二叉树上的递归删除

recursive delete on a binary tree

本文关键字：删除 递归 二叉树      更新时间：2023-10-16

我试图了解二叉搜索树删除的递归方法是如何工作的。我在很多地方遇到的代码如下所示:

void destroy_tree(struct node *leaf)
{
  if( leaf != 0 )
  {
      destroy_tree(leaf->left);
      destroy_tree(leaf->right);
      free( leaf );
  }
}

我不能理解然而a)如果在例程中没有返回，它是如何工作的?B) free()何时被调用?我想到，例如，这样一棵树:

                           10
                         /    
                        6      14
                       /     /  
                      5   8  11  18

所以我的理解是我遍历10->6->5，然后调用destroy_tree(5->left)。因此，if内部的leaf为NULL，并且不执行与if相关的内容，因此5不会被删除。我在这个推理中哪里出错了?卷绕和unwind是如何工作的呢?任何帮助都非常感谢:-)

在那个点是这样的:

void destroy_tree(struct node *leaf_5)
{
  if( leaf_5 != 0 )  // it's not
  {
      destroy_tree(leaf_5->left); // it's NULL so the call does nothing
      destroy_tree(leaf_5->right); // it's NULL so the call does nothing
      free( leaf_5 );  // free here
  }
}

不需要返回…步骤的"历史记录"位于调用堆栈中，此时看起来像这样:

destroy_tree(leaf_10)
  destroy_tree(leaf_10->left, which is leaf_6)
    destroy_tree(leaf_6->left, which is leaf_5)

所以在leaf_5消失后，它回到堆栈并执行destroy_tree(leaf_6->right, which is leaf_8)…等等…

函数的基本工作原理:

void destroy_tree(struct node *leaf)
{
  if( leaf_5 != 0 )  // it's not
  {
      destroy_tree(leaf->left); 
       // Traverse the tree all the way left before any of the code below gets executed.
      destroy_tree(leaf->right); 
       // Traverse the tree all the way right from the final left node before any of 
       //the code below gets executed
      free( leaf );  // Free the final node
  }
}

下面是递归删除的完整实现代码:

void DeleteNode(TreeNode*& tree);
void Delete(TreeNode*& tree, ItemType item);
void TreeType::DeleteItem(ItemType item)
// Calls the recursive function Delete to delete item from tree.
{
Delete(root, item);
}
void Delete(TreeNode*& tree, ItemType item)
// Deletes item from tree.
// Post: item is not in tree.
{
if (item < tree->info)
Delete(tree->left, item); // Look in left subtree.
else if (item > tree->info)
Delete(tree->right, item); // Look in right subtree.
else
DeleteNode(tree); // Node found; call DeleteNode.
}

void GetPredecessor(TreeNode* tree, ItemType& data);
void DeleteNode(TreeNode*& tree)
// Deletes the node pointed to by tree.
// Post: The user's data in the node pointed to by tree is no
// longer in the tree. If tree is a leaf node or has only one
// non-NULL child pointer, the node pointed to by tree is
// deleted; otherwise, the user's data is replaced by its
// logical predecessor and the predecessor's node is deleted.
{
ItemType data;
TreeNode* tempPtr;
tempPtr = tree;
if (tree->left == NULL)
{
tree = tree->right;
delete tempPtr;
}
else if (tree->right == NULL)
{
tree = tree->left;
delete tempPtr;
}
else
{
GetPredecessor(tree->left, data);
tree->info = data;
Delete(tree->left, data); // Delete predecessor node.
}
}
void GetPredecessor(TreeNode* tree, ItemType& data)
// Sets data to the info member of the rightmost node in tree.
{
while (tree->right != NULL)
tree = tree->right;
data = tree->info;
}
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