Leetcode_235_Lowest Common Ancestor of a Binary Search Tree

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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 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.

思路：

（1）题意为给定一个BST以及该树上两节点，求这两节点的最近公共祖先。

（2）该题比较简单，通过递归很好实现。如果两节点分别分布在根节点的左右子树上，那么它们的最近公共祖先只能是树根；如果两节点同时分部在根节点的相同子树上，则需要分别递归进行判定。

（3）详情见下方代码。希望本文对你有所帮助。

算法代码实现如下：

package leetcode;

import leetcode.utils.TreeNode;

/**
 *
 * @author liqqc
 *
 */
public class Lowest_Common_Ancestor_of_a_Binary_Search_Tree {

	public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
		// 在树的两边
		if (p.val >= root.val && q.val <= root.val)
			return root;

		else if (p.val <= root.val && q.val >= root.val)
			return root;

		// 在树的一边 左边或右边
		else if (p.val < root.val && q.val < root.val) {
			// 左边

			return lowestCommonAncestor(root.left, p, q);

		}

		else {

			// 右边

			return lowestCommonAncestor(root.right, p, q);

		}

	}
}