264 lines
25 KiB
HTML
264 lines
25 KiB
HTML
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<title>std::ranges::make_heap</title>
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<body class="mediawiki ltr sitedir-ltr ns-0 ns-subject page-cpp_algorithm_ranges_make_heap skin-cppreference2 action-view cpp-navbar">
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<h1 id="firstHeading" class="firstHeading"><span style="font-size:0.7em; line-height:130%">std::ranges::</span>make_heap</h1>
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<div id="contentSub"><span class="subpages">< <a href="cpp.html">cpp</a>‎ | <a href="cpp-algorithm.html">algorithm</a>‎ | <a href="cpp-algorithm-ranges.html">ranges</a></span></div>
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<div>定义于头文件 <code><a href="cpp-header-algorithm.html"><algorithm></a></code></div>
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<td></td>
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<div>调用签名</div>
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<div><span class="mw-geshi cpp source-cpp"><span class="kw1">template</span><span class="sy1"><</span> std<span class="sy4">::</span><span class="me2">random_access_iterator</span> I, std<span class="sy4">::</span><span class="me2">sentinel_for</span><span class="sy1"><</span>I<span class="sy1">></span> S,<br /></span>
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<p> <span class="kw1">class</span> Comp <span class="sy1">=</span> ranges<span class="sy4">::</span><span class="me2">less</span>, <span class="kw1">class</span> Proj <span class="sy1">=</span> std<span class="sy4">::</span><span class="me2">identity</span> <span class="sy1">></span><br />
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requires std<span class="sy4">::</span><span class="me2">sortable</span><span class="sy1"><</span>I, Comp, Proj<span class="sy1">></span><br />
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<span class="kw4">constexpr</span> I<br /></p>
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make_heap<span class="br0">(</span> I first, S last, Comp comp <span class="sy1">=</span> <span class="br0">{</span><span class="br0">}</span>, Proj proj <span class="sy1">=</span> <span class="br0">{</span><span class="br0">}</span> <span class="br0">)</span><span class="sy4">;</span></div>
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<td>(1)</td>
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<td><span class="t-mark-rev t-since-cxx20">(C++20 起)</span></td>
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<div><span class="mw-geshi cpp source-cpp"><span class="kw1">template</span><span class="sy1"><</span> ranges<span class="sy4">::</span><span class="me2">random_access_range</span> R, <span class="kw1">class</span> Comp <span class="sy1">=</span> ranges<span class="sy4">::</span><span class="me2">less</span>,<br /></span>
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<p> <span class="kw1">class</span> Proj <span class="sy1">=</span> std<span class="sy4">::</span><span class="me2">identity</span> <span class="sy1">></span><br />
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requires std<span class="sy4">::</span><span class="me2">sortable</span><span class="sy1"><</span>ranges<span class="sy4">::</span><span class="me2">iterator_t</span><span class="sy1"><</span>R<span class="sy1">></span>, Comp, Proj<span class="sy1">></span><br />
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<span class="kw4">constexpr</span> ranges<span class="sy4">::</span><span class="me2">borrowed_iterator_t</span><span class="sy1"><</span>R<span class="sy1">></span><br /></p>
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make_heap<span class="br0">(</span> R<span class="sy3">&&</span> r, Comp comp <span class="sy1">=</span> <span class="br0">{</span><span class="br0">}</span>, Proj proj <span class="sy1">=</span> <span class="br0">{</span><span class="br0">}</span> <span class="br0">)</span><span class="sy4">;</span></div>
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<td>(2)</td>
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<td><span class="t-mark-rev t-since-cxx20">(C++20 起)</span></td>
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<p>在范围 <code>[first, last)</code> 中构造<a href="https://en.wikipedia.org/wiki/Binary_heap" class="extiw" title="enwiki:Binary heap"><i>最大堆</i></a>。</p>
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<div class="t-li1"><span class="t-li">1)</span> 用二元比较函数 <code>comp</code> 与投影对象 <code>proj</code> 比较元素。</div>
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<div class="t-li1"><span class="t-li">2)</span> 同 <span class="t-v">(1)</span> ，但以 <code>r</code> 为范围，如同以 <span class="t-c"><span class="mw-geshi cpp source-cpp">ranges<span class="sy4">::</span><span class="me2">begin</span><span class="br0">(</span>r<span class="br0">)</span></span></span> 为 <code>first</code> 并以 <span class="t-c"><span class="mw-geshi cpp source-cpp">ranges<span class="sy4">::</span><span class="me2">end</span><span class="br0">(</span>r<span class="br0">)</span></span></span> 为 <code>last</code> 。</div>
