浅谈决策树算法以及matlab实现ID3算法

http://blog.csdn.net/lfdanding/article/details/50753239

决策树方法在分类、预测、规则提取等领域有着广泛的应用。在20世纪70年代后期和80年代初期，机器学习研究者J.Ross Quinilan提出了ID3算法以后，决策树在机器学习、数据挖掘领域得到极大的发展。Quinilan后来又提出了C4.5，成为新的监督学习算法。1984年几位统计学家提出了CART分类算法。ID3和ART算法大约同时被提出，但都是采用类似的方法从训练样本中学习决策树的。

决策树是一树状结构，它的每一个叶子节点对应着一个分类，非叶子节点对应着在某个属性上的划分，根据样本在该属性上的不同取值将其划分成若干个子集。构造决策树的核心问题是在每一步如何选择适当的属性对样本进行拆分。对一个分类问题，从已知类标记的训练样本中学习并构造出决策树是一个自上而下分而治之的过程。

常用的决策树算法如图所示。 

本文将详细介绍ID3算法，其也是最经典的决策树分类算法。

1、ID3算法简介及基本原理 
ID3算法基于信息熵来选择最佳的测试属性，它选择当前样本集中具有最大信息增益值的属性作为测试属性；样本集的划分则依据测试属性的取值进行，测试属性有多少个不同的取值就将样本集划分为多少个子样本集，同时决策树上相应于该样本集的节点长出新的叶子节点。ID3算法根据信息论的理论，采用划分后样本集的不确定性作为衡量划分好坏的标准，用信息增益值度量不确定性：信息增益值越大，不确定性越小。因此，ID3算法在每个非叶节点选择信息增益最大的属性作为测试属性，这样可以得到当前情况下最纯的划分，从而得到较小的决策树。

设S是s个数据样本的集合。假定类别属性具有m个不同的值：，设是类中的样本数。对一个给定的样本，它总的信息熵为，其中，是任意样本属于的概率，一般可以用估计。

设一个属性A具有k个不同的值，利用属性A将集合S划分为k个子集，其中包含了集合S中属性A取值的样本。若选择属性A为测试属性，则这些子集就是从集合S的节点生长出来的新的叶节点。设是子集中类别为的样本数，则根据属性A划分样本的信息熵为 
其中，，是子集中类别为的样本的概率。

最后，用属性A划分样本集S后所得的信息增益（Gain）为

显然越小，Gain(A)的值就越大，说明选择测试属性A对于分类提供的信息越大，选择A之后对分类的不确定程度越小。属性A的k个不同的值对应的样本集S的k个子集或分支，通过递归调用上述过程（不包括已经选择的属性），生成其他属性作为节点的子节点和分支来生成整个决策树。ID3决策树算法作为一个典型的决策树学习算法，其核心是在决策树的各级节点上都用信息增益作为判断标准来进行属性的选择，使得在每个非叶子节点上进行测试时，都能获得最大的类别分类增益，使分类后的数据集的熵最小。这样的处理方法使得树的平均深度较小，从而有效地提高了分类效率。

2、ID3算法的具体流程 
ID3算法的具体流程如下： 
1）对当前样本集合，计算所有属性的信息增益； 
2）选择信息增益最大的属性作为测试属性，把测试属性取值相同的样本划为同一个子样本集； 
3）若子样本集的类别属性只含有单个属性，则分支为叶子节点，判断其属性值并标上相应的符号，然后返回调用处；否则对子样本集递归调用本算法。

数据如图所示

<code class="hljs  has-numbering" style="display: block; padding: 0px; color: inherit; box-sizing: border-box; font-family: 'Source Code Pro', monospace;font-size:undefined; white-space: pre; border-radius: 0px; word-wrap: normal; background: transparent;">序号  天气  是否周末    是否有促销   销量1   坏   是   是   高2   坏   是   是   高3   坏   是   是   高4   坏   否   是   高5   坏   是   是   高6   坏   否   是   高7   坏   是   否   高8   好   是   是   高9   好   是   否   高10  好   是   是   高11  好   是   是   高12  好   是   是   高13  好   是   是   高14  坏   是   是   低15  好   否   是   高16  好   否   是   高17  好   否   是   高18  好   否   是   高19  好   否   否   高20  坏   否   否   低21  坏   否   是   低22  坏   否   是   低23  坏   否   是   低24  坏   否   否   低25  坏   是   否   低26  好   否   是   低27  好   否   是   低28  坏   否   否   低29  坏   否   否   低30  好   否   否   低31  坏   是   否   低32  好   否   是   低33  好   否   否   低34  好   否   否   低</code><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right-width: 1px; border-right-style: solid; border-right-color: rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li><li style="box-sizing: border-box; padding: 0px 5px;">29</li><li style="box-sizing: border-box; padding: 0px 5px;">30</li><li style="box-sizing: border-box; padding: 0px 5px;">31</li><li style="box-sizing: border-box; padding: 0px 5px;">32</li><li style="box-sizing: border-box; padding: 0px 5px;">33</li><li style="box-sizing: border-box; padding: 0px 5px;">34</li><li style="box-sizing: border-box; padding: 0px 5px;">35</li><li style="box-sizing: border-box; padding: 0px 5px;">36</li></ul>

采用ID3算法构建决策树模型的具体步骤如下： 
1）根据公式，计算总的信息熵，其中数据中总记录数为34，而销售数量为“高”的数据有18，“低”的有16 

2）根据公式和，计算每个测试属性的信息熵。

对于天气属性，其属性值有“好”和“坏”两种。其中天气为“好”的条件下，销售数量为“高”的记录为11，销售数量为“低”的记录为6，可表示为（11，6）；天气为“坏”的条件下，销售数量为“高”的记录为7，销售数量为“低”的记录为10，可表示为（7，10）。则天气属性的信息熵计算过程如下： 
 
