题目如下:

Given a rooted binary tree, return the lowest common ancestor of its deepest leaves.

Recall that:

  • The node of a binary tree is a leaf if and only if it has no children
  • The depth of the root of the tree is 0, and if the depth of a node is d, the depth of each of its children is d+1.
  • The lowest common ancestor of a set S of nodes is the node A with the largest depth such that every node in S is in the subtree with root A.

Example 1:

Input: root = [1,2,3]
Output: [1,2,3]
Explanation:
The deepest leaves are the nodes with values 2 and 3.
The lowest common ancestor of these leaves is the node with value 1.
The answer returned is a TreeNode object (not an array) with serialization "[1,2,3]".

Example 2:

Input: root = [1,2,3,4]
Output: [4]

Example 3:

Input: root = [1,2,3,4,5]
Output: [2,4,5]

Constraints:

  • The given tree will have between 1 and 1000 nodes.
  • Each node of the tree will have a distinct value between 1 and 1000.

解题思路:首先求出最深的所有叶子节点的索引,存入列表中;然后把索引列表排序,取出最大的索引值记为val,显然其父节点的索引值是(val - val%2)/2,把父节点的索引值加入索引列表,并重复这个过程,知道索引列表中所有的值都相等为止,这个值就是所有最深叶子的节点的公共父节点。得到公共父节点索引值,可以反推出从根节点到该节点的遍历路径,从而可以求出具体的节点。

代码如下:

# Definition for a binary tree node.
# class TreeNode(object):
# def __init__(self, x):
# self.val = x
# self.left = None
# self.right = None class Solution(object):
dic = {}
maxLevel = 0
def recursive(self,node,level,number):
self.maxLevel = max(self.maxLevel,level)
self.dic[level] = self.dic.setdefault(level,[]) + [number]
if node.left != None:
self.recursive(node.left,level+1,number*2)
if node.right != None:
self.recursive(node.right,level+1,number*2+1)
def lcaDeepestLeaves(self, root):
"""
:type root: TreeNode
:rtype: TreeNode
"""
self.dic = {}
self.maxLevel = 0
self.recursive(root,1,1)
node_list = sorted(self.dic[self.maxLevel])
def isEqual(node_list):
v = node_list[0]
for i in node_list:
if v != i:
return False
return True
while not isEqual(node_list):
node_list.sort(reverse=True)
val = node_list.pop(0)
val = (val - val%2)/2
node_list.append(val)
number = node_list[0]
path = []
while number > 1:
if number%2 == 0:
path = ['L'] + path
else:
path = ['R'] + path
number = (number - number % 2) / 2 node = root
while len(path) > 0:
p = path.pop(0)
if p == 'L':node = node.left
else:node = node.right
return node

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