【leetcode】1026. Maximum Difference Between Node and Ancestor

题目如下：

Given the root of a binary tree, find the maximum value V for which there exists different nodes A and B where V = |A.val - B.val| and A is an ancestor of B.

(A node A is an ancestor of B if either: any child of A is equal to B, or any child of A is an ancestor of B.)

Example 1:

Input: [8,3,10,1,6,null,14,null,null,4,7,13]
Output: 7
Explanation: 
We have various ancestor-node differences, some of which are given below :
|8 - 3| = 5
|3 - 7| = 4
|8 - 1| = 7
|10 - 13| = 3
Among all possible differences, the maximum value of 7 is obtained by |8 - 1| = 7.

Note:

1. The number of nodes in the tree is between 2 and 5000.
2. Each node will have value between 0 and 100000.

解题思路：题目要求最大的差值的绝对值。对于任意一个节点来说，其可以得到的最大差值的绝对值只有在这四种情况中：与左子树的最大值，与左子树的最小值，与右子树的最大值，与右子树的最小值。所以只要遍历树，求出每个节点的最大差值，即可得到整棵树的最大差值。当然，为了提高效率，可以缓存每个节点的左子树的最大值、左子树的最小值、右子树的最大值、右子树的最小值。

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 = {} #(max,min)
    res = 0
    def recursive(self,node,num):
        self.dic[num] = (-float('inf'),float('inf'))
        if node.left != None:
            if num*2 not in self.dic:
                self.recursive(node.left, num * 2)
            self.res = max(self.res,abs(node.val - self.dic[num*2][0]),abs(node.val - self.dic[num*2][1]))
            self.dic[num] = (max(node.val,self.dic[num][0],self.dic[num*2][0]),min(node.val,self.dic[num][1],self.dic[num*2][1]))

        if node.right != None:
            inx = num*2 + 1
            if inx not in self.dic:
                self.recursive(node.right, num * 2+1)
            self.res = max(self.res,abs(node.val - self.dic[inx][0]),abs(node.val - self.dic[inx][1]))
            self.dic[num] = (max(node.val,self.dic[num][0],self.dic[inx][0]),min(node.val,self.dic[num][1],self.dic[inx][1]))

        if node.left == None and node.right == None:
            self.dic[num] = (node.val,node.val)


    def maxAncestorDiff(self, root):
        """
        :type root: TreeNode
        :rtype: int
        """
        self.dic = {}
        self.res = 0
        self.recursive(root,1)
        #print self.dic
        return self.res