PHP实现图的邻接矩阵表示及几种简单遍历算法分析


Posted in PHP onNovember 24, 2017

本文实例讲述了PHP实现图的邻接矩阵表示及几种简单遍历算法。分享给大家供大家参考,具体如下:

在web开发中图这种数据结构的应用比树要少很多,但在一些业务中也常有出现,下面介绍几种图的寻径算法,并用PHP加以实现.

佛洛依德算法,主要是在顶点集内,按点与点相邻边的权重做遍历,如果两点不相连则权重无穷大,这样通过多次遍历可以得到点到点的最短路径,逻辑上最好理解,实现也较为简单,时间复杂度为O(n^3);

迪杰斯特拉算法,OSPF中实现最短路由所用到的经典算法,djisktra算法的本质是贪心算法,不断的遍历扩充顶点路径集合S,一旦发现更短的点到点路径就替换S中原有的最短路径,完成所有遍历后S便是所有顶点的最短路径集合了.迪杰斯特拉算法的时间复杂度为O(n^2);

克鲁斯卡尔算法,在图内构造最小生成树,达到图中所有顶点联通.从而得到最短路径.时间复杂度为O(N*logN);

<?php
/**
 * PHP 实现图邻接矩阵
 */
class MGraph{
  private $vexs; //顶点数组
  private $arc; //边邻接矩阵,即二维数组
  private $arcData; //边的数组信息
  private $direct; //图的类型(无向或有向)
  private $hasList; //尝试遍历时存储遍历过的结点
  private $queue; //广度优先遍历时存储孩子结点的队列,用数组模仿
  private $infinity = 65535;//代表无穷,即两点无连接,建带权值的图时用,本示例不带权值
  private $primVexs; //prim算法时保存顶点
  private $primArc; //prim算法时保存边
  private $krus;//kruscal算法时保存边的信息
  public function MGraph($vexs, $arc, $direct = 0){
    $this->vexs = $vexs;
    $this->arcData = $arc;
    $this->direct = $direct;
    $this->initalizeArc();
    $this->createArc();
  }
  private function initalizeArc(){
    foreach($this->vexs as $value){
      foreach($this->vexs as $cValue){
        $this->arc[$value][$cValue] = ($value == $cValue ? 0 : $this->infinity);
      }
    }
  }
  //创建图 $direct:0表示无向图,1表示有向图
  private function createArc(){
    foreach($this->arcData as $key=>$value){
      $strArr = str_split($key);
      $first = $strArr[0];
      $last = $strArr[1];
      $this->arc[$first][$last] = $value;
      if(!$this->direct){
        $this->arc[$last][$first] = $value;
      }
    }
  }
  //floyd算法
  public function floyd(){
    $path = array();//路径数组
    $distance = array();//距离数组
    foreach($this->arc as $key=>$value){
      foreach($value as $k=>$v){
        $path[$key][$k] = $k;
        $distance[$key][$k] = $v;
      }
    }
    for($j = 0; $j < count($this->vexs); $j ++){
      for($i = 0; $i < count($this->vexs); $i ++){
        for($k = 0; $k < count($this->vexs); $k ++){
          if($distance[$this->vexs[$i]][$this->vexs[$k]] > $distance[$this->vexs[$i]][$this->vexs[$j]] + $distance[$this->vexs[$j]][$this->vexs[$k]]){
            $path[$this->vexs[$i]][$this->vexs[$k]] = $path[$this->vexs[$i]][$this->vexs[$j]];
            $distance[$this->vexs[$i]][$this->vexs[$k]] = $distance[$this->vexs[$i]][$this->vexs[$j]] + $distance[$this->vexs[$j]][$this->vexs[$k]];
          }
        }
      }
    }
    return array($path, $distance);
  }
  //djikstra算法
  public function dijkstra(){
    $final = array();
    $pre = array();//要查找的结点的前一个结点数组
    $weight = array();//权值和数组
    foreach($this->arc[$this->vexs[0]] as $k=>$v){
      $final[$k] = 0;
      $pre[$k] = $this->vexs[0];
      $weight[$k] = $v;
    }
    $final[$this->vexs[0]] = 1;
    for($i = 0; $i < count($this->vexs); $i ++){
      $key = 0;
      $min = $this->infinity;
      for($j = 1; $j < count($this->vexs); $j ++){
        $temp = $this->vexs[$j];
        if($final[$temp] != 1 && $weight[$temp] < $min){
          $key = $temp;
          $min = $weight[$temp];
        }
      }
      $final[$key] = 1;
      for($j = 0; $j < count($this->vexs); $j ++){
        $temp = $this->vexs[$j];
        if($final[$temp] != 1 && ($min + $this->arc[$key][$temp]) < $weight[$temp]){
          $pre[$temp] = $key;
          $weight[$temp] = $min + $this->arc[$key][$temp];
        }
      }
    }
    return $pre;
  }
  //kruscal算法
  private function kruscal(){
    $this->krus = array();
    foreach($this->vexs as $value){
      $krus[$value] = 0;
    }
    foreach($this->arc as $key=>$value){
      $begin = $this->findRoot($key);
      foreach($value as $k=>$v){
        $end = $this->findRoot($k);
        if($begin != $end){
          $this->krus[$begin] = $end;
        }
      }
    }
  }
  //查找子树的尾结点
