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<article>
<h2>D堆的C语言实现</h2>
<div class="toc">
<ul>
<li><a href="#_1">添加元素图解</a></li>
<li><a href="#_2">删除堆顶元素图解</a></li>
<li><a href="#_3">完整源码</a></li>
<li><a href="#_4">测试程序的运行结果</a></li>
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<p>D堆是二叉堆的简单推广，跟二叉堆的区别是所有的节点都有d个儿子，代码也跟二叉堆的相似。下图表示一个D=3的最小D堆。</p>
<p><img alt="图" src="/images/d_heap/heap.png"/></p>
<p>D堆插入操作的时间改进为O(log(d,N)),然面删除操作要花费较大时间，一般需要O(d*log(d,N))。如果D不是2的幂，也不能通过二进制移位来实现乘法和除法，这样也大大增加运行时间。
大部分时候总是使用二叉堆，但D堆也在一些情况下使用。比如，插入操作多删除操作多很多时，或是<strong><em>优先队列太大不能完全装入内存</em></strong>时。</p>
<p>通常D堆也跟二叉堆一样以数组存储，层为 log(d,n)，以下的代码来定义D堆结构。</p>
<div class="highlight"><pre><span></span><span class="k">typedef</span> <span class="k">struct</span> <span class="n">d_heap_s</span><span class="o">*</span> <span class="n">d_heap_pt</span><span class="p">;</span>
<span class="k">typedef</span> <span class="k">struct</span> <span class="n">d_heap_s</span> <span class="p">{</span>
<span class="kt">int</span> <span class="n">size</span><span class="p">;</span>
<span class="kt">int</span> <span class="n">degree</span><span class="p">;</span>
<span class="kt">int</span> <span class="n">current</span><span class="p">;</span>
<span class="n">Item</span> <span class="o">*</span><span class="n">data</span><span class="p">;</span>
<span class="p">}</span> <span class="n">d_heap_t</span><span class="p">;</span>
</pre></div>
<p>当以数组存储时，D堆的父子节点下标存在如下关系。</p>
<ul>
<li>索引为i的孩子的索引是 (i*d + j)，其中j = 1, 2, ..., d;</li>
<li>索引为i的父结点的索引是 (i - 1) / d;</li>
</ul>
<h3 id="_1"><strong> 添加元素图解 </strong></h3>
<p>D堆的元素插入步骤跟二叉树相同，在堆中添加元素时需要执行向上堆化操作，假设在最小堆中添加15，需要执行以下步骤。</p>
<p><img alt="图一" src="/images/d_heap/push1.png"/></p>
<p><img alt="图二" src="/images/d_heap/push2.png"/></p>
<p><img alt="图三" src="/images/d_heap/push3.png"/></p>
<p>代码实现如下：</p>
<div class="highlight"><pre><span></span><span class="cm">/* </span>
<span class="cm"> * Name: fixup</span>
<span class="cm"> * Description: 向上堆化</span>
<span class="cm"> * </span>
<span class="cm"> */</span>
<span class="k">static</span> <span class="kt">void</span>
<span class="nf">fixup</span><span class="p">(</span><span class="n">d_heap_pt</span> <span class="n">heap</span><span class="p">,</span> <span class="kt">int</span> <span class="n">k</span><span class="p">)</span>
<span class="p">{</span>
<span class="kt">int</span> <span class="n">degree</span> <span class="o">=</span> <span class="n">heap</span><span class="o">-></span><span class="n">degree</span><span class="p">;</span>
<span class="k">while</span> <span class="p">(</span><span class="n">k</span><span class="o">></span><span class="mi">0</span> <span class="o">&&</span> <span class="n">item_cmp</span><span class="p">(</span><span class="n">heap</span><span class="o">-></span><span class="n">data</span><span class="p">[(</span><span class="n">k</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="n">degree</span><span class="p">],</span><span class="n">heap</span><span class="o">-></span><span class="n">data</span><span class="p">[</span><span class="n">k</span><span class="p">]))</span> <span class="p">{</span>
<span class="n">swap</span><span class="p">(</span><span class="n">heap</span><span class="o">-></span><span class="n">data</span><span class="p">,</span> <span class="n">k</span><span class="p">,</span> <span class="p">(</span><span class="n">k</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="n">degree</span><span class="p">);</span>
<span class="n">k</span> <span class="o">=</span> <span class="p">(</span><span class="n">k</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="n">degree</span><span class="p">;</span>
<span class="p">}</span>
<span class="p">}</span>
<span class="kt">int</span>
<span class="nf">d_heap_push</span><span class="p">(</span><span class="n">d_heap_pt</span> <span class="n">heap</span><span class="p">,</span> <span class="n">Item</span> <span class="n">element</span><span class="p">)</span>
<span class="p">{</span>
<span class="k">if</span> <span class="p">(</span><span class="n">heap</span> <span class="o">==</span> <span class="nb">NULL</span><span class="p">)</span> <span class="p">{</span>
<span class="k">return</span> <span class="mi">0</span><span class="p">;</span>
<span class="p">}</span>
<span class="k">if</span> <span class="p">(</span><span class="n">heap</span><span class="o">-></span><span class="n">current</span> <span class="o">==</span> <span class="n">heap</span><span class="o">-></span><span class="n">size</span><span class="p">)</span> <span class="p">{</span>
<span class="k">return</span> <span class="mi">0</span><span class="p">;</span>
<span class="p">}</span>
<span class="n">heap</span><span class="o">-></span><span class="n">data</span><span class="p">[</span><span class="n">heap</span><span class="o">-></span><span class="n">current</span><span class="p">]</span> <span class="o">=</span> <span class="n">element</span><span class="p">;</span>
