LeetCode 236 Lowest Common Ancestor of a Binary Tree

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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).”

Example 1:

<pre>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. </pre>

Example 2:

<pre>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. </pre>

Example 3:

<pre>Input: root = [1,2], p = 1, q = 2 Output: 1 </pre>

Constraints:

The number of nodes in the tree is in the range [2, 10<sup>5</sup>].
-10<sup>9</sup> <= Node.val <= 10<sup>9</sup>
All Node.val are unique.
p != q
p and q will exist in the tree.

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题目大意：

二叉树中求给定的两节点的最低共同父亲节点

解题思路：

DFS

解题步骤：

N/A

注意事项：

pq一定存在，所以有**三种情况： 1) p或q是root，另一是其子孙。 2) p，q分列root两边。 3) p，q在root的一边

Python代码：

def lowestCommonAncestor(self, root: 'TreeNode', p: 'TreeNode', q: 'TreeNode') -> 'TreeNode':
	if not root:
		return None
	if root == p or root == q:
		return root
	left = self.lowestCommonAncestor(root.left, p, q)
	right = self.lowestCommonAncestor(root.right, p, q)
	if left and right:
		return root
	return left if left else right

算法分析：

时间复杂度为O(n)，空间复杂度O(1)。

算法II解题思路：

BFS遍历树（可以找到就停止），然后记录子节点到父节点的映射，将所有父节点放到set中，同样查找另一个节点的父节点们，找到第一个在set中的节点。