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<p>此页面上描述的仿函数实体是 <i>niebloid</i> ，即：</p>
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<ul>
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<li>调用它们中的任何一者时不可指定显式模板实参。</li>
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<li>它们无一对<a href="cpp-language-adl.html">实参依赖查找</a>可见。</li>
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<li>在<a href="cpp-language-unqualified_lookup.html">通常无限定查找</a>寻找函数调用运算符左侧的名称找到它们之一时，它禁止<a href="cpp-language-adl.html">实参依赖查找</a>。</li>
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</ul>
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<p>实际上，它们能以函数对象，或以某些特殊编译器扩展实现。</p>
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<h3><span class="mw-headline" id=".E5.8F.82.E6.95.B0">参数</span></h3>
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<table class="t-par-begin">
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<tr class="t-par">
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<td>first, last</td>
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<td>-</td>
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<td>要作出堆的元素范围</td>
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</tr>
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<tr class="t-par">
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<td>r</td>
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<td>-</td>
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<td>要作出堆的元素范围</td>
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</tr>
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<tr class="t-par">
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<td>pred</td>
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<td>-</td>
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<td>应用到投影后元素的谓词</td>
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</tr>
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<tr class="t-par">
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<td>proj</td>
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<td>-</td>
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<td>应用到元素的投影</td>
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</tr>
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</table>
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<h3><span class="mw-headline" id=".E8.BF.94.E5.9B.9E.E5.80.BC">返回值</span></h3>
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<p>等于 <code>last</code> 的迭代器。</p>
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<h3><span class="mw-headline" id=".E5.A4.8D.E6.9D.82.E5.BA.A6">复杂度</span></h3>
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<p>给定 <span class="t-c"><span class="mw-geshi cpp source-cpp">N <span class="sy1">=</span> ranges<span class="sy4">::</span><span class="me2">distance</span><span class="br0">(</span>first, last<span class="br0">)</span></span></span> ，至多比较 <span class="mjax" style="display:none">\(\scriptsize 3\cdot N\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">3•N</span> 次，投影 <span class="mjax" style="display:none">\(\scriptsize 6\cdot N\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">6•N</span> 次。</p>
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<h3><span class="mw-headline" id=".E6.B3.A8.E8.A7.A3">注解</span></h3>
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<p><i>最大堆</i>是按照比较器 <code>comp</code> 与投影 <code>proj</code> 排列的元素范围 <code>[f, l)</code> ，拥有下列属性：</p>
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<dl>
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<dd>
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<ul>
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<li>令 <span class="t-c"><span class="mw-geshi cpp source-cpp">N <span class="sy1">==</span> l <span class="sy2">-</span> f</span></span> ，对于所有 <code>0 < i < N</code> ， <span class="t-c"><span class="mw-geshi cpp source-cpp">p <span class="sy1">==</span> f<span class="br0">[</span><span class="br0">(</span>i <span class="sy2">-</span> <span class="nu0">1</span><span class="br0">)</span> <span class="sy2">/</span> <span class="nu0">2</span><span class="br0">]</span></span></span> 和 <span class="t-c"><span class="mw-geshi cpp source-cpp">q <span class="sy1">==</span> f<span class="br0">[</span>i<span class="br0">]</span></span></span> ，表达式 <span class="t-c"><span class="mw-geshi cpp source-cpp"><a href="cpp-utility-functional-invoke.html"><span class="kw1058">std::<span class="me2">invoke</span></span></a><span class="br0">(</span>comp, <a href="cpp-utility-functional-invoke.html"><span class="kw1058">std::<span class="me2">invoke</span></span></a><span class="br0">(</span>proj, p<span class="br0">)</span>, <a href="cpp-utility-functional-invoke.html"><span class="kw1058">std::<span class="me2">invoke</span></span></a><span class="br0">(</span>proj, q<span class="br0">)</span><span class="br0">)</span></span></span> 求值为 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw2">false</span></span></span> 。</li>
