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
一个php作的文本留言本的例子(五)
Oct 09 PHP
生成静态页面的php函数,php爱好者站推荐
Mar 19 PHP
基于PHP编程注意事项的小结
Apr 27 PHP
用PHP代码给图片加水印
Jul 01 PHP
四个PHP非常实用的功能
Sep 29 PHP
分享php代码将360浏览器导出的favdb的sqlite数据库文件转换为html
Dec 09 PHP
php实现简单爬虫的开发
Mar 28 PHP
laravel创建类似ThinPHP中functions.php的全局函数
Nov 26 PHP
PHP面向对象之工作单元(实例讲解)
Jun 26 PHP
360搜索引擎自动收录php改写方案
Apr 28 PHP
PHP7匿名类的用法示例
Apr 05 PHP
php设计模式之正面模式实例分析【星际争霸游戏案例】
Mar 24 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
php下获取Discuz论坛登录用户名、用户组、用户ID等信息的实现代码
2010/12/29 PHP
thinkphp3.2.2前后台公用类架构问题分析
2014/11/25 PHP
php+xml实现在线英文词典之添加词条的方法
2015/01/23 PHP
php socket通信简单实现
2016/11/18 PHP
Laravel 中使用简单的方法跟踪用户是否在线(推荐)
2019/10/30 PHP
Package.js  现代化的JavaScript项目make工具
2012/05/23 Javascript
创建公共调用 jQuery Ajax 带返回值
2012/08/01 Javascript
JavaScript控制Session操作方法
2013/01/17 Javascript
让元素在网页中可拖动示例代码
2013/08/13 Javascript
JS匀速运动演示示例代码
2013/11/26 Javascript
纯javascript实现四方向文本无缝滚动效果
2015/06/16 Javascript
css如何让浮动元素水平居中
2015/08/07 Javascript
javaScript实现可缩放的显示区效果代码
2015/10/26 Javascript
最简单的JavaScript图片轮播代码(两种方法)
2015/12/18 Javascript
JavaScript拖拽、碰撞、重力及弹性运动实例分析
2016/01/08 Javascript
JavaScript插件Tab选项卡效果
2017/11/14 Javascript
改进 JavaScript 和 Rust 的互操作性并深入认识 wasm-bindgen 组件
2019/07/13 Javascript
Vuex,iView UI面包屑导航使用扩展详解
2019/11/04 Javascript
python使用PyV8执行javascript代码示例分享
2013/12/04 Python
python使用多线程不断刷新网页的方法
2015/03/31 Python
python的socket编程入门
2018/01/29 Python
python实现微信远程控制电脑
2018/02/22 Python
Django框架实现的分页demo示例
2019/05/25 Python
python编写简单端口扫描器
2019/09/04 Python
pycharm 更改创建文件默认路径的操作
2020/02/15 Python
利用python实现凯撒密码加解密功能
2020/03/31 Python
python 列表推导和生成器表达式的使用
2021/02/01 Python
伦敦平价潮流珠宝首饰品牌:Astrid & Miyu
2016/10/10 全球购物
加拿大鞋网:Globo Shoes
2019/12/26 全球购物
乡镇食品安全责任书
2014/07/28 职场文书
2014年林业工作总结
2014/12/05 职场文书
帝企鹅日记观后感
2015/06/10 职场文书
2016年“11.11”光棍节活动总结
2016/04/05 职场文书
完美解决golang go get私有仓库的问题
2021/05/05 Golang
MySQL 数据 data 基本操作
2022/05/04 MySQL
Moment的feature导致线上bug解决分析
2022/09/23 Javascript