" title="Python语言版本"></a>Python语言版本</h4><figure class="highlight python"><table><tr><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">findRepeatNumber</span><span class="params">(self, nums: [int])</span> -> int:</span></span><br><span class="line"> i = <span class="number">0</span></span><br><span class="line"> <span class="keyword">while</span> i < len(nums):</span><br><span class="line"> <span class="keyword">if</span> nums[i] == i: //值在它该在的位置上</span><br><span class="line"> i += <span class="number">1</span></span><br><span class="line"> <span class="keyword">continue</span></span><br><span class="line"> <span class="keyword">if</span> nums[nums[i]] == nums[i]: <span class="keyword">return</span> nums[i] //哈希冲突</span><br><span class="line"> nums[nums[i]], nums[i] = nums[i], nums[nums[i]] //交换</span><br><span class="line"> <span class="keyword">return</span> <span class="number">-1</span></span><br></pre></td></tr></table></figure>
]]></content>
<categories>
<category>剑指offer</category>
</categories>
<tags>
<tag>leetcode</tag>
</tags>
</entry>
<entry>
<title>完全背包问题</title>
<url>/sublog.github.io/2020/08/20/%E5%AE%8C%E5%85%A8%E8%83%8C%E5%8C%85%E9%97%AE%E9%A2%98/</url>
<content><![CDATA[<link rel="stylesheet" class="aplayer-secondary-style-marker" href="\sublog.github.io\css\APlayer.min.css"><script src="\sublog.github.io\js\APlayer.min.js" class="aplayer-secondary-script-marker"></script><script class="meting-secondary-script-marker" src="\sublog.github.io\js\Meting.min.js"></script>
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></div>
<h4 id="01背包问题是：每件物品只能选或不选"><a href="#01背包问题是：每件物品只能选或不选" class="headerlink" title="01背包问题是：每件物品只能选或不选"></a>01背包问题是：每件物品只能选或不选</h4><h4 id="完全背包问题是：每件物品有无限件可用"><a href="#完全背包问题是：每件物品有无限件可用" class="headerlink" title="完全背包问题是：每件物品有无限件可用"></a>完全背包问题是：每件物品有无限件可用</h4><p>例题：</p>
<p><img src= "/sublog.github.io/img/loading.gif" data-src="https://i.loli.net/2020/08/20/wsXD8SQ96LdvRcm.png" alt="image-20200820142308586"></p>
<p><img src= "/sublog.github.io/img/loading.gif" data-src="https://i.loli.net/2020/08/20/uGS8ogMtPybqaOR.png" alt="image-20200820142327939"></p>
<h4 id="考虑状态表示："><a href="#考虑状态表示：" class="headerlink" title="考虑状态表示："></a>考虑状态表示：</h4><p>f [ i ] : 表示总体积i情况下，最大价值是多少</p>
<p>result = max{ f [ 0 . . . m ] } //m表示背包容量</p>
<figure class="highlight plain"><table><tr><td class="code"><pre><span class="line">for(int i = 0;i < n;i++)</span><br><span class="line">{</span><br><span class="line"> for(int j = v[i];j <= m;j++)//从小到大枚举</span><br><span class="line"> {</span><br><span class="line"> f[j] = max(f[j],f[j - v[i]] + w[i]);</span><br><span class="line"> }</span><br><span class="line"> //可替换成为</span><br><span class="line"> for(int j = m;j >= v[i];j--) //从大到小枚举</span><br><span class="line"> {</span><br><span class="line"> for(int k = 0;k * v[i] <= j;k++) //枚举选择的物品</span><br><span class="line"> {</span><br><span class="line"> f[j] = max(f[j],f[j - k * v[i]] + k * w[i]);</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure>
<h4 id="数学归纳法："><a href="#数学归纳法：" class="headerlink" title="数学归纳法："></a>数学归纳法：</h4><ol>
<li>假设考虑第 i- 1个物品之后，所有的f [ j ]都是正确的</li>
<li>来证明：考虑完第 i 个物品后，所有的f [ j ] 也都是正确的</li>
</ol>
<p> 对于某个 j 来说，如果最优解包含 k 个v [ i ] ,那么一定有过这个状态</p>
<p> f [ j - k * v [ i ] ]</p>
<p>-> f [ j - k * v [ i ] - v[ i ] ] + w[i] </p>
<p>包含一个v [ i ]</p>
<p>……</p>
<p>f [ j ] f [ j - v [ i ] ] + w[ i ]</p>
<figure class="highlight c++"><table><tr><td class="code"><pre><span class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string"><bits/stdc++.h></span></span></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="built_in">std</span>;</span><br><span class="line"></span><br><span class="line"><span class="keyword">const</span> <span class="keyword">int</span> N = <span class="number">1010</span>;</span><br><span class="line"></span><br><span class="line"><span class="keyword">int</span> n,m;</span><br><span class="line"><span class="keyword">int</span> f[N];</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">int</span> <span class="title">main</span><span