Lowest Common Ancestor of a Binary Search Tree

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本文介绍了一种在二叉搜索树中寻找两个指定节点的最低公共祖先的有效方法，并提供了一个递归算法实现。该算法通过比较根节点与目标节点值的关系来决定搜索方向，最终找到公共祖先。

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.

公共祖先要么在左子树，要么在右子树，要么就在根节点，采用递归算法，代码如下：

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