【leetcode】1104. Path In Zigzag Labelled Binary Tree

题目如下：

In an infinite binary tree where every node has two children, the nodes are labelled in row order.

In the odd numbered rows (ie., the first, third, fifth,...), the labelling is left to right, while in the even numbered rows (second, fourth, sixth,...), the labelling is right to left.

Given the label of a node in this tree, return the labels in the path from the root of the tree to the node with that label.

Example 1:

Input: label = 14
Output: [1,3,4,14]

Example 2:

Input: label = 26
Output: [1,2,6,10,26]

Constraints:

• 1 <= label <= 10^6

解题思路：先把正常的路径(即不是蛇形排列的数)求出来，接下来自底向顶遍历，偶数行的值需要交换，交换的逻辑也很简单，求出该层最左边和最右边的节点的number，记为low和一个high，那么对于number为inx的节点，其交换后的number就是： (low + high) - inx。

代码如下：

class Solution(object):
    def pathInZigZagTree(self, label):
        """
        :type label: int
        :rtype: List[int]
        """
        res = []
        level = 0
        while label != 0:
            res.insert(0,label)
            label = label/2
            level += 1

        swap = False
        while level > 0:
            if swap:
                low = 2**(level-1)
                high = (low * 2 - 1)
                res[level-1] = (low + high) - res[level-1]
            swap = not swap
            level -= 1
        return res