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PHP实现二叉排序树的插入&查询&删除

代码实现

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<?php

class BNode
{
    public $data;
    public $left;
    public $right;

    public function __construct($data = null)
    {
        $this->data = $data;
    }
}

class BTree
{
    public $root;

    public function insert($value): BTree
    {
        $node = new BNode($value);
        if (!$this->root) {
            $this->root = $node;
            return $this;
        }
        $current = $this->root;

        while (true) {
            if ($value < $current->data) {
                if (!$current->left) {
                    $current->left = $node;
                    break;
                }
                $current = $current->left;
            } else {
                if (!$current->right) {
                    $current->right = $node;
                    break;
                }
                $current = $current->right;
            }
        }
        return $this;
    }

    public function search($value): ?BNode
    {
        if (!$this->root) {
            return null;
        }
        $current = $this->root;
        while (true) {
            if ($value === $current->data) {
                return $current;
            }
            if ($value < $current->data) {
                if (!$current->left) {
                    $current = null;
                    break;
                }
                $current = $current->left;
            } else {
                if (!$current->right) {
                    $current = null;
                    break;
                }
                $current = $current->right;
            }
        }
        return $current;
    }

    public function delete($value)
    {
        $parent = null;
        $current = $this->root;
        while (true) {
            // 已找到要删除的节点
            if ($value === $current->data) {
                // 1. 删除的节点没有子节点
                if (!$current->left && !$current->right) {
                    // 如果父节点是null,说明删除的是根节点，把根节点设置为null
                    if (!$parent) {
                        $this->root = null;
                        break;
                    }
                    if ($parent->left === $current) {
                        $parent->left = null;
                    } else {
                        $parent->right = null;
                    }
                    break;
                }
                // 2. 删除的节点有一个子节点
                // 当前节点有左子节点，没有右子节点
                if ($current->left && !$current->right) {
                    // 如果父节点是null,说明删除的是根节点，把删除的节点的左子节点设置为根节点
                    if (!$parent) {
                        $this->root = $current->left;
                        break;
                    }
                    // 如果父节点的左子节点等于当前节点，说明要删除的节点是父节点的左子节点，把当前节点的左子节点设置为父节点的左子节点
                    if ($parent->left === $current) {
                        $parent->left = $current->left;
                    } else {
                        // 反之，如果父节点的右子节点等于当前节点，说明要删除的节点是父节点的右子节点，把当前节点的左子节点设置为父节点的右子节点
                        $parent->right = $current->left;
                    }
                    break;
                }
                // 当前节点有右子节点，没有左子节点
                if (!$current->left && $current->right) {
                    // 如果父节点为null，说明删除的是根节点，把删除的节点的右子节点设置为根节点
                    if (!$parent) {
                        $this->root = $current->right;
                        break;
                    }
                    if ($parent->left === $current) {
                        // 如果父节点的左子节点等于当前节点，说明要删除的节点是父节点的左子节点，把当前节点的右子节点设置为父节点的左子节点
                        $parent->left = $current->right;
                    } else {
                        // 反之，如果父节点的右子节点等于当前节点，说明要删除的节点是父节点的右子节点，把当前节点的右子节点设置为父节点的右子节点
                        $parent->right = $current->right;
                    }
                    break;
                }
                // 3. 删除的节点有两个子节点
                if ($current->left && $current->right) {
                    // 这里首先要明白一个概念，二叉树的中序后继节点/中序前驱节点，我这里找的是中序后继节点
                    $minParent = $current;
                    $minNode = $current->right;
                    while ($minNode->left) {
                        $minParent = $minNode;
                        $minNode = $minNode->letf;
                    }
                    $current->data = $minNode->data;


                    if ($current->right === $minNode) {
                        $current->right = $minNode->right;
                        break;
                    }

                    // 这中情况是删除的节点有两个子节点，且找到了中序后继节点，因为中序后继节点需要替换到被删除的节点位置
                    // 所以中序后继节点的父节点的左子节点需要设置为中序后继节点的右子节点，因为中序后继节点的左子节点一定是null
                    $minParent->left = $minNode->right;
                    break;
                }
            }
            if ($value < $current->data) {
                $parent = $current;
                $current = $current->left;
            }
            if ($value > $current->data) {
                $parent = $current;
                $current = $current->right;
            }
        }
        return $this;
    }
}

示例

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// 插入
$bTree = new BTree();
$bTree->insert(20)->insert(10)->insert(30)->insert(7)->insert(3)->insert(23)->insert(15)->insert(12)->insert(17)->insert(8);
echo "<pre>";
print_r($bTree);


// 查找
$node = $bTree->search(30);
print_r($node);

// 删除
$bTree->delete(7);
print_r($bTree);