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算法系列—— Lowest Common Ancestor of a Binary Search Tree

2017-08-23 17:09 471 查看

题目描述

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.

解题思路

对于二叉搜索树,公共祖先的值一定大于等于较小的节点,小于等于较大的节点。换言之,在遍历树的时候,如果当前结点大于两个节点,则结果在当前结点的左子树里,如果当前结点小于两个节点,则结果在当前节点的右子树里。

程序实现

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