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  <meta name="description" content="题目大意 花花对计算几何有着浓厚的兴趣。他经常对着平面直角坐标系发呆，思考一些有趣的问题。今天，他想到了一个十分有意思的题目：首先，花花会在$x$轴正半轴和$y$轴正半轴分别挑选$n$个点。随后，他将$x$轴的点与$y$轴的点一一连接，形成$n$条线段，并保证任意两条线段不相交。花花确定这种连接方式有且仅有一种。最后，花花会给出$m$个询问。对于每个询问，将会给定一个点$P(x_p,y_p)$，问">
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<meta property="og:description" content="题目大意 花花对计算几何有着浓厚的兴趣。他经常对着平面直角坐标系发呆，思考一些有趣的问题。今天，他想到了一个十分有意思的题目：首先，花花会在$x$轴正半轴和$y$轴正半轴分别挑选$n$个点。随后，他将$x$轴的点与$y$轴的点一一连接，形成$n$条线段，并保证任意两条线段不相交。花花确定这种连接方式有且仅有一种。最后，花花会给出$m$个询问。对于每个询问，将会给定一个点$P(x_p,y_p)$，问">
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<meta name="twitter:description" content="题目大意 花花对计算几何有着浓厚的兴趣。他经常对着平面直角坐标系发呆，思考一些有趣的问题。今天，他想到了一个十分有意思的题目：首先，花花会在$x$轴正半轴和$y$轴正半轴分别挑选$n$个点。随后，他将$x$轴的点与$y$轴的点一一连接，形成$n$条线段，并保证任意两条线段不相交。花花确定这种连接方式有且仅有一种。最后，花花会给出$m$个询问。对于每个询问，将会给定一个点$P(x_p,y_p)$，问">

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          「bsoj5087」计算几何 - 二分
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        <h2 id="题目大意"><a href="#题目大意" class="headerlink" title="题目大意"></a>题目大意</h2><blockquote>
<p>花花对计算几何有着浓厚的兴趣。他经常对着平面直角坐标系发呆，思考一些有趣的问题。今天，他想到了一个十分有意思的题目：<br>首先，花花会在$x$轴正半轴和$y$轴正半轴分别挑选$n$个点。随后，他将$x$轴的点与$y$轴的点一一连接，形成$n$条线段，并保证任意两条线段不相交。花花确定这种连接方式有且仅有一种。最后，花花会给出$m$个询问。对于每个询问，将会给定一个点$P(x_p,y_p)$，问线段$OP$（$O$为坐标原点）与$n$条线段会产生多少个交点？</p>
</blockquote>
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<hr>
<h2 id="题目分析"><a href="#题目分析" class="headerlink" title="题目分析"></a>题目分析</h2><p>根据题目要求，需要分别对$x,y$排序。<br>排完序后不难发现问题具有单调性，因此可以二分得到一条线段，判断这条线段是否与$OP$相交，最后即可得到交点个数。  </p>
<hr>
<h2 id="代码"><a href="#代码" class="headerlink" title="代码"></a>代码</h2><figure class="highlight cpp"><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><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">#<span class="meta-keyword">include</span><span class="meta-string">&lt;algorithm&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">include</span><span class="meta-string">&lt;iostream&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">include</span><span class="meta-string">&lt;iomanip&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">include</span><span class="meta-string">&lt;cstring&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">include</span><span class="meta-string">&lt;cstdlib&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">include</span><span class="meta-string">&lt;vector&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">include</span><span class="meta-string">&lt;cstdio&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">include</span><span class="meta-string">&lt;cmath&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">include</span><span class="meta-string">&lt;queue&gt;</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="function"><span class="keyword">inline</span> <span class="keyword">const</span> <span class="keyword">int</span> <span class="title">Get_Int</span><span class="params">()</span> </span>&#123;</span><br><span class="line">	<span class="keyword">int</span> num=<span class="number">0</span>,bj=<span class="number">1</span>;</span><br><span class="line">	<span class="keyword">char</span> x=getchar();</span><br><span class="line">	<span class="keyword">while</span>(x&lt;<span class="string">'0'</span>||x&gt;<span class="string">'9'</span>) &#123;</span><br><span class="line">		<span class="keyword">if</span>(x==<span class="string">'-'</span>)bj=<span class="number">-1</span>;</span><br><span class="line">		x=getchar();</span><br><span class="line">	&#125;</span><br><span class="line">	<span class="keyword">while</span>(x&gt;=<span class="string">'0'</span>&amp;&amp;x&lt;=<span class="string">'9'</span>) &#123;</span><br><span class="line">		num=num*<span class="number">10</span>+x-<span class="string">'0'</span>;</span><br><span class="line">		x=getchar();</span><br><span class="line">	&#125;</span><br><span class="line">	<span class="keyword">return</span> num*bj;</span><br><span class="line">&#125;</span><br><span class="line"><span class="keyword">int</span> n,m,a[<span class="number">100005</span>],b[<span class="number">100005</span>];</span><br><span class="line"><span class="function"><span class="keyword">bool</span> <span class="title">Check</span><span class="params">(<span class="keyword">int</span> num,<span class="keyword">int</span> x,<span class="keyword">int</span> y)</span> </span>&#123;</span><br><span class="line">	<span class="keyword">return</span> (<span class="keyword">long</span> <span class="keyword">long</span>)-b[num]*x+(<span class="keyword">long</span> <span class="keyword">long</span>)b[num]*a[num]&lt;=(<span class="keyword">long</span> <span class="keyword">long</span>)y*a[num];</span><br><span class="line">&#125;</span><br><span class="line"><span class="function"><span class="keyword">int</span> <span class="title">main</span><span class="params">()</span> </span>&#123;</span><br><span class="line">	n=Get_Int();</span><br><span class="line">	<span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">1</span>; i&lt;=n; i++)a[i]=Get_Int();</span><br><span class="line">	<span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">1</span>; i&lt;=n; i++)b[i]=Get_Int();</span><br><span class="line">	sort(a+<span class="number">1</span>,a+n+<span class="number">1</span>);</span><br><span class="line">	sort(b+<span class="number">1</span>,b+n+<span class="number">1</span>);</span><br><span class="line">	m=Get_Int();</span><br><span class="line">	<span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">1</span>; i&lt;=m; i++) &#123;</span><br><span class="line">		<span class="keyword">int</span> x=Get_Int(),y=Get_Int();</span><br><span class="line">		<span class="keyword">int</span> Left=<span class="number">1</span>,Right=n;</span><br><span class="line">		<span class="keyword">while</span>(Left&lt;=Right) &#123;</span><br><span class="line">			<span class="keyword">int</span> mid=(Left+Right)&gt;&gt;<span class="number">1</span>;</span><br><span class="line">			<span class="keyword">if</span>(Check(mid,x,y))Left=mid+<span class="number">1</span>;</span><br><span class="line">			<span class="keyword">else</span> Right=mid<span class="number">-1</span>;</span><br><span class="line">		&#125;</span><br><span class="line">		<span class="built_in">printf</span>(<span class="string">"%d\n"</span>,Right);</span><br><span class="line">	&#125;</span><br><span class="line">	<span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
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