  private function findRoot($node){
    while($this->krus[$node] > 0){
      $node = $this->krus[$node];
    }
    return $node;
  }
  //prim算法,生成最小生成树
  public function prim(){
    $this->primVexs = array();
    $this->primArc = array($this->vexs[0]=>0);
    for($i = 1; $i < count($this->vexs); $i ++){
      $this->primArc[$this->vexs[$i]] = $this->arc[$this->vexs[0]][$this->vexs[$i]];
      $this->primVexs[$this->vexs[$i]] = $this->vexs[0];
    }
    for($i = 0; $i < count($this->vexs); $i ++){
      $min = $this->infinity;
      $key;
      foreach($this->vexs as $k=>$v){
        if($this->primArc[$v] != 0 && $this->primArc[$v] < $min){
          $key = $v;
          $min = $this->primArc[$v];
        }
      }
      $this->primArc[$key] = 0;
      foreach($this->arc[$key] as $k=>$v){
        if($this->primArc[$k] != 0 && $v < $this->primArc[$k]){
          $this->primArc[$k] = $v;
          $this->primVexs[$k] = $key;
        }
      }
    }
    return $this->primVexs;
  }
  //一般算法,生成最小生成树
  public function bst(){
    $this->primVexs = array($this->vexs[0]);
    $this->primArc = array();
    next($this->arc[key($this->arc)]);
    $key = NULL;
    $current = NULL;
    while(count($this->primVexs) < count($this->vexs)){
      foreach($this->primVexs as $value){
        foreach($this->arc[$value] as $k=>$v){
          if(!in_array($k, $this->primVexs) && $v != 0 && $v != $this->infinity){
            if($key == NULL || $v < current($current)){
              $key = $k;
              $current = array($value . $k=>$v);
            }
          }
        }
      }
      $this->primVexs[] = $key;
      $this->primArc[key($current)] = current($current);
      $key = NULL;
      $current = NULL;
    }
    return array('vexs'=>$this->primVexs, 'arc'=>$this->primArc);
  }
  //一般遍历
  public function reserve(){
    $this->hasList = array();
    foreach($this->arc as $key=>$value){
      if(!in_array($key, $this->hasList)){
        $this->hasList[] = $key;
      }
      foreach($value as $k=>$v){
        if($v == 1 && !in_array($k, $this->hasList)){
          $this->hasList[] = $k;
        }
      }
    }
    foreach($this->vexs as $v){
      if(!in_array($v, $this->hasList))
        $this->hasList[] = $v;
    }
    return implode($this->hasList);
  }
  //广度优先遍历
  public function bfs(){
    $this->hasList = array();
    $this->queue = array();
    foreach($this->arc as $key=>$value){
      if(!in_array($key, $this->hasList)){
        $this->hasList[] = $key;
        $this->queue[] = $value;
        while(!empty($this->queue)){
          $child = array_shift($this->queue);
          foreach($child as $k=>$v){
            if($v == 1 && !in_array($k, $this->hasList)){
              $this->hasList[] = $k;
              $this->queue[] = $this->arc[$k];
            }
          }
        }
      }
    }
    return implode($this->hasList);
  }
  //执行深度优先遍历
  public function excuteDfs($key){
    $this->hasList[] = $key;
    foreach($this->arc[$key] as $k=>$v){
      if($v == 1 && !in_array($k, $this->hasList))
        $this->excuteDfs($k);
    }
  }
  //深度优先遍历
  public function dfs(){
    $this->hasList = array();
    foreach($this->vexs as $key){
      if(!in_array($key, $this->hasList))
        $this->excuteDfs($key);
    }
    return implode($this->hasList);
  }
  //返回图的二维数组表示
  public function getArc(){
    return $this->arc;
  }
  //返回结点个数
  public function getVexCount(){
    return count($this->vexs);
  }
}
$a = array('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i');
$b = array('ab'=>'10', 'af'=>'11', 'bg'=>'16', 'fg'=>'17', 'bc'=>'18', 'bi'=>'12', 'ci'=>'8', 'cd'=>'22', 'di'=>'21', 'dg'=>'24', 'gh'=>'19', 'dh'=>'16', 'de'=>'20', 'eh'=>'7','fe'=>'26');//键为边,值权值
$test = new MGraph($a, $b);
print_r($test->bst());