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<li>能用 <span class="t-c"><span class="mw-geshi cpp source-cpp">ranges<span class="sy4">::</span><span class="me2">push_heap</span><span class="br0">(</span><span class="br0">)</span></span></span> 在 <span class="mjax" style="display:none">\(\scriptsize \mathcal{O}(\log N)\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">𝓞(log N)</span> 时间内添加新元素。</li>
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<li>能用 <span class="t-c"><span class="mw-geshi cpp source-cpp">ranges<span class="sy4">::</span><span class="me2">pop_heap</span><span class="br0">(</span><span class="br0">)</span></span></span> 在 <span class="mjax" style="display:none">\(\scriptsize \mathcal{O}(\log N)\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">𝓞(log N)</span> 时间内移除首元素。</li>
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</ul>
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</dd>
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</dl>
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<h3><span class="mw-headline" id=".E7.A4.BA.E4.BE.8B">示例</span></h3>
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<div class="t-example">
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<div class="t-example-live-link"></div>
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<div dir="ltr" class="mw-geshi" style="text-align: left;">
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<div class="cpp source-cpp">
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<pre class="de1"><span class="co2">#include <algorithm></span>
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<span class="co2">#include <vector></span>
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<span class="co2">#include <cmath></span>
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<span class="co2">#include <functional></span>
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<span class="co2">#include <iostream></span>
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<span class="kw4">void</span> draw_heap<span class="br0">(</span><span class="kw4">auto</span> <span class="kw4">const</span><span class="sy3">&</span> v<span class="br0">)</span><span class="sy4">;</span>
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<span class="kw4">void</span> out<span class="br0">(</span><span class="kw4">const</span> <span class="kw4">auto</span><span class="sy3">&</span> what, <span class="kw4">int</span> n <span class="sy1">=</span> <span class="nu0">1</span><span class="br0">)</span> <span class="br0">{</span> <span class="kw1">while</span> <span class="br0">(</span>n<span class="sy2">--</span> <span class="sy1">></span> <span class="nu0">0</span><span class="br0">)</span> <a href="cpp-io-cout.html"><span class="kw1758">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> what<span class="sy4">;</span> <span class="br0">}</span>
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<span class="kw4">void</span> print<span class="br0">(</span><span class="kw4">auto</span> rem, <span class="kw4">auto</span> <span class="kw4">const</span><span class="sy3">&</span> v<span class="br0">)</span> <span class="br0">{</span>
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out<span class="br0">(</span>rem<span class="br0">)</span><span class="sy4">;</span>
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<span class="kw1">for</span> <span class="br0">(</span><span class="kw4">auto</span> e <span class="sy4">:</span> v<span class="br0">)</span> <span class="br0">{</span> out<span class="br0">(</span>e<span class="br0">)</span>, out<span class="br0">(</span><span class="st0">' '</span><span class="br0">)</span><span class="sy4">;</span> <span class="br0">}</span>
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out<span class="br0">(</span><span class="st0">'<span class="es1">\n</span>'</span><span class="br0">)</span><span class="sy4">;</span>
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<span class="br0">}</span>
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<span class="kw4">int</span> main<span class="br0">(</span><span class="br0">)</span>
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<span class="br0">{</span>
