First 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.
Solution
This problem can be solved by using BST property, i.e., left < parent < right for each node. There are 3 cases to handle.
Complexity
时间复杂度 O(n),空间复杂度 O(h)
Code
/**
* 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) {
TreeNode m = root;
if(m.val > p.val && m.val < q.val){
return m;
}else if(m.val>p.val && m.val > q.val){
return lowestCommonAncestor(root.left, p, q);
}else if(m.val<p.val && m.val < q.val){
return lowestCommonAncestor(root.right, p, q);
}
return root;
}
}