PHP實(shí)現(xiàn)圖的鄰接矩陣表示及幾種簡(jiǎn)單遍歷算法分析

?php
/**
 * PHP 實(shí)現(xiàn)圖鄰接矩陣
 */
class MGraph{
  private $vexs; //頂點(diǎn)數(shù)組
  private $arc; //邊鄰接矩陣,即二維數(shù)組
  private $arcData; //邊的數(shù)組信息
  private $direct; //圖的類型(無(wú)向或有向)
  private $hasList; //嘗試遍歷時(shí)存儲(chǔ)遍歷過(guò)的結(jié)點(diǎn)
  private $queue; //廣度優(yōu)先遍歷時(shí)存儲(chǔ)孩子結(jié)點(diǎn)的隊(duì)列,用數(shù)組模仿
  private $infinity = 65535;//代表無(wú)窮,即兩點(diǎn)無(wú)連接,建帶權(quán)值的圖時(shí)用,本示例不帶權(quán)值
  private $primVexs; //prim算法時(shí)保存頂點(diǎn)
  private $primArc; //prim算法時(shí)保存邊
  private $krus;//kruscal算法時(shí)保存邊的信息
  public function MGraph($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);
      }
    }
  }
  //創(chuàng)建圖 $direct:0表示無(wú)向圖,1表示有向圖
  private function createArc(){
    foreach($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();//路徑數(shù)組
    $distance = array();//距離數(shù)組
    foreach($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();//要查找的結(jié)點(diǎn)的前一個(gè)結(jié)點(diǎn)數(shù)組
    $weight = array();//權(quán)值和數(shù)組
    foreach($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] = $end;
        }
      }
    }
  }
  //查找子樹(shù)的尾結(jié)點(diǎn)
  private function findRoot($node){
    while($this->krus[$node] > 0){
      $node = $this->krus[$node];
    }
    return $node;
  }
  //prim算法,生成最小生成樹(shù)
  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,生成最小生成樹(shù)
  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);
  }
  //一般遍歷
  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);
  }
  //廣度優(yōu)先遍歷
  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($this->hasList);
  }
  //執(zhí)行深度優(yōu)先遍歷
  public function excuteDfs($key){
    $this->hasList[] = $key;
    foreach($this->arc[$key] as $k=>$v){
      if($v == 1  !in_array($k, $this->hasList))
        $this->excuteDfs($k);
    }
  }
  //深度優(yōu)先遍歷
  public function dfs(){
    $this->hasList = array();
    foreach($this->vexs as $key){
      if(!in_array($key, $this->hasList))
        $this->excuteDfs($key);
    }
    return implode($this->hasList);
  }
  //返回圖的二維數(shù)組表示
  public function getArc(){
    return $this->arc;
  }
  //返回結(jié)點(diǎn)個(gè)數(shù)
  public function getVexCount(){
    return count($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');//鍵為邊,值權(quán)值
$test = new MGraph($a, $b);
print_r($test->bst());

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
    )
)