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<a href="cpp-container-vector.html"><span class="kw1269">std::<span class="me2">vector</span></span></a> h <span class="br0">{</span><span class="nu0">1</span>, <span class="nu0">6</span>, <span class="nu0">1</span>, <span class="nu0">8</span>, <span class="nu0">0</span>, <span class="nu0">3</span>, <span class="nu0">3</span>, <span class="nu0">9</span>, <span class="nu0">8</span>, <span class="nu0">8</span>, <span class="nu0">7</span>, <span class="nu0">4</span>, <span class="nu0">9</span>, <span class="nu0">8</span>, <span class="nu0">9</span><span class="br0">}</span><span class="sy4">;</span>
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print<span class="br0">(</span><span class="st0">"source: "</span>, h<span class="br0">)</span><span class="sy4">;</span>
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std<span class="sy4">::</span><span class="me2">ranges</span><span class="sy4">::</span><span class="me2">make_heap</span><span class="br0">(</span>h<span class="br0">)</span><span class="sy4">;</span>
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print<span class="br0">(</span><span class="st0">"<span class="es1">\n</span>"</span> <span class="st0">"max-heap: "</span>, h<span class="br0">)</span><span class="sy4">;</span>
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draw_heap<span class="br0">(</span>h<span class="br0">)</span><span class="sy4">;</span>
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std<span class="sy4">::</span><span class="me2">ranges</span><span class="sy4">::</span><span class="me2">make_heap</span><span class="br0">(</span>h, <a href="cpp-utility-functional-greater.html"><span class="kw1037">std::<span class="me2">greater</span></span></a><span class="br0">{</span><span class="br0">}</span><span class="br0">)</span><span class="sy4">;</span>
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print<span class="br0">(</span><span class="st0">"<span class="es1">\n</span>"</span> <span class="st0">"min-heap: "</span>, h<span class="br0">)</span><span class="sy4">;</span>
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draw_heap<span class="br0">(</span>h<span class="br0">)</span><span class="sy4">;</span>
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<span class="br0">}</span>
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<span class="kw4">void</span> draw_heap<span class="br0">(</span><span class="kw4">auto</span> <span class="kw4">const</span><span class="sy3">&</span> v<span class="br0">)</span>
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<span class="br0">{</span>
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<span class="kw4">auto</span> bails <span class="sy1">=</span> <span class="br0">[</span><span class="br0">]</span><span class="br0">(</span><span class="kw4">int</span> n, <span class="kw4">int</span> w<span class="br0">)</span> <span class="br0">{</span>
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<span class="kw4">auto</span> b <span class="sy1">=</span> <span class="br0">[</span><span class="br0">]</span><span class="br0">(</span><span class="kw4">int</span> w<span class="br0">)</span> <span class="br0">{</span> out<span class="br0">(</span><span class="st0">"┌"</span><span class="br0">)</span>, out<span class="br0">(</span><span class="st0">"─"</span>, w<span class="br0">)</span>, out<span class="br0">(</span><span class="st0">"┴"</span><span class="br0">)</span>, out<span class="br0">(</span><span class="st0">"─"</span>, w<span class="br0">)</span>, out<span class="br0">(</span><span class="st0">"┐"</span><span class="br0">)</span><span class="sy4">;</span> <span class="br0">}</span><span class="sy4">;</span>
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<span class="kw1">if</span> <span class="br0">(</span><span class="sy3">!</span><span class="br0">(</span>n <span class="sy2">/</span><span class="sy1">=</span> <span class="nu0">2</span><span class="br0">)</span><span class="br0">)</span> <span class="kw1">return</span><span class="sy4">;</span>
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<span class="kw1">for</span> <span class="br0">(</span>out<span class="br0">(</span><span class="st0">' '</span>, w<span class="br0">)</span><span class="sy4">;</span> n<span class="sy2">--</span> <span class="sy1">></span> <span class="nu0">0</span><span class="sy4">;</span> <span class="br0">)</span> b<span class="br0">(</span>w<span class="br0">)</span>, out<span class="br0">(</span><span class="st0">' '</span>, w <span class="sy2">+</span> w <span class="sy2">+</span> <span class="nu0">1</span><span class="br0">)</span><span class="sy4">;</span>
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out<span class="br0">(</span><span class="st0">'<span class="es1">\n</span>'</span><span class="br0">)</span><span class="sy4">;</span>
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<span class="br0">}</span><span class="sy4">;</span>