class="params">()</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="built_in">cin</span> >> n >> m;</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> i = <span class="number">0</span>;i < n;i++)</span><br><span class="line"> {</span><br><span class="line"> <span class="keyword">int</span> v,w;</span><br><span class="line"> <span class="built_in">cin</span> >> v >> w;</span><br><span class="line"> <span class="keyword">for</span>(<span class="keyword">int</span> j = v;j <= m;j++)</span><br><span class="line"> {</span><br><span class="line"> f[j] = <span class="built_in">max</span>(f[j],f[j - v] + w);</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> <span class="built_in">cout</span> << f[m] << <span class="built_in">endl</span>;</span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br></pre></td></tr></table></figure>
<h4 id="总结："><a href="#总结：" class="headerlink" title="总结："></a>总结：</h4><p>01背包与完全背包第一重循环一样</p>
<p>第二重循环时：</p>
<p>01背包从大到小枚举；</p>
<p>完全背包从小到大枚举；</p>
]]></content>
<categories>
<category>ACwing</category>
</categories>
<tags>
<tag>背包</tag>
</tags>
</entry>
<entry>
<title>花书 --应用数学与机器学习基础</title>
<url>/sublog.github.io/2020/06/25/%E8%8A%B1%E4%B9%A6-%E5%BA%94%E7%94%A8%E6%95%B0%E5%AD%A6%E4%B8%8E%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0%E5%9F%BA%E7%A1%80/</url>
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<sup>top_img</sup>. 莱辛巴赫瀑布，瑞士伯尼尔高地<a href="#reffn_top_img" title="Jump back to footnote [top_img] in the text."> ↩</a>
</blockquote>
<p><del>以下皆为本人花书的笔记</del></p>
<h3 id="标量、向量、矩阵和张量"><a href="#标量、向量、矩阵和张量" class="headerlink" title="标量、向量、矩阵和张量"></a>标量、向量、矩阵和张量</h3><p><font color="#0000dd">标量</font>：一个标量就是一个单独的数。用斜体表示标量。当我们介绍标量时，会明确它们是哪种类型的数。</p>
<p> 例：实数标量：“令<em>s</em>∈R表示一条线的斜率”；自然数标量：”令<em>n</em>∈N表示元素的数目”。</p>
<p><font color="#0000dd">向量</font>：一个向量就是一列数。这些数有序排列。通常我们赋予向量粗体小写变量名称，比如<strong>x</strong>。向量<strong>x</strong>的第一个元素x1……如果每个元素都属于R，并且该向量有n个元素，那么该向量属于实数集R的n次笛卡尔乘积构成的集合，记为Rn。当需要明确表示向量元素是，我们会将元素排列成一个方括号包围的纵列：</p>
<p><img src= "/sublog.github.io/img/loading.gif" data-src="https://i.loli.net/2020/06/25/uSeznLZmQ8RMBci.png" alt="image-20200625165749119.png"></p>
<p>当我们需要索引向量中的一些元素，我们定义一个包含这些元素索引的集合，然后将该集合写在脚标处。</p>
<p> 例：指定x1，x3，x5,定义集合S = {1,3,5}，然后写作<strong>x</strong>~s~</p>
<p> 同时我们用符号_表示集合补集的索引，<strong>x</strong> _~1~表示<strong>x</strong>中除了x1外的元素，而<strong>x</strong> _~S~表示<strong>x</strong>中除了x1,x3,x5外的所有元素构成的向量。</p>
<p>==矩阵==： 二维数组。赋予粗体大写变量名称，<strong>A</strong>。A~1，1~表示左上的元素。我们通过用”:”表示水平坐标，以表示垂直坐标i中的所有元素。<strong>A</strong>~i,:~ 表示 <strong>A</strong> 中垂直坐标 <em>i</em> 上的一横排元素。这也被称为 <strong>A</strong> 的第 <em>i</em> 行（row）。<em>f</em>(<strong>A</strong>)<em>i,j</em> 表示函数 <em>f</em> 作用在 <strong>A</strong> 上输出的矩阵的第 <em>i</em> 行第 <em>j</em> 列元素。</p>
<p>==张量==： 一般地，一个数组中的元素分布在若干维坐标的规则网格中，我们称之为张量。我们使用字体 <strong>A</strong> 来表示张量 “A’’。张量 <strong>A</strong> 中坐标为 (<em>i, j, k</em>) 的元素记作 <em>A</em>~i,j,k~。</p>
<h3 id="矩阵和向量相乘"><a href="#矩阵和向量相乘" class="headerlink" title="矩阵和向量相乘"></a>矩阵和向量相乘</h3><p>==转置==：以主对角线为轴的镜像。我们将矩阵 <strong>A</strong> 的转置表示为 <strong>A</strong>^⊤^，</p>
<p> 定义如下 (<strong>A</strong>⊤<em>)</em>~i,j~ = <em>A<strong>~j,i~</strong>.</em> </p>
<ol>
<li>只要矩阵的形状一样，我们可以把两个矩阵相加。两个矩阵相加是指对应位置的元素相加，比如 <strong>C</strong> = <strong>A</strong> + <strong>B</strong>，其中 <em>C</em>~i,j~ = <em>A</em>~i,j~ + <em>B</em>~i,j~。</li>
<li>标量和矩阵相乘，或是和矩阵相加时，我们只需将其与矩阵的每个元素相乘或相加，比如 <strong>D</strong> = <em>a</em> <em>·</em> <strong>B</strong> + <em>c</em>，其中 <em>D</em>~i,j~= <em>a</em> <em>·</em> <em>B</em>~i,j~ + <em>c</em></li>
<li>在深度学习中，我们也使用一些不那么常规的符号。我们允许矩阵和向量相加，产生另一个矩阵：<strong>C</strong> = <strong>A</strong> + <strong>b</strong>，其中 <em>C</em>~i,j~ = <em>A</em>~i,j~ + <em>b</em>~j~。。这个简写方法使我们无需在加法操作前定义一个将向量 <strong>b</strong> 复制到每一行而生成的矩阵。这种隐式地复制向量 <strong>b</strong> 到很多位置的方式，被称为 广播。</li>
</ol>
<p>矩阵相乘：<img src= "/sublog.github.io/img/loading.gif" data-src="https://i.loli.net/2020/06/25/X5MsvRouW1piVBA.png" alt="image-20200625182340300.png"></p>
]]></content>
<categories>
<category>机器学习</category>
</categories>
<tags>
<tag>线性代数</tag>
</tags>
</entry>
</search>