PHP实现图的邻接矩阵表示及几种简单遍历算法分析

　　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 ) )

　　更多关于PHP相关内容感兴趣的读者可查看本站专题：《PHP数据结构与算法教程》、《php程序设计算法总结》、《php字符串(string)用法总结》、《PHP数组(Array)操作技巧大全》、《PHP常用遍历算法与技巧总结》及《PHP数学运算技巧总结》

　　希望本文所述对大家PHP程序设计有所帮助。