LeetCode (236):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:

节点a与节点b的公共祖先c一定满足：a与b分别出现在c的左右子树上（如果a或者b本身不是祖先的话）。

Java代码：

class TreeNode {
     int val;
     TreeNode left;
     TreeNode right;
     TreeNode(int x) { val = x; }
 }

public class Solution {
     public static TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
         if(root==null) return null;
         if(root==p||root==q) return root;
         TreeNode L=lowestCommonAncestor(root.left,p,q);
         TreeNode R=lowestCommonAncestor(root.right,p,q);
         if(L!=null&&R!=null) return root;
        return L!=null?L:R;
        }
//test
    public static void main(String[] args) {
        // TODO Auto-generated method stub
        TreeNode tr=new TreeNode(1);
        TreeNode nodeB=new TreeNode(2);
        TreeNode nodeC=new TreeNode(3);
        TreeNode nodeD=new TreeNode(4);
        TreeNode nodeE=new TreeNode(5);
        tr.left=nodeB;
        tr.right=nodeC;
        tr.left.right=nodeD;
        tr.left.left=nodeE;
        System.out.print(lowestCommonAncestor(tr, nodeC, nodeE).val);
    }

}