<span class="n">fixup</span><span class="p">(</span><span class="n">heap</span><span class="p">,</span> <span class="n">heap</span><span class="o">-></span><span class="n">current</span><span class="o">++</span><span class="p">);</span>
<span class="k">return</span> <span class="mi">1</span><span class="p">;</span>
<span class="p">}</span>
</pre></div>
<h3 id="_2"><strong> 删除堆顶元素图解 </strong></h3>
<p>D堆的元素插入步骤也跟二叉树相同，在堆中移除堆顶元素时需要执行向下堆化操作，假设在最小堆中移除堆顶完素，需要执行以下步骤。</p>
<p><img alt="图一" src="/images/d_heap/pop1.png"/></p>
<p><img alt="图二" src="/images/d_heap/pop2.png"/></p>
<p><img alt="图三" src="/images/d_heap/pop3.png"/></p>
<p><img alt="图四" src="/images/d_heap/pop4.png"/></p>
<p>代码实现如下：</p>
<div class="highlight"><pre><span></span><span class="cm">/* </span>
<span class="cm"> * Name: fixdown</span>
<span class="cm"> * Description: 向下堆化</span>
<span class="cm"> * </span>
<span class="cm"> */</span>
<span class="k">static</span> <span class="kt">void</span>
<span class="nf">fixdown</span><span class="p">(</span><span class="n">d_heap_pt</span> <span class="n">heap</span><span class="p">,</span> <span class="kt">int</span> <span class="n">k</span><span class="p">,</span> <span class="kt">int</span> <span class="n">end</span><span class="p">)</span>
<span class="p">{</span>
<span class="kt">int</span> <span class="n">temp</span><span class="p">,</span> <span class="n">tail</span><span class="p">,</span> <span class="n">i</span><span class="p">;</span>
<span class="kt">int</span> <span class="n">degree</span> <span class="o">=</span> <span class="n">heap</span><span class="o">-></span><span class="n">degree</span><span class="p">;</span>
<span class="k">while</span> <span class="p">(</span><span class="n">k</span><span class="o">*</span><span class="n">degree</span> <span class="o">+</span> <span class="mi">1</span> <span class="o"><=</span> <span class="n">end</span><span class="p">)</span> <span class="p">{</span>
<span class="n">tail</span> <span class="o">=</span> <span class="n">k</span><span class="o">*</span><span class="n">degree</span> <span class="o">+</span> <span class="n">degree</span><span class="p">;</span>
<span class="n">tail</span> <span class="o">=</span> <span class="n">tail</span> <span class="o"><</span> <span class="n">end</span> <span class="o">?</span> <span class="nl">tail</span> <span class="p">:</span> <span class="n">end</span><span class="p">;</span>
<span class="k">for</span> <span class="p">(</span><span class="n">i</span> <span class="o">=</span> <span class="n">k</span><span class="o">*</span><span class="n">degree</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">temp</span> <span class="o">=</span> <span class="n">i</span><span class="p">;</span> <span class="n">i</span> <span class="o"><</span> <span class="n">tail</span><span class="p">;</span> <span class="n">i</span><span class="o">++</span><span class="p">)</span> <span class="p">{</span>
<span class="k">if</span> <span class="p">(</span><span class="n">item_cmp</span><span class="p">(</span><span class="n">heap</span><span class="o">-></span><span class="n">data</span><span class="p">[</span><span class="n">temp</span><span class="p">],</span> <span class="n">heap</span><span class="o">-></span><span class="n">data</span><span class="p">[</span><span class="n">i</span><span class="p">]))</span> <span class="p">{</span>
<span class="n">temp</span> <span class="o">=</span> <span class="n">i</span><span class="p">;</span>
<span class="p">}</span>
<span class="p">}</span>
<span class="k">if</span> <span class="p">(</span><span class="o">!</span><span class="n">item_cmp</span><span class="p">(</span><span class="n">heap</span><span class="o">-></span><span class="n">data</span><span class="p">[</span><span class="n">k</span><span class="p">],</span> <span class="n">heap</span><span class="o">-></span><span class="n">data</span><span class="p">[</span><span class="n">temp</span><span class="p">]))</span> <span class="p">{</span>
<span class="k">break</span><span class="p">;</span>
<span class="p">}</span>
<span class="n">swap</span><span class="p">(</span><span class="n">heap</span><span class="o">-></span><span class="n">data</span><span class="p">,</span> <span class="n">k</span><span class="p">,</span> <span class="n">temp</span><span class="p">);</span>
<span class="n">k</span> <span class="o">=</span> <span class="n">temp</span><span class="p">;</span>
<span class="p">}</span>
<span class="p">}</span>
<span class="n">Item</span>
<span class="nf">d_heap_pop</span><span class="p">(</span><span class="n">d_heap_pt</span> <span class="n">heap</span><span class="p">)</span>
<span class="p">{</span>