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<span class="kw4">auto</span> data <span class="sy1">=</span> <span class="br0">[</span><span class="br0">]</span><span class="br0">(</span><span class="kw4">int</span> n, <span class="kw4">int</span> w, <span class="kw4">auto</span><span class="sy3">&</span> first, <span class="kw4">auto</span> last<span class="br0">)</span> <span class="br0">{</span>
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<span class="kw1">for</span><span class="br0">(</span>out<span class="br0">(</span><span class="st0">' '</span>, w<span class="br0">)</span><span class="sy4">;</span> n<span class="sy2">--</span> <span class="sy1">></span> <span class="nu0">0</span> <span class="sy3">&&</span> first <span class="sy3">!</span><span class="sy1">=</span> last<span class="sy4">;</span> <span class="sy2">++</span>first<span class="br0">)</span>
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out<span class="br0">(</span><span class="sy2">*</span>first<span class="br0">)</span>, out<span class="br0">(</span><span class="st0">' '</span>, w <span class="sy2">+</span> w <span class="sy2">+</span> <span class="nu0">1</span><span class="br0">)</span><span class="sy4">;</span>
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out<span class="br0">(</span><span class="st0">'<span class="es1">\n</span>'</span><span class="br0">)</span><span class="sy4">;</span>
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<span class="br0">}</span><span class="sy4">;</span>
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<span class="kw4">auto</span> tier <span class="sy1">=</span> <span class="br0">[</span><span class="sy3">&</span><span class="br0">]</span><span class="br0">(</span><span class="kw4">int</span> t, <span class="kw4">int</span> m, <span class="kw4">auto</span><span class="sy3">&</span> first, <span class="kw4">auto</span> last<span class="br0">)</span> <span class="br0">{</span>
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<span class="kw4">const</span> <span class="kw4">int</span> n <span class="br0">{</span><span class="nu0">1</span> <span class="sy1"><<</span> t<span class="br0">}</span><span class="sy4">;</span>
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<span class="kw4">const</span> <span class="kw4">int</span> w <span class="br0">{</span><span class="br0">(</span><span class="nu0">1</span> <span class="sy1"><<</span> <span class="br0">(</span>m <span class="sy2">-</span> t <span class="sy2">-</span> <span class="nu0">1</span><span class="br0">)</span><span class="br0">)</span> <span class="sy2">-</span> <span class="nu0">1</span><span class="br0">}</span><span class="sy4">;</span>
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bails<span class="br0">(</span>n, w<span class="br0">)</span>, data<span class="br0">(</span>n, w, first, last<span class="br0">)</span><span class="sy4">;</span>
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<span class="br0">}</span><span class="sy4">;</span>
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<span class="kw4">const</span> <span class="kw4">int</span> m <span class="br0">{</span><span class="kw1">static_cast</span><span class="sy1"><</span><span class="kw4">int</span><span class="sy1">></span><span class="br0">(</span><a href="cpp-numeric-math-ceil.html"><span class="kw1350">std::<span class="me2">ceil</span></span></a><span class="br0">(</span>std<span class="sy4">::</span><span class="me2">log2</span><span class="br0">(</span><span class="nu0">1</span> <span class="sy2">+</span> v.<span class="me1">size</span><span class="br0">(</span><span class="br0">)</span><span class="br0">)</span><span class="br0">)</span><span class="br0">)</span><span class="br0">}</span><span class="sy4">;</span>
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<span class="kw4">auto</span> first <span class="br0">{</span>v.<span class="me1">cbegin</span><span class="br0">(</span><span class="br0">)</span><span class="br0">}</span><span class="sy4">;</span>
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<span class="kw1">for</span> <span class="br0">(</span><span class="kw4">int</span> i<span class="br0">{</span><span class="br0">}</span><span class="sy4">;</span> i <span class="sy3">!</span><span class="sy1">=</span> m<span class="sy4">;</span> <span class="sy2">++</span>i<span class="br0">)</span> <span class="br0">{</span> tier<span class="br0">(</span>i, m, first, v.<span class="me1">cend</span><span class="br0">(</span><span class="br0">)</span><span class="br0">)</span><span class="sy4">;</span> <span class="br0">}</span>
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<span class="br0">}</span></pre></div>
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</div>
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<p>输出：</p>
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<div dir="ltr" class="mw-geshi" style="text-align: left;">
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<div class="text source-text">
