235. Lowest Common Ancestor of a Binary Search Tree (E)

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本文介绍了一种在二叉查找树中寻找两个指定节点最近公共祖先的有效方法。通过利用二叉查找树的特性，算法能够在O(h)的时间复杂度内找到目标节点，其中h为树的高度。

Lowest Common Ancestor of a Binary Search Tree (E)

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]
在这里插入图片描述
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.

题意

在二叉查找树BST中找到两个指定结点的最近共同祖先。

思路

根据定义，两个结点分列于共同祖先的左右两侧(也可以共同祖先重合)，又有BST的排列规则，可以有以下搜索方法：如果p、q的值都小于当前结点，说明共同祖先只可能在左子树；如果p、q的值都大于当前结点，说明共同祖先只可能在右子树；如果p值小于当前结点、q值大于当前结点，或p值大于当前结点、q值小于当前结点，或p、q中一点就是当前结点，说明当前结点就是要找的共同祖先。

代码实现

class Solution {
    public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
        while (root != null) {
            if (p.val < root.val && q.val < root.val) {
                root = root.left;
            } else if (p.val > root.val && q.val > root.val) {
                root = root.right;
            } else {
                break;
            }
        }
        return root;
    }
}