<span class="n">swap</span><span class="p">(</span><span class="n">heap</span><span class="o">-></span><span class="n">data</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">heap</span><span class="o">-></span><span class="n">current</span> <span class="o">-</span> <span class="mi">1</span><span class="p">);</span>
<span class="n">fixdown</span><span class="p">(</span><span class="n">heap</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">heap</span><span class="o">-></span><span class="n">current</span> <span class="o">-</span> <span class="mi">2</span><span class="p">);</span>
<span class="k">return</span> <span class="n">heap</span><span class="o">-></span><span class="n">data</span><span class="p">[</span><span class="o">--</span><span class="n">heap</span><span class="o">-></span><span class="n">current</span><span class="p">];</span>
<span class="p">}</span>
</pre></div>
<h3 id="_3"><strong> 完整源码 </strong></h3>
<div class="highlight"><pre><span></span><span class="cm">/* d_heap.h */</span>
<span class="cp">#ifndef D_HEAP_H</span>
<span class="cp">#define D_HEAP_H</span>
<span class="k">typedef</span> <span class="kt">int</span> <span class="n">Item</span><span class="p">;</span>
<span class="k">typedef</span> <span class="k">struct</span> <span class="n">d_heap_s</span><span class="o">*</span> <span class="n">d_heap_pt</span><span class="p">;</span>
<span class="k">typedef</span> <span class="k">struct</span> <span class="n">d_heap_s</span> <span class="p">{</span>
<span class="kt">int</span> <span class="n">size</span><span class="p">;</span>
<span class="kt">int</span> <span class="n">degree</span><span class="p">;</span>
<span class="kt">int</span> <span class="n">current</span><span class="p">;</span>
<span class="n">Item</span> <span class="o">*</span><span class="n">data</span><span class="p">;</span>
<span class="p">}</span> <span class="n">d_heap_t</span><span class="p">;</span>
<span class="n">d_heap_pt</span> <span class="nf">d_heap_init</span><span class="p">(</span><span class="kt">int</span> <span class="n">size</span><span class="p">,</span> <span class="kt">int</span> <span class="n">degree</span><span class="p">);</span>
<span class="kt">void</span> <span class="nf">d_heap_free</span><span class="p">(</span><span class="n">d_heap_pt</span> <span class="n">heap</span><span class="p">);</span>
<span class="kt">void</span> <span class="nf">d_heap_print</span><span class="p">(</span><span class="n">d_heap_pt</span> <span class="n">heap</span><span class="p">);</span>
<span class="kt">int</span> <span class="nf">d_heap_push</span><span class="p">(</span><span class="n">d_heap_pt</span> <span class="n">heap</span><span class="p">,</span> <span class="n">Item</span> <span class="n">element</span><span class="p">);</span>
<span class="n">Item</span> <span class="nf">d_heap_pop</span><span class="p">(</span><span class="n">d_heap_pt</span> <span class="n">heap</span><span class="p">);</span>
<span class="n">Item</span> <span class="nf">d_heap_top</span><span class="p">(</span><span class="n">d_heap_pt</span> <span class="n">heap</span><span class="p">);</span>
<span class="kt">int</span> <span class="nf">d_heap_empty</span><span class="p">(</span><span class="n">d_heap_pt</span> <span class="n">heap</span><span class="p">);</span>
<span class="cp">#endif</span>
</pre></div>
<p>d_heap.h</p>
<div class="highlight"><pre><span></span><span class="cm">/* d_heap.c */</span>
<span class="cm">/*</span>
<span class="cm"> * =====================================================================================</span>
<span class="cm"> *</span>
<span class="cm"> * Filename: d_heap.c</span>
<span class="cm"> *</span>
<span class="cm"> * Description: D堆实现</span>
<span class="cm"> *</span>
<span class="cm"> * Version: 1.0</span>
<span class="cm"> * Created: 2016-09-23 22:00</span>
<span class="cm"> * Revision: none</span>
<span class="cm"> * Compiler: gcc</span>
<span class="cm"> *</span>
<span class="cm"> * Author: simon</span>
<span class="cm"> *</span>
<span class="cm"> * =====================================================================================</span>
<span class="cm"> */</span>
<span class="cp">#include</span> <span class="cpf"><stdio.h></span><span class="cp"></span>
<span class="cp">#include</span> <span class="cpf"><stdlib.h></span><span class="cp"></span>
<span class="cp">#include</span> <span class="cpf">"d_heap.h"</span><span class="cp"></span>
<span class="k">static</span> <span class="kt">void</span>
<span class="nf">swap</span><span class="p">(</span><span class="n">Item</span> <span class="o">*</span><span class="n">data</span><span class="p">,</span> <span class="kt">int</span> <span class="n">a</span><span class="p">,</span> <span class="kt">int</span> <span class="n">b</span><span class="p">)</span>
<span class="p">{</span>
<span class="n">Item</span> <span class="n">c</span><span class="p">;</span>