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<pre class="de1">
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source: 1 6 1 8 0 3 3 9 8 8 7 4 9 8 9
|
|
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max-heap: 9 8 9 8 8 4 9 6 1 0 7 1 3 8 3
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9
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┌───┴───┐
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8 9
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|
┌─┴─┐ ┌─┴─┐
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8 8 4 9
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|
┌┴┐ ┌┴┐ ┌┴┐ ┌┴┐
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6 1 0 7 1 3 8 3
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|
|
|
min-heap: 0 1 1 8 6 3 3 9 8 8 7 4 9 8 9
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|
0
|
|
┌───┴───┐
|
|
1 1
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|
┌─┴─┐ ┌─┴─┐
|
|
8 6 3 3
|
|
┌┴┐ ┌┴┐ ┌┴┐ ┌┴┐
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|
9 8 8 7 4 9 8 9</pre></div>
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</div>
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</div>
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<h3><span class="mw-headline" id=".E5.8F.82.E9.98.85">参阅</span></h3>
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<table class="t-dsc-begin">
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-algorithm-ranges-is_heap.html"><span class="t-lines"><span>ranges::is_heap</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div>
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</div>
|
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</td>
|
|
<td>检查给定范围是否为最大堆<br />
|
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<span class="t-mark">(niebloid)</span></td>
|
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</tr>
|
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<tr class="t-dsc">
|
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<td>
|
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<div class="t-dsc-member-div">
|
|
<div><a href="cpp-algorithm-ranges-is_heap_until.html"><span class="t-lines"><span>ranges::is_heap_until</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div>
|
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</div>
|
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</td>
|
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<td>寻找能成为最大堆的最大子范围<br />
|
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<span class="t-mark">(niebloid)</span></td>
|
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</tr>
|
|
<tr class="t-dsc">
|
|
<td>
|
|
<div class="t-dsc-member-div">
|
|
<div><a href="cpp-algorithm-ranges-push_heap.html"><span class="t-lines"><span>ranges::push_heap</span></span></a></div>
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|
<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div>
|
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</div>
|
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</td>
|
|
<td>将一个元素加入到一个最大堆<br />
|
|
<span class="t-mark">(niebloid)</span></td>
|
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</tr>
|
|
<tr class="t-dsc">
|
|
<td>
|
|
<div class="t-dsc-member-div">
|
|
<div><a href="cpp-algorithm-ranges-pop_heap.html"><span class="t-lines"><span>ranges::pop_heap</span></span></a></div>
|
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div>
|
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</div>
|
|
</td>
|
|
<td>从最大堆中移除最大元素<br />
|
|
<span class="t-mark">(niebloid)</span></td>
|
|
</tr>
|
|
<tr class="t-dsc">
|
|
<td>
|
|
<div class="t-dsc-member-div">
|
|
<div><a href="cpp-algorithm-ranges-sort_heap.html"><span class="t-lines"><span>ranges::sort_heap</span></span></a></div>
|
|
<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div>
|
|
</div>
|
|
</td>
|
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<td>将一个最大堆变成一个按升序排序的元素范围<br />
|
|
<span class="t-mark">(niebloid)</span></td>
|
|
</tr>
|
|
<tr class="t-dsc">
|
|
<td>
|
|
<div class="t-dsc-member-div">
|
|
<div><a href="cpp-algorithm-make_heap.html"><span class="t-lines"><span>make_heap</span></span></a></div>
|
|
</div>
|
|
</td>
|
|
<td>从一个元素范围创建出一个最大堆<br />
|
|
<span class="t-mark">(函数模板)</span></td>
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</tr>
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</table>
|
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</div>
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<div class="visualClear"></div>
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</div>
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</div>
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</div>
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</body>
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</html>
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