PHP实现绘制二叉树图形显示功能详解【包括二叉搜索树、平衡树及红黑树】

<?php
/**
 * author:LSGOZJ
 * description: 绘制二叉树图像
 */
class image
{
  //树相关设置
  //每层之间的间隔高度
  private $level_high = 100;
  //最底层叶子结点之间的宽度
  private $leaf_width = 50;
  //结点圆的半径
  private $rad = 20;
  //根节点离边框顶端距离
  private $leave = 20;
  //树（保存树对象的引用）
  private $tree;
  //树的层数
  private $level;
  //完全二叉树中最底层叶子结点数量（计算图像宽度时用到，论如何实现图片大小自适应）
  private $maxCount;
  //图像相关设置
  //画布宽度
  private $width;
  //画布高度
  private $height;
  //画布背景颜色（RGB）
  private $bg = array(
    220, 220, 220
  );
  //节点颜色（搜索二叉树和平衡二叉树时用）
  private $nodeColor = array(
    255, 192, 203
  );
  //图像句柄
  private $image;
  /**
   * 构造函数，类属性初始化
   * @param $tree 传递一个树的对象
   * @return null
   */
  public function __construct($tree)
  {
    $this->tree = $tree;
    $this->level = $this->getLevel();
    $this->maxCount = $this->GetMaxCount($this->level);
    $this->width = ($this->rad * 2 * $this->maxCount) + $this->maxCount * $this->leaf_width;
    $this->height = $this->level * ($this->rad * 2) + $this->level_high * ($this->level - 1) + $this->leave;
    //1.创建画布
    $this->image = imagecreatetruecolor($this->width, $this->height); //新建一个真彩色图像，默认背景是黑色
    //填充背景色
    $bgcolor = imagecolorallocate($this->image, $this->bg[0], $this->bg[1], $this->bg[2]);
    imagefill($this->image, 0, 0, $bgcolor);
  }
  /**
   * 返回传进来的树对象对应的完全二叉树中最底层叶子结点数量
   * @param $level 树的层数
   * @return 结点数量
   */
  function GetMaxCount($level)
  {
    return pow(2, $level - 1);
  }
  /**
   * 获取树对象的层数
   * @param null
   * @return 树的层数
   */
  function getLevel()
  {
    return $this->tree->Depth();
  }
  /**
   * 显示二叉树图像
   * @param null
   * @return null
   */
  public function show()
  {
    $this->draw($this->tree->root, 1, 0, 0);
    header("Content-type:image/png");
    imagepng($this->image);
    imagedestroy($this->image);
  }
  /**
   * （递归）画出二叉树的树状结构
   * @param $root，根节点（树或子树） $i，该根节点所处的层 $p_x，父节点的x坐标 $p_y,父节点的y坐标
   * @return null
   */
  private function draw($root, $i, $p_x, $p_y)
  {
    if ($i <= $this->level) {
      //当前节点的y坐标
      $root_y = $i * $this->rad + ($i - 1) * $this->level_high;
      //当前节点的x坐标
      if (!is_null($parent = $root->parent)) {
        if ($root == $parent->left) {
          $root_x = $p_x - $this->width / (pow(2, $i));
        } else {
          $root_x = $p_x + $this->width / (pow(2, $i));
        }
      } else {
        //根节点
        $root_x = (1 / 2) * $this->width;
        $root_y += $this->leave;
      }
      //画结点（确定所画节点的类型（平衡、红黑、排序）和方法）
      $method = 'draw' . get_class($this->tree) . 'Node';
      $this->$method($root_x, $root_y, $root);
      //将当前节点和父节点连线（黑色线）
      $black = imagecolorallocate($this->image, 0, 0, 0);
      if (!is_null($parent = $root->parent)) {
        imageline($this->image, $p_x, $p_y, $root_x, $root_y, $black);
      }
      //画左子节点
      if (!is_null($root->left)) {
        $this->draw($root->left, $i + 1, $root_x, $root_y);
      }
      //画右子节点
      if (!is_null($root->right)) {
        $this->draw($root->right, $i + 1, $root_x, $root_y);
      }
    }
  }
  /**
   * 画搜索二叉树结点
   * @param $x，当前节点的x坐标 $y，当前节点的y坐标 $node，当前节点的引用
   * @return null
   */
  private function drawBstNode($x, $y, $node)
  {
    //节点圆的线颜色
    $black = imagecolorallocate($this->image, 0, 0, 0);
    $nodeColor = imagecolorallocate($this->image, $this->nodeColor[0], $this->nodeColor[1], $this->nodeColor[2]);
    //画节点圆
    imageellipse($this->image, $x, $y, $this->rad * 2, $this->rad * 2, $black);
    //节点圆颜色填充
    imagefill($this->image, $x, $y, $nodeColor);
    //节点对应的数字
    imagestring($this->image, 4, $x, $y, $node->key, $black);
  }
  /**
   * 画平衡二叉树结点
   * @param $x，当前节点的x坐标 $y，当前节点的y坐标 $node，当前节点的引用
   * @return null
   */
  private function drawAvlNode($x, $y, $node)
  {
    $black = imagecolorallocate($this->image, 0, 0, 0);
    $nodeColor = imagecolorallocate($this->image, $this->nodeColor[0], $this->nodeColor[1], $this->nodeColor[2]);
    imageellipse($this->image, $x, $y, $this->rad * 2, $this->rad * 2, $black);
    imagefill($this->image, $x, $y, $nodeColor);
    imagestring($this->image, 4, $x, $y, $node->key . '(' . $node->bf . ')', $black);
  }
  /**
   * 画红黑树结点
   * @param $x，当前节点的x坐标 $y，当前节点的y坐标 $node，当前节点的引用
   * @return null
   */
  private function drawRbtNode($x, $y, $node)
  {
    $black = imagecolorallocate($this->image, 0, 0, 0);
    $gray = imagecolorallocate($this->image, 180, 180, 180);
    $pink = imagecolorallocate($this->image, 255, 192, 203);
    imageellipse($this->image, $x, $y, $this->rad * 2, $this->rad * 2, $black);
    if ($node->IsRed == TRUE) {
      imagefill($this->image, $x, $y, $pink);
    } else {
      imagefill($this->image, $x, $y, $gray);
    }
    imagestring($this->image, 4, $x, $y, $node->key, $black);
  }
}