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.

解法：二插搜索树特点，根节点值大于左子节点值小于右子节点值。设树中任两节点为p和q,分三种情况考虑：

①root.val > p.val && root.val > q.val,说明p和q的LCA在root的左子树中；

②root.val < p.val && root.val < q.val,说明p和q的LCA在root的右子树中；

③其他情况，说明p和q的LCA就是root;

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