Lowest Common Ancestor of a Binary Search Tree

最新推荐文章于 2022-10-04 11:47:29 发布

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本文探讨了在二叉搜索树中查找两个指定节点的最低公共祖先（LCA）的问题。提供了详细的解题思路及算法实现，通过递归方式判断节点位置，巧妙利用BST特性快速定位LCA。

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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 p and q as the lowest node in T that has both p and q as descendants (where we allow a node to be a descendant of itself).”

Given binary search tree: root = [6,2,8,0,4,7,9,null,null,3,5]

Example 1:

Input: root = [6,2,8,0,4,7,9,null,null,3,5], p = 2, q = 8
Output: 6
Explanation: The LCA of nodes 2 and 8 is 6.

Example 2:

Input: root = [6,2,8,0,4,7,9,null,null,3,5], p = 2, q = 4
Output: 2
Explanation: The LCA of nodes 2 and 4 is 2, since a node can be a descendant of itself according to the LCA definition.

Note:

All of the nodes' values will be unique.
p and q are different and both values will exist in the BST.

解法：

如果p,q都小于root，那么结果在左边；

如果p,q都大于root，那么结果在右边；

如果一大一小，那么root就是答案；

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
class Solution {
    public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
        
        if(root.val> q.val && root.val > p.val){
            return lowestCommonAncestor(root.left, p, q);
        }else if(root.val < p.val && root.val <q.val){
            return lowestCommonAncestor(root.right, p, q);
        }else{
            return root;
        }
    }
}