 

对于是否周末属性，其属性值有“是”和“否”两种。其中是否周末属性为“是”的条件下，销售数量为“高”的记录为11，销售数量为“低”的记录为3，可表示为（11，3）；是否周末属性为“否”的条件下，销售数量为“高”的记录为7，销售数量为“低”的记录为13，可表示为（7，13）。则节假日属性的信息熵计算过程如下： 
 
 

对于是否有促销属性，其属性值有“是”和“否”两种。其中是否有促销属性为“是”的条件下，销售数量为“高”的记录为15，销售数量为“低”的记录为7，可表示为（15，7）；其中是否有促销属性为“否”的条件下，销售数量为“高”的记录为3，销售数量为“低”的记录为9，可表示为（3，9）。则是否有促销属性的信息熵计算过程如下： 
 
 

根据公式，计算天气、是否周末和是否有促销属性的信息增益值。 
 
 

3）由计算结果可以知道是否周末属性的信息增益值最大，它的两个属性值“是”和“否”作为该根节点的两个分支。然后按照上面的步骤继续对该根节点的两个分支进行节点的划分，针对每一个分支节点继续进行信息增益的计算，如此循环反复，直到没有新的节点分支，最终构成一棵决策树。生成的决策树模型如图所示 
 
若周末属性为“是”，天气为“好”，则销售数量为“高”； 
若周末属性为“是”，天气为“坏”，促销属性为“是”，则销售数量为“高”； 
若周末属性为“是”，天气为“坏”，促销属性为“否”，则销售数量为“低”； 
若周末属性为“否”，促销属性为“否”，则销售数量为“低”； 
若周末属性为“否”，促销属性为“是”，天气为“好”，则销售数量为“高”； 
若周末属性为“否”，促销属性为“是”，天气为“坏”，则销售数量为“低”；

由于ID3决策树算法采用了信息增益作为选择测试属性的标准，会偏向于选择取值较多的即所谓的高度分支属性，而这类属性并不一定是最优的属性。同时ID3决策树算法只能处理离散属性，对于连续型的属性，在分类前需要对其进行离散化。为了解决倾向于选择高度分支属性的问题，人们采用信息增益率作为选择测试属性的标准，这样便得到C4.5决策树的算法。此外常用的决策树算法还有CART算法、SLIQ算法、SPRINT算法和PUBLIC算法等等。

使用ID3算法建立决策树的MATLAB代码如下所示 
ID3_decision_tree.m

<code class="hljs ruby has-numbering" style="display: block; padding: 0px; color: inherit; box-sizing: border-box; font-family: 'Source Code Pro', monospace;font-size:undefined; white-space: pre; border-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">%% 使用ID3决策树算法预测销量高低clear ;%</span>% 数据预处理disp(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'正在进行数据预处理...'</span>);[matrix,attributes_label,attributes] =  id3_preprocess();<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">%% 构造ID3决策树，其中id3()为自定义函数disp('数据预处理完成，正在进行构造树...');tree = id3(matrix,attributes_label,attributes);%</span>% 打印并画决策树[nodeids,nodevalues] = print_tree(tree);tree_plot(nodeids,nodevalues);disp(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'ID3算法构建决策树完成！'</span>);</code><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right-width: 1px; border-right-style: solid; border-right-color: rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li></ul>