运行结果:

Array
(
  [vexs] => Array
    (
      [0] => a
      [1] => b
      [2] => f
      [3] => i
      [4] => c
      [5] => g
      [6] => h
      [7] => e
      [8] => d
    )
  [arc] => Array
    (
      [ab] => 10
      [af] => 11
      [bi] => 12
      [ic] => 8
      [bg] => 16
      [gh] => 19
      [he] => 7
      [hd] => 16
    )
)

希望本文所述对大家PHP程序设计有所帮助。

PHP 相关文章推荐
PHP概述.
Oct 09 PHP
怎样才能成为PHP高手?学会“懒惰”的编程
Dec 05 PHP
php curl的深入解析
Jun 02 PHP
优化PHP代码技巧的小结
Jun 02 PHP
CodeIgniter实现更改view文件夹路径的方法
Jul 04 PHP
合并ThinkPHP配置文件以消除代码冗余的实现方法
Jul 22 PHP
php+jQuery+Ajax实现点赞效果的方法(附源码下载)
Jul 21 PHP
PHP+MySQL实现的简单投票系统实例
Feb 24 PHP
CakePHP框架Model关联对象用法分析
Aug 04 PHP
php报错502badgateway解决方法
Oct 11 PHP
PHP时间相关常用函数用法示例
Jun 03 PHP
PHP哈希表实现算法原理解析
Dec 11 PHP
PHP+Apache环境中如何隐藏Apache版本
Nov 24 #PHP
实例分析基于PHP微信网页获取用户信息
Nov 24 #PHP
thinkPHP通用控制器实现方法示例
Nov 23 #PHP
PHP substr()函数参数解释及用法讲解
Nov 23 #PHP
Laravle eloquent 多对多模型关联实例详解
Nov 22 #PHP
PHP多维数组排序array详解
Nov 21 #PHP
Ecshop 后台添加新功能栏目及管理权限设置教程
Nov 21 #PHP
You might like
JpGraph php柱状图使用介绍
2011/08/23 PHP
php数组函数序列之array_push() 数组尾部添加一个或多个元素(入栈),返回新长度。
2011/11/07 PHP
ThinkPHP安装和设置
2015/07/27 PHP
基于命令行执行带参数的php脚本并取得参数的方法
2016/01/25 PHP
Laravel多用户认证系统示例详解
2018/03/13 PHP
php7函数,声明,返回值等新特性介绍
2018/05/25 PHP
Laravel中validation验证 返回中文提示 全局设置的方法
2019/09/29 PHP
jQuery 图像裁剪插件Jcrop的简单使用
2009/05/22 Javascript
js 模拟气泡屏保效果代码
2010/07/10 Javascript
jQuery编写widget的一些技巧分享
2010/10/28 Javascript
jQuery.extend 函数的详细用法
2012/06/27 Javascript
Jquery.addClass始终无效原因分析
2013/09/08 Javascript
JS 毫秒转时间示例代码
2013/09/22 Javascript
javascript中 try catch用法
2015/08/16 Javascript
javascript基础语法——全面理解变量和标识符
2016/06/02 Javascript
深入浅析JavaScript的API设计原则
2016/06/14 Javascript
AngularJs Scope详解及示例代码
2016/09/01 Javascript
js编写三级联动简单案例
2016/12/21 Javascript
Mongoose学习全面理解(推荐)
2017/01/21 Javascript
Vue实现自带的过滤器实例
2017/03/09 Javascript
JavaScript观察者模式(publish/subscribe)原理与实现方法
2017/03/30 Javascript
JS简单判断字符在另一个字符串中出现次数的2种常用方法
2017/04/20 Javascript
NodeJS实现同步的方法
2019/03/02 NodeJs
vue canvas绘制矩形并解决由clearRec带来的闪屏问题
2019/09/02 Javascript
原生JavaScript实现日历功能代码实例(无引用Jq)
2019/09/23 Javascript
JavaScript十大取整方法实例教程
2020/12/03 Javascript
Python使用matplotlib填充图形指定区域代码示例
2018/01/16 Python
python实现关键词提取的示例讲解
2018/04/28 Python
django 链接多个数据库 并使用原生sql实现
2020/03/28 Python
python如何查看网页代码
2020/06/07 Python
简述python Scrapy框架
2020/08/17 Python
canvas里面如何基于随机点绘制一个多边形的方法
2018/06/13 HTML / CSS
信用社竞聘演讲稿
2014/05/16 职场文书
银行职员工作失误检讨书
2014/10/14 职场文书
贷款担保书
2015/01/20 职场文书
Python利用FlashText算法实现替换字符串
2022/03/31 Python