leetcode之Lowest Common Ancestor of a Binary Search Tree

最新推荐文章于 2025-08-13 22:03:49 发布

原创最新推荐文章于 2025-08-13 22:03:49 发布 · 186 阅读

0 ·

CC 4.0 BY-SA版权

文章标签：

#leetcode #算法 #面试

本文介绍了一种在二叉搜索树中寻找两个节点最低共同祖先(LCA)的有效算法。利用二叉搜索树的特性，该算法通过递归方式在树中进行搜索，当找到目标节点或达到叶节点时返回相应的节点信息。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

题目：

Given a binary search tree (BST), find the lowest common ancestor (LCA) of two given nodes in the BST.

According to the definition of LCA on Wikipedia: “The lowest common ancestor is defined between two nodes v and w as the lowest node in T that has both v and w as descendants (where we allow a node to be a descendant of itself).”

        _______6______
       /              \
    ___2__          ___8__
   /      \        /      \
   0      _4       7       9
         /  \
         3   5

For example, the lowest common ancestor (LCA) of nodes 2 and 8 is 6. Another example is LCA of nodes 2 and 4 is 2, since a node can be a descendant of itself according to the LCA definition.

解答：

和之前的BST找LCA有相似之处，不同的是BST有特性可以更加方便的查找，一般的二叉树则没有，需要利用前序遍历来进行查找，总体的思路就是在递归的同时如果出现了查找的目标就将其返回，没有就返回NULL，直到找到LCA即可（看代码就懂了，不是很善于口头描述），一开始还傻傻的把整个搜索路径保存下来了，(⊙﹏⊙)b。。。

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    TreeNode* lowestCommonAncestor(TreeNode* root, TreeNode* p, TreeNode* q) {
        if(root == NULL || root == q || root == p)
            return root;
        TreeNode *left = lowestCommonAncestor(root->left, p, q);
        TreeNode *right = lowestCommonAncestor(root->right, p, q);
        if(left && right)//表示已经找到了LCA
            return root;
        if(left == NULL)
            return right;
        if(right == NULL)
            return left;
    }
};