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https://leetcode.com/problems/lowest-common-ancestor-of-a-binary-search-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 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：
CC150里4.7，但是原题是任意二叉树，这里更为简单，被限定为二叉搜索树。
根据BST的性质，root.left.val < root.val < root.right.val，并且所有子树也都是BST。我们的思路就变成判断p和q到底是在root的哪边。
1. 如果都小于root.val，一定同时在左侧，root不是lca，递归搜索左子树。
2. 如果都大于root.val，递归搜索右子树。
3. 否则，分别在root两侧，root就是lca。
/** * 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) { return null; } if(root == p || root == q) { return root; } TreeNode left = lowestCommonAncestor(root.left, p, q); TreeNode right = lowestCommonAncestor(root.right, p, q); if(left == null || right == null) { return left == null ? right : left; } return root; } }
上面算法的时间复杂度是O(logn)，等于树的高度。下面的算法可以用在任意二叉树，不一定是BST。
仅在root左右子树都分别找到p和q的情况下返回root，说明root是p和q的lca。否则找不到的返回null，找到的一侧返回p或者q。
/** * 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) { return null; } if(root == p || root == q) { return root; } TreeNode left = lowestCommonAncestor(root.left, p, q); TreeNode right = lowestCommonAncestor(root.right, p, q); if(left == null || right == null) { return left == null ? right : left; } return root; } }
上面的解法时间复杂度为O(n)。
Lowest Common Ancestor of a Binary Search Tree
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原文地址：http://www.cnblogs.com/NickyYe/p/4638644.html
