掌握二叉搜索树，剑指Offer第54题迎刃而解

前端

2024-02-13 11:57:51

二叉搜索树概述

二叉搜索树（Binary Search Tree，BST）是一种特殊的二叉树，其结点遵循以下性质：

每个结点的左子树中所有结点的值均小于其根结点的值。
每个结点的右子树中所有结点的值均大于其根结点的值。
左子树和右子树也是二叉搜索树。

二叉搜索树的结构特性使其在查找、插入和删除操作上具有较高的效率。

解题思路

剑指Offer第54题要求我们找到二叉搜索树中第k大的节点。由于二叉搜索树的性质，我们可以利用中序遍历来解决这个问题。

中序遍历二叉搜索树，可以得到一个有序的序列。在这个序列中，第k大的元素就是我们要找的答案。

代码实现

def kth_largest(root, k):
  """
  Finds the kth largest element in a binary search tree.

  Args:
    root: The root node of the binary search tree.
    k: The index of the kth largest element.

  Returns:
    The value of the kth largest element.
  """

  # Initialize a stack to store the nodes that have been visited.
  stack = []

  # Push the root node onto the stack.
  stack.append(root)

  # While the stack is not empty, keep popping nodes and pushing their right child nodes onto the stack.
  while stack:
    # Pop the top node from the stack.
    node = stack.pop()

    # If the node has a right child, push it onto the stack.
    if node.right:
      stack.append(node.right)

    # If the node has no right child, then it is the kth largest element.
    if not node.right or k == 0:
      return node.val

    # Decrement k by 1.
    k -= 1

  # If the stack is empty and k is not 0, then the kth largest element does not exist.
  raise ValueError('Kth largest element does not exist.')