id3_preprocess.m

<code class="hljs matlab has-numbering" style="display: block; padding: 0px; color: inherit; box-sizing: border-box; font-family: 'Source Code Pro', monospace;font-size:undefined; white-space: pre; border-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-function" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">function</span> <span class="hljs-params" style="color: rgb(102, 0, 102); box-sizing: border-box;">[ matrix,attributes,activeAttributes ]</span> = <span class="hljs-title" style="box-sizing: border-box;">id3_preprocess</span><span class="hljs-params" style="color: rgb(102, 0, 102); box-sizing: border-box;">(  )</span></span><span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">%% ID3算法数据预处理，把字符串转换为0,1编码</span><span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">% 输出参数：</span><span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">% matrix： 转换后的0,1矩阵；</span><span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">% attributes: 属性和Label；</span><span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">% activeAttributes : 属性向量，全1；</span><span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">%% 读取数据</span>txt = <span class="hljs-cell" style="box-sizing: border-box;">{  <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'序号'</span>    <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'天气'</span>    <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'是否周末'</span>    <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'是否有促销'</span>    <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'销量'</span>        <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">''</span>        <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'坏'</span>      <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'是'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'是'</span>            <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'高'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">''</span>        <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'坏'</span>      <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'是'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'是'</span>            <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'高'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">''</span>        <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'坏'</span>      <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'是'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'是'</span>            <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'高'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">''</span>        <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'坏'</span>      <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'否'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'是'</span>            <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'高'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">''</span>        <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'坏'</span>      <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'是'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'是'</span>            <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'高'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">''</span>        <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'坏'</span>      <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'否'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'是'</span>            <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'高'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">''</span>        <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'坏'</span>      <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'是'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'否'</span>            <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'高'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">''</span>        <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'好'</span>      <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'是'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'是'</span>            <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'高'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">''</span>        <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'好'</span>      <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'是'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'否'</span>            <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'高'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">''</span>        <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'好'</span>      <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'是'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'是'</span>            <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'高'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">''</span>        <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'好'</span>      <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'是'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'是'</span>            <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'高'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">''</span>        <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'好'</span>      <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'是'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'是'</span>            <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'高'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">''</span>        <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'好'</span>      <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'是'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'是'</span>            <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'高'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">''</span>        <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'坏'</span>      <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'是'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'是'</span>            <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'低'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">''</span>        <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'好'</span>      <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'否'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'是'</span>            <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'高'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">''</span>        <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'好'</span>      <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'否'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'是'</span>            <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'高'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">''</span>        <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'好'</span>      <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'否'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'是'</span>            <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'高'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">''</span>        <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'好'</span>      <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'否'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'是'</span>            <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'高'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">''</span>        <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'好'</span>      <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'否'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'否'</span>            <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'高'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">''</span>        <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'坏'</span>      <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'否'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'否'</span>            <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'低'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">''</span>        <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'坏'</span>      <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'否'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'是'</span>            <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'低'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">''</span>        <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'坏'</span>      <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'否'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'是'</span>            <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'低'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">''</span>        <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'坏'</span>      <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'否'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'是'</span>            <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'低'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">''</span>        <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'坏'</span>      <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'否'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'否'</span>            <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'低'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">''</span>        <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'坏'</span>      <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'是'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'否'</span>            <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'低'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">''</span>        <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'好'</span>      <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'否'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'是'</span>            <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'低'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">''</span>        <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'好'</span>      <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'否'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'是'</span>            <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'低'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">''</span>        <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'坏'</span>      <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'否'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'否'</span>            <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'低'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">''</span>        <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'坏'</span>      <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'否'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'否'</span>            <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'低'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">''</span>        <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'好'</span>      <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'否'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'否'</span>            <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'低'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">''</span>        <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'坏'</span>      <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'是'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'否'</span>            <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'低'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">''</span>        <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'好'</span>      <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'否'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'是'</span>            <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'低'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">''</span>        <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'好'</span>      <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'否'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'否'</span>            <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'低'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">''</span>        <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'好'</span>      <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'否'</span>          <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'否'</span>            <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'低'</span>  }</span>attributes=txt(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>:<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span>);activeAttributes = <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">ones</span>(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">length</span>(attributes)-<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>);data = txt(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>:<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>:<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span>);<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">%% 针对每列数据进行转换</span><span class="hljs-matrix" style="box-sizing: border-box;">[rows,cols]</span> = <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">size</span>(data);matrix = <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">zeros</span>(rows,cols);<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">for</span> <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">j</span>=<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>:cols    matrix(:,<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">j</span>) = cellfun(@trans2onezero,data(:,<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">j</span>));<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span><span class="hljs-function" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">function</span> <span class="hljs-title" style="box-sizing: border-box;">flag</span> = <span class="hljs-title" style="box-sizing: border-box;">trans2onezero</span><span class="hljs-params" style="color: rgb(102, 0, 102); box-sizing: border-box;">(data)</span></span>    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> strcmp(data,<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'坏'</span>) ||strcmp(data,<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'否'</span>)...        ||strcmp(data,<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'低'</span>)        flag =<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">return</span> ;    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span>    flag =<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>;<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span></code><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right-width: 1px; border-right-style: solid; border-right-color: rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li><li style="box-sizing: border-box; padding: 0px 5px;">29</li><li style="box-sizing: border-box; padding: 0px 5px;">30</li><li style="box-sizing: border-box; padding: 0px 5px;">31</li><li style="box-sizing: border-box; padding: 0px 5px;">32</li><li style="box-sizing: border-box; padding: 0px 5px;">33</li><li style="box-sizing: border-box; padding: 0px 5px;">34</li><li style="box-sizing: border-box; padding: 0px 5px;">35</li><li style="box-sizing: border-box; padding: 0px 5px;">36</li><li style="box-sizing: border-box; padding: 0px 5px;">37</li><li style="box-sizing: border-box; padding: 0px 5px;">38</li><li style="box-sizing: border-box; padding: 0px 5px;">39</li><li style="box-sizing: border-box; padding: 0px 5px;">40</li><li style="box-sizing: border-box; padding: 0px 5px;">41</li><li style="box-sizing: border-box; padding: 0px 5px;">42</li><li style="box-sizing: border-box; padding: 0px 5px;">43</li><li style="box-sizing: border-box; padding: 0px 5px;">44</li><li style="box-sizing: border-box; padding: 0px 5px;">45</li><li style="box-sizing: border-box; padding: 0px 5px;">46</li><li style="box-sizing: border-box; padding: 0px 5px;">47</li><li style="box-sizing: border-box; padding: 0px 5px;">48</li><li style="box-sizing: border-box; padding: 0px 5px;">49</li><li style="box-sizing: border-box; padding: 0px 5px;">50</li><li style="box-sizing: border-box; padding: 0px 5px;">51</li><li style="box-sizing: border-box; padding: 0px 5px;">52</li><li style="box-sizing: border-box; padding: 0px 5px;">53</li><li style="box-sizing: border-box; padding: 0px 5px;">54</li><li style="box-sizing: border-box; padding: 0px 5px;">55</li><li style="box-sizing: border-box; padding: 0px 5px;">56</li><li style="box-sizing: border-box; padding: 0px 5px;">57</li><li style="box-sizing: border-box; padding: 0px 5px;">58</li><li style="box-sizing: border-box; padding: 0px 5px;">59</li><li style="box-sizing: border-box; padding: 0px 5px;">60</li><li style="box-sizing: border-box; padding: 0px 5px;">61</li><li style="box-sizing: border-box; padding: 0px 5px;">62</li><li style="box-sizing: border-box; padding: 0px 5px;">63</li><li style="box-sizing: border-box; padding: 0px 5px;">64</li><li style="box-sizing: border-box; padding: 0px 5px;">65</li><li style="box-sizing: border-box; padding: 0px 5px;">66</li></ul>

