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235. Lowest Common Ancestor of a Binary Search Tree

Leetcode Tree

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]

        _______6______
       /              \
    ___2__          ___8__
   /      \        /      \
   0      _4       7       9
         /  \
         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.

分析

最近公共祖先，有两层主要含义：第一，必须是公共祖先，第二，节点所在的高度要是最高的。

那么怎么寻找最近公共祖先呢？注意，题目的限定————二叉搜索树，这里要用到二叉搜索树的性质。

  • 如果p, q都比根节点小，则在左子树中递归查找LCA。
  • 如果p, q都比根节点大，则在右子树中递归查找LCA。
  • 如果p, q一个比根节点大，一个比根节点小，或有一个等于根节点，则根节点为LCA。
public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
    if (p.val < root.val && q.val < root.val) return lowestCommonAncestor(root.left, p, q);
    if (p.val > root.val && q.val > root.val) return lowestCommonAncestor(root.right, p, q);
    return root;
}