《leetCode》:Lowest Common Ancestor of a Binary Search Tree

题目

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

简单来说：就是寻找某个节点的值在所要找的节点的中间，则此节点即为所求。

由于是二叉搜索树，因此，利用二叉搜索树的特点即可完成。如果要判断的节点的值比root的值一大一小(包括等于)，则root节点即为所求，如果要判断的节点的值均比root小，则其Lowest Common Ancestor就在roo节点的左边，同理，如果要判断的节点的值均比root的值大，则则其Lowest Common Ancestor就在roo节点的右边，这样利用递归就可以找到他们的Lowest Common Ancestor。

实现代码如下：

public class Solution {

public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
if(root==null||p==null||q==null){
return null;
}
if(p.val<=root.val&&root.val<=q.val||(q.val<=root.val&&root.val<=p.val)){
return root;
}
else if(p.val<root.val&&p.val<root.val){
return lowestCommonAncestor(root.left,p,q);
}
else/* if(p.val>root.val&&q.val>root.val)*/{
return lowestCommonAncestor(root.right,p,q);
}

}
}