id3.m

<code class="hljs ruby has-numbering" style="display: block; padding: 0px; color: inherit; box-sizing: border-box; font-family: 'Source Code Pro', monospace;font-size:undefined; white-space: pre; border-radius: 0px; word-wrap: normal; background: transparent;">function [ tree ] = id3( examples, attributes, activeAttributes )<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">%% ID3 算法 ，构建ID3决策树    ...参考：https://github.com/gwheaton/ID3-Decision-Tree%</span> 输入参数：% <span class="hljs-symbol" style="color: rgb(0, 102, 102); box-sizing: border-box;">example:</span> 输入<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>、<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>矩阵；% <span class="hljs-symbol" style="color: rgb(0, 102, 102); box-sizing: border-box;">attributes:</span> 属性值，含有<span class="hljs-constant" style="box-sizing: border-box;">Label</span>；% <span class="hljs-symbol" style="color: rgb(0, 102, 102); box-sizing: border-box;">activeAttributes:</span> 活跃的属性值；-<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>向量，<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>表示活跃；% 输出参数：% tree：构建的决策树；<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">%% 提供的数据为空，则报异常if (isempty(examples));    error('必须提供数据！');end%</span> 常量numberAttributes = length(activeAttributes);numberExamples = length(examples(<span class="hljs-symbol" style="color: rgb(0, 102, 102); box-sizing: border-box;">:</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>));% 创建树节点tree = struct(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'value'</span>, <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'null'</span>, <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'left'</span>, <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'null'</span>, <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'right'</span>, <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'null'</span>);% 如果最后一列全部为<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>，则返回“<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">true</span>”lastColumnSum = sum(examples(<span class="hljs-symbol" style="color: rgb(0, 102, 102); box-sizing: border-box;">:</span>, numberAttributes + <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>));<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> (lastColumnSum == numberExamples);    tree.value = <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'true'</span>;    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">return</span><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span>% 如果最后一列全部为<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>，则返回“<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">false</span>”<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> (lastColumnSum == <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>);    tree.value = <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'false'</span>;    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">return</span><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span>% 如果活跃的属性为空，则返回label最多的属性值<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> (sum(activeAttributes) == <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>);    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> (lastColumnSum >= numberExamples / <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>);        tree.value = <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'true'</span>;    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">else</span>        tree.value = <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'false'</span>;    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span>    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">return</span><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span><span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">%% 计算当前属性的熵p1 = lastColumnSum / numberExamples;if (p1 == 0);    p1_eq = 0;else    p1_eq = -1*p1*log2(p1);endp0 = (numberExamples - lastColumnSum) / numberExamples;if (p0 == 0);    p0_eq = 0;else    p0_eq = -1*p0*log2(p0);endcurrentEntropy = p1_eq + p0_eq;%</span>% 寻找最大增益gains = -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>*ones(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,numberAttributes); % 初始化增益<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">for</span> i=<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span><span class="hljs-symbol" style="color: rgb(0, 102, 102); box-sizing: border-box;">:numberAttributes</span>;    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> (activeAttributes(i)) % 该属性仍处于活跃状态，对其更新        s<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span> = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>; s0_and_true = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;        s1 = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>; s1_and_true = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">for</span> j=<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span><span class="hljs-symbol" style="color: rgb(0, 102, 102); box-sizing: border-box;">:numberExamples</span>;            <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> (examples(j,i));                 s1 = s1 + <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>;                <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> (examples(j, numberAttributes + <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>));                     s1_and_true = s1_and_true + <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>;                <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span>            <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">else</span>                s<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span> = s<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span> + <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>;                <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> (examples(j, numberAttributes + <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>));                     s0_and_true = s0_and_true + <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>;                <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span>            <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span>        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span>        % 熵 <span class="hljs-constant" style="box-sizing: border-box;">S</span>(v=<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>)        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> (~s1);            p1 = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">else</span>            p1 = (s1_and_true / s1);         <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span>        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> (p1 == <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>);            p1_eq = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">else</span>            p1_eq = -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>*(p1)*log2(p1);        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span>        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> (~s1);            p<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span> = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">else</span>            p<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span> = ((s1 - s1_and_true) / s1);        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span>        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> (p<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span> == <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>);            p0_eq = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">else</span>            p0_eq = -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>*(p<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>)*log2(p<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>);        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span>        entropy_s1 = p1_eq + p0_eq;        % 熵 <span class="hljs-constant" style="box-sizing: border-box;">S</span>(v=<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>)        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> (~s<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>);            p1 = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">else</span>            p1 = (s0_and_true / s<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>);         <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span>        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> (p1 == <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>);            p1_eq = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">else</span>            p1_eq = -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>*(p1)*log2(p1);        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span>        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> (~s<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>);            p<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span> = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">else</span>            p<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span> = ((s<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span> - s0_and_true) / s<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>);        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span>        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> (p<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span> == <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>);            p0_eq = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">else</span>            p0_eq = -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>*(p<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>)*log2(p<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>);        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span>        entropy_s<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span> = p1_eq + p0_eq;        gains(i) = currentEntropy - ((s1/numberExamples)*entropy_s1) - ((s<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>/numberExamples)*entropy_s<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>);    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span>% 选出最大增益[~, bestAttribute] = max(gains);% 设置相应值tree.value = attributes{bestAttribute};% 去活跃状态activeAttributes(bestAttribute) = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;% 根据bestAttribute把数据进行分组examples_<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>= examples(examples(<span class="hljs-symbol" style="color: rgb(0, 102, 102); box-sizing: border-box;">:</span>,bestAttribute)==<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>,<span class="hljs-symbol" style="color: rgb(0, 102, 102); box-sizing: border-box;">:</span>);examples_1= examples(examples(<span class="hljs-symbol" style="color: rgb(0, 102, 102); box-sizing: border-box;">:</span>,bestAttribute)==<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,<span class="hljs-symbol" style="color: rgb(0, 102, 102); box-sizing: border-box;">:</span>);% 当 value = <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">false</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">or</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>, 左分支<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> (isempty(examples_<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>));    leaf = struct(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'value'</span>, <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'null'</span>, <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'left'</span>, <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'null'</span>, <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'right'</span>, <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'null'</span>);    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> (lastColumnSum >= numberExamples / <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>); % <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">for</span> matrix examples        leaf.value = <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'true'</span>;    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">else</span>        leaf.value = <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'false'</span>;    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span>    tree.left = leaf;<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">else</span>    % 递归    tree.left = id3(examples_<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>, attributes, activeAttributes);<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span>% 当 value = <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">true</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">or</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>, 右分支<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> (isempty(examples_1));    leaf = struct(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'value'</span>, <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'null'</span>, <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'left'</span>, <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'null'</span>, <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'right'</span>, <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'null'</span>);    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> (lastColumnSum >= numberExamples / <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>);         leaf.value = <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'true'</span>;    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">else</span>        leaf.value = <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'false'</span>;    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span>    tree.right = leaf;<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">else</span>    % 递归    tree.right = id3(examples_1, attributes, activeAttributes);<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span>% 返回<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">return</span><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span></code><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right-width: 1px; border-right-style: solid; border-right-color: rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li><li style="box-sizing: border-box; padding: 0px 5px;">29</li><li style="box-sizing: border-box; padding: 0px 5px;">30</li><li style="box-sizing: border-box; padding: 0px 5px;">31</li><li style="box-sizing: border-box; padding: 0px 5px;">32</li><li style="box-sizing: border-box; padding: 0px 5px;">33</li><li style="box-sizing: border-box; padding: 0px 5px;">34</li><li style="box-sizing: border-box; padding: 0px 5px;">35</li><li style="box-sizing: border-box; padding: 0px 5px;">36</li><li style="box-sizing: border-box; padding: 0px 5px;">37</li><li style="box-sizing: border-box; padding: 0px 5px;">38</li><li style="box-sizing: border-box; padding: 0px 5px;">39</li><li style="box-sizing: border-box; padding: 0px 5px;">40</li><li style="box-sizing: border-box; padding: 0px 5px;">41</li><li style="box-sizing: border-box; padding: 0px 5px;">42</li><li style="box-sizing: border-box; padding: 0px 5px;">43</li><li style="box-sizing: border-box; padding: 0px 5px;">44</li><li style="box-sizing: border-box; padding: 0px 5px;">45</li><li style="box-sizing: border-box; padding: 0px 5px;">46</li><li style="box-sizing: border-box; padding: 0px 