Lowest Common Ancestor of a Binary Tree
描述
Given a binary tree, find the lowest common ancestor (LCA) of two given nodes in the tree.
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).”
_______3______
/ \
___5__ ___1__
/ \ / \
6 _2 0 8
/ \
7 4
For example, the lowest common ancestor (LCA) of nodes 5 and 1 is 3. Another example is LCA of nodes 5 and 4 is 5, since a node can be a descendant of itself according to the LCA definition.
分析
用自底向上(bottom-up)的思路，先看看是否能在root的左子树中找到p或q，再看看能否在右子树中找到，
- 如果两边都能找到，说明当前节点就是最近公共祖先
- 如果左边没找到，则说明
p和q都在右子树 - 如果右边没找到，则说明
p和q都在左子树
代码
// Lowest Common Ancestor of a Binary Tree
// Time complexity: O(n), Space complexity: O(h)
public class Solution {
public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
// if root is null or found p or q
if (root == null || root == p || root == q) return root;
// find p or q in the left subtree
final TreeNode left = lowestCommonAncestor(root.left, p, q);
// find p or q in the right subtree
final TreeNode right = lowestCommonAncestor(root.right, p, q);
if (left != null && right != null) return root;
else return left == null ? right : left;
}
}