leetcode 236 Lowest Common Ancestor of a Binary Tree
z
 2019-04-09 11:39:36  

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 p and q as the lowest node in T that has both p and q as descendants (where we allow a node to be a descendant of itself).”

Given the following binary tree: root = [3,5,1,6,2,0,8,null,null,7,4]

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Example 1:

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Input: root = [3,5,1,6,2,0,8,null,null,7,4], p = 5, q = 1
Output: 3
Explanation: The LCA of nodes 5 and 1 is 3.

Example 2:

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Input: root = [3,5,1,6,2,0,8,null,null,7,4], p = 5, q = 4
Output: 5
Explanation: The LCA of nodes 5 and 4 is 5, since a node can be a descendant of itself according to the LCA definition.

Note:

  • All of the nodes’ values will be unique.
  • p and q are different and both values will exist in the binary tree.
  • 最小公共节点的特征: p 和 q 要么分别来自它的左右分支，要么p和q中有一本身就是最小公共节点。
  • 这样一来，可以用递归的方式，先依次遍历每一个节点。递归的在每一个节点的左右节点查找p和q
  • 如果当前节点的左右分支都有返回值，那么当前节点就是一个最小公共节点
  • 否则，由于公共最小节点可定存在，那么左右分支中必有一个是返回值。返回左右节点中非空的那个
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class Solution {
  public TreeNode smallestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
    if (root == null || root == p || root == q)
      return root;
    TreeNode left = smallestCommonAncesstor(root.left, p, q);
    TreeNode right = smallestCommonAncesstor(root.right, p, q);
    if (left != null && right != null) {
      return root;
    }
    if (left == null)
      return right;
    return left;
  }
}