5px;">47</li><li style="box-sizing: border-box; padding: 0px 5px;">48</li><li style="box-sizing: border-box; padding: 0px 5px;">49</li><li style="box-sizing: border-box; padding: 0px 5px;">50</li><li style="box-sizing: border-box; padding: 0px 5px;">51</li><li style="box-sizing: border-box; padding: 0px 5px;">52</li><li style="box-sizing: border-box; padding: 0px 5px;">53</li><li style="box-sizing: border-box; padding: 0px 5px;">54</li><li style="box-sizing: border-box; padding: 0px 5px;">55</li><li style="box-sizing: border-box; padding: 0px 5px;">56</li><li style="box-sizing: border-box; padding: 0px 5px;">57</li><li style="box-sizing: border-box; padding: 0px 5px;">58</li><li style="box-sizing: border-box; padding: 0px 5px;">59</li><li style="box-sizing: border-box; padding: 0px 5px;">60</li><li style="box-sizing: border-box; padding: 0px 5px;">61</li><li style="box-sizing: border-box; padding: 0px 5px;">62</li><li style="box-sizing: border-box; padding: 0px 5px;">63</li><li style="box-sizing: border-box; padding: 0px 5px;">64</li><li style="box-sizing: border-box; padding: 0px 5px;">65</li><li style="box-sizing: border-box; padding: 0px 5px;">66</li><li style="box-sizing: border-box; padding: 0px 5px;">67</li><li style="box-sizing: border-box; padding: 0px 5px;">68</li><li style="box-sizing: border-box; padding: 0px 5px;">69</li><li style="box-sizing: border-box; padding: 0px 5px;">70</li><li style="box-sizing: border-box; padding: 0px 5px;">71</li><li style="box-sizing: border-box; padding: 0px 5px;">72</li><li style="box-sizing: border-box; padding: 0px 5px;">73</li><li style="box-sizing: border-box; padding: 0px 5px;">74</li><li style="box-sizing: border-box; padding: 0px 5px;">75</li><li style="box-sizing: border-box; padding: 0px 5px;">76</li><li style="box-sizing: border-box; padding: 0px 5px;">77</li><li style="box-sizing: border-box; padding: 0px 5px;">78</li><li style="box-sizing: border-box; padding: 0px 5px;">79</li><li style="box-sizing: border-box; padding: 0px 5px;">80</li><li style="box-sizing: border-box; padding: 0px 5px;">81</li><li style="box-sizing: border-box; padding: 0px 5px;">82</li><li style="box-sizing: border-box; padding: 0px 5px;">83</li><li style="box-sizing: border-box; padding: 0px 5px;">84</li><li style="box-sizing: border-box; padding: 0px 5px;">85</li><li style="box-sizing: border-box; padding: 0px 5px;">86</li><li style="box-sizing: border-box; padding: 0px 5px;">87</li><li style="box-sizing: border-box; padding: 0px 5px;">88</li><li style="box-sizing: border-box; padding: 0px 5px;">89</li><li style="box-sizing: border-box; padding: 0px 5px;">90</li><li style="box-sizing: border-box; padding: 0px 5px;">91</li><li style="box-sizing: border-box; padding: 0px 5px;">92</li><li style="box-sizing: border-box; padding: 0px 5px;">93</li><li style="box-sizing: border-box; padding: 0px 5px;">94</li><li style="box-sizing: border-box; padding: 0px 5px;">95</li><li style="box-sizing: border-box; padding: 0px 5px;">96</li><li style="box-sizing: border-box; padding: 0px 5px;">97</li><li style="box-sizing: border-box; padding: 0px 5px;">98</li><li style="box-sizing: border-box; padding: 0px 5px;">99</li><li style="box-sizing: border-box; padding: 0px 5px;">100</li><li style="box-sizing: border-box; padding: 0px 5px;">101</li><li style="box-sizing: border-box; padding: 0px 5px;">102</li><li style="box-sizing: border-box; padding: 0px 5px;">103</li><li style="box-sizing: border-box; padding: 0px 5px;">104</li><li style="box-sizing: border-box; padding: 0px 5px;">105</li><li style="box-sizing: border-box; padding: 0px 5px;">106</li><li style="box-sizing: border-box; padding: 0px 5px;">107</li><li style="box-sizing: border-box; padding: 0px 5px;">108</li><li style="box-sizing: border-box; padding: 0px 5px;">109</li><li style="box-sizing: border-box; padding: 0px 5px;">110</li><li style="box-sizing: border-box; padding: 0px 5px;">111</li><li style="box-sizing: border-box; padding: 0px 5px;">112</li><li style="box-sizing: border-box; padding: 0px 5px;">113</li><li style="box-sizing: border-box; padding: 0px 5px;">114</li><li style="box-sizing: border-box; padding: 0px 5px;">115</li><li style="box-sizing: border-box; padding: 0px 5px;">116</li><li style="box-sizing: border-box; padding: 0px 5px;">117</li><li style="box-sizing: border-box; padding: 0px 5px;">118</li><li style="box-sizing: border-box; padding: 0px 5px;">119</li><li style="box-sizing: border-box; padding: 0px 5px;">120</li><li style="box-sizing: border-box; padding: 0px 5px;">121</li><li style="box-sizing: border-box; padding: 0px 5px;">122</li><li style="box-sizing: border-box; padding: 0px 5px;">123</li><li style="box-sizing: border-box; padding: 0px 5px;">124</li><li style="box-sizing: border-box; padding: 0px 5px;">125</li><li style="box-sizing: border-box; padding: 0px 5px;">126</li><li style="box-sizing: border-box; padding: 0px 5px;">127</li><li style="box-sizing: border-box; padding: 0px 5px;">128</li><li style="box-sizing: border-box; padding: 0px 5px;">129</li><li style="box-sizing: border-box; padding: 0px 5px;">130</li><li style="box-sizing: border-box; padding: 0px 5px;">131</li><li style="box-sizing: border-box; padding: 0px 5px;">132</li><li style="box-sizing: border-box; padding: 0px 5px;">133</li><li style="box-sizing: border-box; padding: 0px 5px;">134</li><li style="box-sizing: border-box; padding: 0px 5px;">135</li><li style="box-sizing: border-box; padding: 0px 5px;">136</li><li style="box-sizing: border-box; padding: 0px 5px;">137</li><li style="box-sizing: border-box; padding: 0px 5px;">138</li><li style="box-sizing: border-box; padding: 0px 5px;">139</li><li style="box-sizing: border-box; padding: 0px 5px;">140</li><li style="box-sizing: border-box; padding: 0px 5px;">141</li><li style="box-sizing: border-box; padding: 0px 5px;">142</li><li style="box-sizing: border-box; padding: 0px 5px;">143</li><li style="box-sizing: border-box; padding: 0px 5px;">144</li><li style="box-sizing: border-box; padding: 0px 5px;">145</li><li style="box-sizing: border-box; padding: 0px 5px;">146</li><li style="box-sizing: border-box; padding: 0px 5px;">147</li><li style="box-sizing: border-box; padding: 0px 5px;">148</li><li style="box-sizing: border-box; padding: 0px 5px;">149</li><li style="box-sizing: border-box; padding: 0px 5px;">150</li><li style="box-sizing: border-box; padding: 0px 5px;">151</li><li style="box-sizing: border-box; padding: 0px 5px;">152</li><li style="box-sizing: border-box; padding: 0px 5px;">153</li><li style="box-sizing: border-box; padding: 0px 5px;">154</li><li style="box-sizing: border-box; padding: 0px 5px;">155</li><li style="box-sizing: border-box; padding: 0px 5px;">156</li><li style="box-sizing: border-box; padding: 0px 5px;">157</li><li style="box-sizing: border-box; padding: 0px 5px;">158</li><li style="box-sizing: border-box; padding: 0px 5px;">159</li><li style="box-sizing: border-box; padding: 0px 5px;">160</li><li style="box-sizing: border-box; padding: 0px 5px;">161</li><li style="box-sizing: border-box; padding: 0px 5px;">162</li><li style="box-sizing: border-box; padding: 0px 5px;">163</li><li style="box-sizing: border-box; padding: 0px 5px;">164</li><li style="box-sizing: border-box; padding: 0px 5px;">165</li><li style="box-sizing: border-box; padding: 0px 5px;">166</li><li style="box-sizing: border-box; padding: 0px 5px;">167</li><li style="box-sizing: border-box; padding: 0px 5px;">168</li><li style="box-sizing: border-box; padding: 0px 5px;">169</li><li style="box-sizing: border-box; padding: 0px 5px;">170</li><li style="box-sizing: border-box; padding: 0px 5px;">171</li><li style="box-sizing: border-box; padding: 0px 5px;">172</li><li style="box-sizing: border-box; padding: 0px 5px;">173</li><li style="box-sizing: border-box; padding: 0px 5px;">174</li></ul>