<span class="n">c</span> <span class="o">=</span> <span class="n">data</span><span class="p">[</span><span class="n">a</span><span class="p">];</span>
<span class="n">data</span><span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="o">=</span> <span class="n">data</span><span class="p">[</span><span class="n">b</span><span class="p">];</span>
<span class="n">data</span><span class="p">[</span><span class="n">b</span><span class="p">]</span> <span class="o">=</span> <span class="n">c</span><span class="p">;</span>
<span class="p">}</span>
<span class="cm">/* </span>
<span class="cm"> * 最小堆 ((a) > (b))</span>
<span class="cm"> * 最大堆 ({a} < (b))</span>
<span class="cm"> * </span>
<span class="cm"> */</span>
<span class="cp">#define item_cmp(a, b) ((a) > (b)) </span><span class="cm">/* 最小堆 */</span><span class="cp"></span>
<span class="cm">/* </span>
<span class="cm"> * Name: fixup</span>
<span class="cm"> * Description: 向上堆化</span>
<span class="cm"> * </span>
<span class="cm"> */</span>
<span class="k">static</span> <span class="kt">void</span>
<span class="nf">fixup</span><span class="p">(</span><span class="n">d_heap_pt</span> <span class="n">heap</span><span class="p">,</span> <span class="kt">int</span> <span class="n">k</span><span class="p">)</span>
<span class="p">{</span>
<span class="kt">int</span> <span class="n">degree</span> <span class="o">=</span> <span class="n">heap</span><span class="o">-></span><span class="n">degree</span><span class="p">;</span>
<span class="k">while</span> <span class="p">(</span><span class="n">k</span><span class="o">></span><span class="mi">0</span> <span class="o">&&</span> <span class="n">item_cmp</span><span class="p">(</span><span class="n">heap</span><span class="o">-></span><span class="n">data</span><span class="p">[(</span><span class="n">k</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="n">degree</span><span class="p">],</span><span class="n">heap</span><span class="o">-></span><span class="n">data</span><span class="p">[</span><span class="n">k</span><span class="p">]))</span> <span class="p">{</span>
<span class="n">swap</span><span class="p">(</span><span class="n">heap</span><span class="o">-></span><span class="n">data</span><span class="p">,</span> <span class="n">k</span><span class="p">,</span> <span class="p">(</span><span class="n">k</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="n">degree</span><span class="p">);</span>
<span class="n">k</span> <span class="o">=</span> <span class="p">(</span><span class="n">k</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="n">degree</span><span class="p">;</span>
<span class="p">}</span>
<span class="p">}</span>
<span class="cm">/* </span>
<span class="cm"> * Name: fixdown</span>
<span class="cm"> * Description: 向下堆化</span>
<span class="cm"> * </span>
<span class="cm"> */</span>
<span class="k">static</span> <span class="kt">void</span>
<span class="nf">fixdown</span><span class="p">(</span><span class="n">d_heap_pt</span> <span class="n">heap</span><span class="p">,</span> <span class="kt">int</span> <span class="n">k</span><span class="p">,</span> <span class="kt">int</span> <span class="n">end</span><span class="p">)</span>
<span class="p">{</span>
<span class="kt">int</span> <span class="n">temp</span><span class="p">,</span> <span class="n">tail</span><span class="p">,</span> <span class="n">i</span><span class="p">;</span>
<span class="kt">int</span> <span class="n">degree</span> <span class="o">=</span> <span class="n">heap</span><span class="o">-></span><span class="n">degree</span><span class="p">;</span>
<span class="k">while</span> <span class="p">(</span><span class="n">k</span><span class="o">*</span><span class="n">degree</span> <span class="o">+</span> <span class="mi">1</span> <span class="o"><=</span> <span class="n">end</span><span class="p">)</span> <span class="p">{</span>
<span class="n">tail</span> <span class="o">=</span> <span class="n">k</span><span class="o">*</span><span class="n">degree</span> <span class="o">+</span> <span class="n">degree</span><span class="p">;</span>
<span class="n">tail</span> <span class="o">=</span> <span class="n">tail</span> <span class="o"><</span> <span class="n">end</span> <span class="o">?</span> <span class="nl">tail</span> <span class="p">:</span> <span class="n">end</span><span class="p">;</span>
<span class="k">for</span> <span class="p">(</span><span class="n">i</span> <span class="o">=</span> <span class="n">k</span><span class="o">*</span><span class="n">degree</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">temp</span> <span class="o">=</span> <span class="n">i</span><span class="p">;</span> <span class="n">i</span> <span class="o"><</span> <span class="n">tail</span><span class="p">;</span> <span class="n">i</span><span class="o">++</span><span class="p">)</span> <span class="p">{</span>
