LCA of 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).”

  1.         _______3______
  2.        /              \
  3.     ___5__          ___1__
  4.    /      \        /      \
  5.    6      _2       0       8
  6.          /  \
  7.          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

  1. // Lowest Common Ancestor of a Binary Tree
  2. // Time complexity: O(n), Space complexity: O(h)
  3. public class Solution {
  4.     public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
  5.         // if root is null or found p or q
  6.         if (root == null || root == p || root == q) return root;
  7.         // find p or q in the left subtree
  8.         final TreeNode left = lowestCommonAncestor(root.left, p, q);
  9.         // find p or q in the right subtree
  10.         final TreeNode right = lowestCommonAncestor(root.right, p, q);
  11.         if (left != null && right != null) return root;
  12.         else return left == null ? right : left;
  13.     }
  14. }

相关题目

原文: https://soulmachine.gitbooks.io/algorithm-essentials/content/java/binary-tree/recursion/lca-of-binary-tree.html