print_tree.m

<code class="hljs matlab has-numbering" style="display: block; padding: 0px; color: inherit; box-sizing: border-box; font-family: 'Source Code Pro', monospace;font-size:undefined; white-space: pre; border-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-function" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">function</span> <span class="hljs-params" style="color: rgb(102, 0, 102); box-sizing: border-box;">[nodeids_,nodevalue_]</span> = <span class="hljs-title" style="box-sizing: border-box;">print_tree</span><span class="hljs-params" style="color: rgb(102, 0, 102); box-sizing: border-box;">(tree)</span></span><span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">%% 打印树，返回树的关系向量</span><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">global</span> nodeid nodeids nodevalue;nodeids(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>)=<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>; <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">% 根节点的值为0</span>nodeid=<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;nodevalue=<span class="hljs-cell" style="box-sizing: border-box;">{}</span>;<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">isempty</span>(tree)     <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">disp</span>(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'空树！'</span>);    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">return</span> ;<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span>queue = queue_push(<span class="hljs-matrix" style="box-sizing: border-box;">[]</span>,tree);<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">while</span> ~<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">isempty</span>(queue) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">% 队列不为空</span>     <span class="hljs-matrix" style="box-sizing: border-box;">[node,queue]</span> = queue_pop(queue); <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">% 出队列</span>     visit(node,queue_curr_size(queue));     <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> ~strcmp(<span class="hljs-transposed_variable" style="box-sizing: border-box;">node.</span>left,<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'null'</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">% 左子树不为空</span>        queue = queue_push(queue,<span class="hljs-transposed_variable" style="box-sizing: border-box;">node.</span>left); <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">% 进队</span>     <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span>     <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> ~strcmp(<span class="hljs-transposed_variable" style="box-sizing: border-box;">node.</span>right,<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'null'</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">% 左子树不为空</span>        queue = queue_push(queue,<span class="hljs-transposed_variable" style="box-sizing: border-box;">node.</span>right); <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">% 进队</span>     <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span><span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">%% 返回 节点关系，用于treeplot画图</span>nodeids_=nodeids;nodevalue_=nodevalue;<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span><span class="hljs-function" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">function</span> <span class="hljs-title" style="box-sizing: border-box;">visit</span><span class="hljs-params" style="color: rgb(102, 0, 102); box-sizing: border-box;">(node,length_)</span></span><span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">%% 访问node 节点，并把其设置值为nodeid的节点</span>    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">global</span> nodeid nodeids nodevalue;    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> isleaf(node)        nodeid=nodeid+<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>;        fprintf(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'叶子节点，node: %d\t，属性值: %s\n'</span>, ...        nodeid, <span class="hljs-transposed_variable" style="box-sizing: border-box;">node.</span>value);        nodevalue<span class="hljs-cell" style="box-sizing: border-box;">{<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,nodeid}</span>=<span class="hljs-transposed_variable" style="box-sizing: border-box;">node.</span>value;    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">else</span> <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">% 要么是叶子节点，要么不是</span>        <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">%if isleaf(node.left) && ~isleaf(node.right) % 左边为叶子节点,右边不是</span>        nodeid=nodeid+<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>;        nodeids(nodeid+length_+<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>)=nodeid;        nodeids(nodeid+length_+<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>)=nodeid;        fprintf(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'node: %d\t属性值: %s\t，左子树为节点：node%d，右子树为节点：node%d\n'</span>, ...        nodeid, <span class="hljs-transposed_variable" style="box-sizing: border-box;">node.</span>value,nodeid+length_+<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,nodeid+length_+<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>);        nodevalue<span class="hljs-cell" style="box-sizing: border-box;">{<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,nodeid}</span>=<span class="hljs-transposed_variable" style="box-sizing: border-box;">node.</span>value;    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span><span class="hljs-function" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">function</span> <span class="hljs-title" style="box-sizing: border-box;">flag</span> = <span class="hljs-title" style="box-sizing: border-box;">isleaf</span><span class="hljs-params" style="color: rgb(102, 0, 102); box-sizing: border-box;">(node)</span></span><span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">%% 是否是叶子节点</span>    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> strcmp(<span class="hljs-transposed_variable" style="box-sizing: border-box;">node.</span>left,<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'null'</span>) && strcmp(<span class="hljs-transposed_variable" style="box-sizing: border-box;">node.</span>right,<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'null'</span>) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">% 左右都为空</span>        flag =<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>;    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">else</span>        flag=<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span></code><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right-width: 1px; border-right-style: solid; border-right-color: rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li><li style="box-sizing: border-box; padding: 0px 5px;">29</li><li style="box-sizing: border-box; padding: 0px 5px;">30</li><li style="box-sizing: border-box; padding: 0px 5px;">31</li><li style="box-sizing: border-box; padding: 0px 5px;">32</li><li style="box-sizing: border-box; padding: 0px 5px;">33</li><li style="box-sizing: border-box; padding: 0px 5px;">34</li><li style="box-sizing: border-box; padding: 0px 5px;">35</li><li style="box-sizing: border-box; padding: 0px 5px;">36</li><li style="box-sizing: border-box; padding: 0px 5px;">37</li><li style="box-sizing: border-box; padding: 0px 5px;">38</li><li style="box-sizing: border-box; padding: 0px 5px;">39</li><li style="box-sizing: border-box; padding: 0px 5px;">40</li><li style="box-sizing: border-box; padding: 0px 5px;">41</li><li style="box-sizing: border-box; padding: 0px 5px;">42</li><li style="box-sizing: border-box; padding: 0px 5px;">43</li><li style="box-sizing: border-box; padding: 0px 5px;">44</li><li style="box-sizing: border-box; padding: 0px 5px;">45</li><li style="box-sizing: border-box; padding: 0px 5px;">46</li><li style="box-sizing: border-box; padding: 0px 5px;">47</li><li style="box-sizing: border-box; padding: 0px 5px;">48</li><li style="box-sizing: border-box; padding: 0px 5px;">49</li><li style="box-sizing: border-box; padding: 0px 5px;">50</li><li style="box-sizing: border-box; padding: 0px 5px;">51</li><li style="box-sizing: border-box; padding: 0px 5px;">52</li><li style="box-sizing: border-box; padding: 0px 5px;">53</li><li style="box-sizing: border-box; padding: 0px 5px;">54</li><li style="box-sizing: border-box; padding: 0px 5px;">55</li><li style="box-sizing: border-box; padding: 0px 5px;">56</li><li style="box-sizing: border-box; padding: 0px 5px;">57</li></ul>