<span class="k">if</span> <span class="p">(</span><span class="n">item_cmp</span><span class="p">(</span><span class="n">heap</span><span class="o">-></span><span class="n">data</span><span class="p">[</span><span class="n">temp</span><span class="p">],</span> <span class="n">heap</span><span class="o">-></span><span class="n">data</span><span class="p">[</span><span class="n">i</span><span class="p">]))</span> <span class="p">{</span>
<span class="n">temp</span> <span class="o">=</span> <span class="n">i</span><span class="p">;</span>
<span class="p">}</span>
<span class="p">}</span>
<span class="k">if</span> <span class="p">(</span><span class="o">!</span><span class="n">item_cmp</span><span class="p">(</span><span class="n">heap</span><span class="o">-></span><span class="n">data</span><span class="p">[</span><span class="n">k</span><span class="p">],</span> <span class="n">heap</span><span class="o">-></span><span class="n">data</span><span class="p">[</span><span class="n">temp</span><span class="p">]))</span> <span class="p">{</span>
<span class="k">break</span><span class="p">;</span>
<span class="p">}</span>
<span class="n">swap</span><span class="p">(</span><span class="n">heap</span><span class="o">-></span><span class="n">data</span><span class="p">,</span> <span class="n">k</span><span class="p">,</span> <span class="n">temp</span><span class="p">);</span>
<span class="n">k</span> <span class="o">=</span> <span class="n">temp</span><span class="p">;</span>
<span class="p">}</span>
<span class="p">}</span>
<span class="n">d_heap_pt</span>
<span class="nf">d_heap_init</span><span class="p">(</span><span class="kt">int</span> <span class="n">size</span><span class="p">,</span> <span class="kt">int</span> <span class="n">degree</span><span class="p">)</span>
<span class="p">{</span>
<span class="k">if</span> <span class="p">(</span><span class="n">size</span><span class="o"><=</span><span class="mi">0</span><span class="p">)</span> <span class="p">{</span>
<span class="k">return</span> <span class="nb">NULL</span><span class="p">;</span>
<span class="p">}</span>
<span class="n">d_heap_pt</span> <span class="n">heap_pt</span> <span class="o">=</span> <span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">d_heap_t</span><span class="p">));</span>
<span class="n">heap_pt</span><span class="o">-></span><span class="n">data</span> <span class="o">=</span> <span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">Item</span><span class="p">)</span><span class="o">*</span><span class="n">size</span><span class="p">);</span>
<span class="n">heap_pt</span><span class="o">-></span><span class="n">size</span> <span class="o">=</span> <span class="n">size</span><span class="p">;</span>
<span class="n">heap_pt</span><span class="o">-></span><span class="n">degree</span> <span class="o">=</span> <span class="n">degree</span><span class="p">;</span>
<span class="n">heap_pt</span><span class="o">-></span><span class="n">current</span> <span class="o">=</span> <span class="mi">0</span><span class="p">;</span>
<span class="k">return</span> <span class="n">heap_pt</span><span class="p">;</span>
<span class="p">}</span>
<span class="kt">void</span>
<span class="nf">d_heap_free</span><span class="p">(</span><span class="n">d_heap_pt</span> <span class="n">heap</span><span class="p">)</span>
<span class="p">{</span>
<span class="k">if</span> <span class="p">(</span><span class="n">heap</span> <span class="o">==</span> <span class="nb">NULL</span><span class="p">)</span> <span class="p">{</span>
<span class="k">return</span><span class="p">;</span>
<span class="p">}</span>
<span class="n">free</span><span class="p">(</span><span class="n">heap</span><span class="o">-></span><span class="n">data</span><span class="p">);</span>
<span class="n">free</span><span class="p">(</span><span class="n">heap</span><span class="p">);</span>
<span class="p">}</span>
<span class="kt">void</span>
<span class="nf">d_heap_print</span><span class="p">(</span><span class="n">d_heap_pt</span> <span class="n">heap</span><span class="p">)</span>
<span class="p">{</span>
<span class="kt">int</span> <span class="n">i</span><span class="p">;</span>
<span class="k">if</span> <span class="p">(</span><span class="n">heap</span> <span class="o">==</span> <span class="nb">NULL</span><span class="p">)</span> <span class="p">{</span>
<span class="k">return</span><span class="p">;</span>
<span class="p">}</span>
<span class="k">for</span> <span class="p">(</span><span class="n">i</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span> <span class="n">i</span><span class="o"><</span><span class="n">heap</span><span class="o">-></span><span class="n">size</span><span class="p">;</span> <span class="n">i</span><span class="o">++</span><span class="p">)</span> <span class="p">{</span>
