PHP实现图的邻接矩阵表示及遍历算法

这篇文章主要介绍了PHP实现图的邻接矩阵表示及几种简单遍历算法,结合实例形式分析了php基于邻接矩阵实现图的定义及相关遍历操作技巧,需要的朋友可以参考下

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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] = $key;        }  <i style="color:transparent">本￥文来源gaodai$ma#com搞$代*码*网(</i><strong>搞代gaodaima码</strong>    }    }    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());

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