tree_plot.m

<code class="hljs matlab has-numbering" style="display: block; padding: 0px; color: inherit; box-sizing: border-box; font-family: 'Source Code Pro', monospace;font-size:undefined; white-space: pre; border-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-function" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">function</span> <span class="hljs-title" style="box-sizing: border-box;">tree_plot</span><span class="hljs-params" style="color: rgb(102, 0, 102); box-sizing: border-box;">( p ,nodevalues)</span></span><span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">%% 参考treeplot函数</span><span class="hljs-matrix" style="box-sizing: border-box;">[x,y,h]</span>=treelayout(p);f = <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">find</span>(p~=<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>);pp = p(f);X = <span class="hljs-matrix" style="box-sizing: border-box;">[x(f); x(pp); NaN(size(f))]</span>;Y = <span class="hljs-matrix" style="box-sizing: border-box;">[y(f); y(pp); NaN(size(f))]</span>;X = X(:);Y = Y(:);    n = <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">length</span>(p);    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> n < <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">500</span>,        hold on ;         plot (x, y, <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'ro'</span>, X, Y, <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'r-'</span>);        nodesize = <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">length</span>(x);        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">for</span> <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">i</span>=<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>:nodesize<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">%            text(x(i)+0.01,y(i),['node' num2str(i)]); </span>            text(x(<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">i</span>)+<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0.01</span>,y(<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">i</span>),nodevalues<span class="hljs-cell" style="box-sizing: border-box;">{<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,i}</span>);         <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span>        hold off;    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">else</span>        plot (X, Y, <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'r-'</span>);    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span>;xlabel(<span class="hljs-matrix" style="box-sizing: border-box;">[<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'height = '</span> int2str(h)]</span>);axis(<span class="hljs-matrix" style="box-sizing: border-box;">[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>]</span>);<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span></code><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right-width: 1px; border-right-style: solid; border-right-color: rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li><li style="box-sizing: border-box; padding: 0px 5px;">29</li><li style="box-sizing: border-box; padding: 0px 5px;">30</li><li style="box-sizing: border-box; padding: 0px 5px;">31</li><li style="box-sizing: border-box; padding: 0px 5px;">32</li></ul>

queue_push.m

<code class="hljs ruby has-numbering" style="display: block; padding: 0px; color: inherit; box-sizing: border-box; font-family: 'Source Code Pro', monospace;font-size:undefined; white-space: pre; border-radius: 0px; word-wrap: normal; background: transparent;">function [ newqueue ] = queue_push( queue,item )<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">%% 进队%</span> cols = size(queue);% newqueue =structs(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,cols+<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>);newqueue=[queue,item];<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span></code><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right-width: 1px; border-right-style: solid; border-right-color: rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li></ul>

queue_pop.m

<code class="hljs matlab has-numbering" style="display: block; padding: 0px; color: inherit; box-sizing: border-box; font-family: 'Source Code Pro', monospace;font-size:undefined; white-space: pre; border-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-function" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">function</span> <span class="hljs-params" style="color: rgb(102, 0, 102); box-sizing: border-box;">[ item,newqueue ]</span> = <span class="hljs-title" style="box-sizing: border-box;">queue_pop</span><span class="hljs-params" style="color: rgb(102, 0, 102); box-sizing: border-box;">( queue )</span></span><span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">%% 访问队列</span><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">isempty</span>(queue)    <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">disp</span>(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">'队列为空，不能访问！'</span>);    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">return</span>;<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span>item = queue(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>); <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">% 第一个元素弹出</span>newqueue=queue(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>:<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span>); <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">% 往后移动一个元素位置</span><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span></code><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right-width: 1px; border-right-style: solid; border-right-color: rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li></ul>

queue_curr_size.m

<code class="hljs matlab has-numbering" style="display: block; padding: 0px; color: inherit; box-sizing: border-box; font-family: 'Source Code Pro', monospace;font-size:undefined; white-space: pre; border-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-function" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">function</span> <span class="hljs-params" style="color: rgb(102, 0, 102); box-sizing: border-box;">[ length_ ]</span> = <span class="hljs-title" style="box-sizing: border-box;">queue_curr_size</span><span class="hljs-params" style="color: rgb(102, 0, 102); box-sizing: border-box;">( queue )</span></span><span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">%% 当前队列长度</span>length_= <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">length</span>(queue);<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">end</span></code><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right-width: 1px; border-right-style: solid; border-right-color: rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li></ul>

生成的图像如图所示：