<span class="n">printf</span><span class="p">(</span><span class="s">"%d "</span><span class="p">,</span> <span class="n">heap</span><span class="o">-></span><span class="n">data</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
<span class="p">}</span>
<span class="p">}</span>
<span class="kt">int</span>
<span class="nf">d_heap_push</span><span class="p">(</span><span class="n">d_heap_pt</span> <span class="n">heap</span><span class="p">,</span> <span class="n">Item</span> <span class="n">element</span><span class="p">)</span>
<span class="p">{</span>
<span class="k">if</span> <span class="p">(</span><span class="n">heap</span> <span class="o">==</span> <span class="nb">NULL</span><span class="p">)</span> <span class="p">{</span>
<span class="k">return</span> <span class="mi">0</span><span class="p">;</span>
<span class="p">}</span>
<span class="k">if</span> <span class="p">(</span><span class="n">heap</span><span class="o">-></span><span class="n">current</span> <span class="o">==</span> <span class="n">heap</span><span class="o">-></span><span class="n">size</span><span class="p">)</span> <span class="p">{</span>
<span class="k">return</span> <span class="mi">0</span><span class="p">;</span>
<span class="p">}</span>
<span class="n">heap</span><span class="o">-></span><span class="n">data</span><span class="p">[</span><span class="n">heap</span><span class="o">-></span><span class="n">current</span><span class="p">]</span> <span class="o">=</span> <span class="n">element</span><span class="p">;</span>
<span class="n">fixup</span><span class="p">(</span><span class="n">heap</span><span class="p">,</span> <span class="n">heap</span><span class="o">-></span><span class="n">current</span><span class="o">++</span><span class="p">);</span>
<span class="k">return</span> <span class="mi">1</span><span class="p">;</span>
<span class="p">}</span>
<span class="n">Item</span>
<span class="nf">d_heap_pop</span><span class="p">(</span><span class="n">d_heap_pt</span> <span class="n">heap</span><span class="p">)</span>
<span class="p">{</span>
<span class="n">swap</span><span class="p">(</span><span class="n">heap</span><span class="o">-></span><span class="n">data</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">heap</span><span class="o">-></span><span class="n">current</span> <span class="o">-</span> <span class="mi">1</span><span class="p">);</span>
<span class="n">fixdown</span><span class="p">(</span><span class="n">heap</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">heap</span><span class="o">-></span><span class="n">current</span> <span class="o">-</span> <span class="mi">2</span><span class="p">);</span>
<span class="k">return</span> <span class="n">heap</span><span class="o">-></span><span class="n">data</span><span class="p">[</span><span class="o">--</span><span class="n">heap</span><span class="o">-></span><span class="n">current</span><span class="p">];</span>
<span class="p">}</span>
<span class="n">Item</span>
<span class="nf">d_heap_top</span><span class="p">(</span><span class="n">d_heap_pt</span> <span class="n">heap</span><span class="p">)</span>
<span class="p">{</span>
<span class="k">return</span> <span class="n">heap</span><span class="o">-></span><span class="n">data</span><span class="p">[</span><span class="mi">0</span><span class="p">];</span>
<span class="p">}</span>
<span class="kt">int</span>
<span class="nf">d_heap_empty</span><span class="p">(</span><span class="n">d_heap_pt</span> <span class="n">heap</span><span class="p">)</span>
<span class="p">{</span>
<span class="k">return</span> <span class="n">heap</span><span class="o">-></span><span class="n">current</span> <span class="o">==</span> <span class="mi">0</span><span class="p">;</span>
<span class="p">}</span>
</pre></div>
<p>d_heap.c</p>
<div class="highlight"><pre><span></span><span class="cm">/* d_heap_test.c */</span>
<span class="cp">#include</span> <span class="cpf"><stdlib.h></span><span class="cp"></span>
<span class="cp">#include</span> <span class="cpf"><stdio.h></span><span class="cp"></span>
<span class="cp">#include</span> <span class="cpf">"d_heap.h"</span><span class="cp"></span>
<span class="cp">#define LENGTH(a) ( (sizeof(a)) / (sizeof(a[0])) )</span>
<span class="kt">int</span>
<span class="nf">main</span><span class="p">(</span><span class="kt">int</span> <span class="n">argc</span><span class="p">,</span> <span class="kt">char</span> <span class="o">*</span><span class="n">argv</span><span class="p">[])</span>
<span class="p">{</span>
<span class="kt">int</span> <span class="n">a</span><span class="p">[]</span> <span class="o">=</span> <span class="p">{</span><span class="mi">10</span><span class="p">,</span> <span class="mi">20</span><span class="p">,</span> <span class="mi">30</span><span class="p">,</span> <span class="mi">50</span><span class="p">,</span> <span class="mi">40</span><span class="p">,</span> <span class="mi">70</span><span class="p">,</span> <span class="mi">100</span><span class="p">,</span> <span class="mi">130</span><span class="p">,</span> <span class="mi">150</span><span class="p">,</span> <span class="mi">60</span><span class="p">,</span> <span class="mi">80</span><span class="p">,</span> <span class="mi">170</span><span class="p">,</span> <span class="mi">90</span><span class="p">,</span> <span class="mi">110</span><span class="p">,</span> <span class="mi">90</span><span class="p">};</span>
<span class="kt">int</span> <span class="n">i</span><span class="p">,</span> <span class="n">len</span><span class="o">=</span><span class="n">LENGTH</span><span class="p">(</span><span class="n">a</span><span class="p">);</span>
<span class="n">d_heap_pt</span> <span class="n">heap</span> <span class="o">=</span> <span class="nb">NULL</span><span class="p">;</span>
<span class="n">heap</span> <span class="o">=</span> <span class="n">d_heap_init</span><span class="p">(</span><span class="n">LENGTH</span><span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="o">+</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">3</span><span class="p">);</span>
<span class="n">printf</span><span class="p">(</span><span class="s">"</span><span class="se">\n</span><span class="s">== 空堆检查: %d"</span><span class="p">,</span> <span class="n">d_heap_empty</span><span class="p">(</span><span class="n">heap</span><span class="p">));</span>
<span class="n">printf</span><span class="p">(</span><span class="s">"</span><span class="se">\n</span><span class="s">== 插入数据: "</span><span class="p">);</span>
<span class="k">for</span><span class="p">(</span><span class="n">i</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span> <span class="n">i</span><span class="o"><</span><span class="n">len</span><span class="p">;</span> <span class="n">i</span><span class="o">++</span><span class="p">)</span>
<span class="p">{</span>
<span class="n">printf</span><span class="p">(</span><span class="s">"%d "</span><span class="p">,</span> <span class="n">a</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
<span class="n">d_heap_push</span><span class="p">(</span><span class="n">heap</span><span class="p">,</span> <span class="n">a</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
<span class="p">}</span>
<span class="n">printf</span><span class="p">(</span><span class="s">"</span><span class="se">\n</span><span class="s">== 空堆检查: %d"</span><span class="p">,</span> <span class="n">d_heap_empty</span><span class="p">(</span><span class="n">heap</span><span class="p">));</span>
<span class="n">printf</span><span class="p">(</span><span class="s">"</span><span class="se">\n</span><span class="s">== 最 小 堆: "</span><span class="p">);</span>
<span class="n">d_heap_print</span><span class="p">(</span><span class="n">heap</span><span class="p">);</span>
<span class="n">i</span><span class="o">=</span><span class="mi">15</span><span class="p">;</span>
<span class="n">d_heap_push</span><span class="p">(</span><span class="n">heap</span><span class="p">,</span> <span class="n">i</span><span class="p">);</span>
<span class="n">printf</span><span class="p">(</span><span class="s">"</span><span class="se">\n</span><span class="s">== 添加元素: %d"</span><span class="p">,</span> <span class="n">i</span><span class="p">);</span>
<span class="n">printf</span><span class="p">(</span><span class="s">"</span><span class="se">\n</span><span class="s">== 最 小 堆: "</span><span class="p">);</span>
<span class="n">d_heap_print</span><span class="p">(</span><span class="n">heap</span><span class="p">);</span>
<span class="n">printf</span><span class="p">(</span><span class="s">"</span><span class="se">\n</span><span class="s">== 堆顶元素: %d</span><span class="se">\n</span><span class="s">"</span><span class="p">,</span> <span class="n">d_heap_top</span><span class="p">(</span><span class="n">heap</span><span class="p">));</span>
<span class="n">i</span> <span class="o">=</span> <span class="n">d_heap_pop</span><span class="p">(</span><span class="n">heap</span><span class="p">);</span>
<span class="n">printf</span><span class="p">(</span><span class="s">"</span><span class="se">\n</span><span class="s">== 删除元素: %d"</span><span class="p">,</span> <span class="n">i</span><span class="p">);</span>
<span class="n">printf</span><span class="p">(</span><span class="s">"</span><span class="se">\n</span><span class="s">== 最 小 堆: "</span><span class="p">);</span>
<span class="n">d_heap_print</span><span class="p">(</span><span class="n">heap</span><span class="p">);</span>
<span class="n">printf</span><span class="p">(</span><span class="s">"</span><span class="se">\n</span><span class="s">"</span><span class="p">);</span>
<span class="n">i</span> <span class="o">=</span> <span class="n">d_heap_pop</span><span class="p">(</span><span class="n">heap</span><span class="p">);</span>
<span class="n">printf</span><span class="p">(</span><span class="s">"</span><span class="se">\n</span><span class="s">== 删除元素: %d"</span><span class="p">,</span> <span class="n">i</span><span class="p">);</span>
<span class="n">printf</span><span class="p">(</span><span class="s">"</span><span class="se">\n</span><span class="s">== 最 小 堆: "</span><span class="p">);</span>
<span class="n">d_heap_print</span><span class="p">(</span><span class="n">heap</span><span class="p">);</span>
<span class="n">printf</span><span class="p">(</span><span class="s">"</span><span class="se">\n</span><span class="s">"</span><span class="p">);</span>
<span class="n">d_heap_free</span><span class="p">(</span><span class="n">heap</span><span class="p">);</span>
<span class="k">return</span> <span class="mi">0</span><span class="p">;</span>
<span class="p">}</span>
</pre></div>
<p>d_heap_test.c</p>
<h3 id="_4"><strong> 测试程序的运行结果 </strong></h3>
<div class="highlight"><pre><span></span><span class="o">==</span> 空堆检查: <span class="nv">1</span>
<span class="o">==</span> 插入数据: <span class="m">10</span> <span class="m">20</span> <span class="m">30</span> <span class="m">50</span> <span class="m">40</span> <span class="m">70</span> <span class="m">100</span> <span class="m">130</span> <span class="m">150</span> <span class="m">60</span> <span class="m">80</span> <span class="m">170</span> <span class="m">90</span> <span class="m">110</span> <span class="nv">90</span>
<span class="o">==</span> 空堆检查: <span class="nv">0</span>
<span class="o">==</span> 最 小 堆: <span class="m">10</span> <span class="m">20</span> <span class="m">30</span> <span class="m">50</span> <span class="m">40</span> <span class="m">70</span> <span class="m">100</span> <span class="m">130</span> <span class="m">150</span> <span class="m">60</span> <span class="m">80</span> <span class="m">170</span> <span class="m">90</span> <span class="m">110</span> <span class="m">90</span> <span class="m">0</span> <span class="m">0</span> <span class="m">0</span> <span class="m">0</span> <span class="m">0</span> <span class="m">0</span> <span class="m">0</span> <span class="m">0</span> <span class="m">0</span> <span class="nv">0</span>
<span class="o">==</span> 添加元素: <span class="nv">15</span>
<span class="o">==</span> 最 小 堆: <span class="m">10</span> <span class="m">15</span> <span class="m">30</span> <span class="m">50</span> <span class="m">20</span> <span class="m">70</span> <span class="m">100</span> <span class="m">130</span> <span class="m">150</span> <span class="m">60</span> <span class="m">80</span> <span class="m">170</span> <span class="m">90</span> <span class="m">110</span> <span class="m">90</span> <span class="m">40</span> <span class="m">0</span> <span class="m">0</span> <span class="m">0</span> <span class="m">0</span> <span class="m">0</span> <span class="m">0</span> <span class="m">0</span> <span class="m">0</span> <span class="nv">0</span>
<span class="o">==</span> 堆顶元素: <span class="nv">10</span>
<span class="o">==</span> 删除元素: <span class="nv">10</span>
<span class="o">==</span> 最 小 堆: <span class="m">15</span> <span class="m">20</span> <span class="m">30</span> <span class="m">50</span> <span class="m">40</span> <span class="m">70</span> <span class="m">100</span> <span class="m">130</span> <span class="m">150</span> <span class="m">60</span> <span class="m">80</span> <span class="m">170</span> <span class="m">90</span> <span class="m">110</span> <span class="m">90</span> <span class="m">10</span> <span class="m">0</span> <span class="m">0</span> <span class="m">0</span> <span class="m">0</span> <span class="m">0</span> <span class="m">0</span> <span class="m">0</span> <span class="m">0</span> <span class="nv">0</span>
<span class="o">==</span> 删除元素: <span class="nv">15</span>
<span class="o">==</span> 最 小 堆: <span class="m">20</span> <span class="m">40</span> <span class="m">30</span> <span class="m">50</span> <span class="m">90</span> <span class="m">70</span> <span class="m">100</span> <span class="m">130</span> <span class="m">150</span> <span class="m">60</span> <span class="m">80</span> <span class="m">170</span> <span class="m">90</span> <span class="m">110</span> <span class="m">15</span> <span class="m">10</span> <span class="m">0</span> <span class="m">0</span> <span class="m">0</span> <span class="m">0</span> <span class="m">0</span> <span class="m">0</span> <span class="m">0</span> <span class="m">0</span> 0
</pre></div>
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<h6 class="subheader"><span class="label secondary radius">Date</span> 2016-09-23(星期五) 19:13 <span class="label secondary radius">By</span> <a href="/author/ming.html">Ming</a> <span class="label secondary radius">In</span> <a href="/category/suan-fa.html">算法</a> <span class="label secondary radius">Tags</span> <a href="/tag/suan-fa.html">算法</a>, </h6>
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