Vertical Order Traversal of a Binary Tree

vertical_order_traversal_binary_tree.py

"""
Given a binary tree, return the vertical order traversal of its nodes values.

For each node at position (X, Y), its left and right children respectively will be at positions (X-1, Y-1)
and (X+1, Y-1).

Running a vertical line from X = -infinity to X = +infinity, whenever the vertical line touches some nodes, we report
the values of the nodes in order from top to bottom (decreasing Y coordinates).

If two nodes have the same position, then the value of the node that is reported first is the value that is smaller.

Return an list of non-empty reports in order of X coordinate.  Every report will have a list of values of nodes.

Example 1:
Input: [3,9,20,null,null,15,7]
Output: [[9],[3,15],[20],[7]]
Explanation:
Without loss of generality, we can assume the root node is at position (0, 0):
Then, the node with value 9 occurs at position (-1, -1);
The nodes with values 3 and 15 occur at positions (0, 0) and (0, -2);
The node with value 20 occurs at position (1, -1);
The node with value 7 occurs at position (2, -2).

Example 2:
Input: [1,2,3,4,5,6,7]
Output: [[4],[2],[1,5,6],[3],[7]]
Explanation:
The node with value 5 and the node with value 6 have the same position according to the given scheme.
However, in the report "[1,5,6]", the node value of 5 comes first since 5 is smaller than 6.

Note:
The tree will have between 1 and 1000 nodes.
Each node's value will be between 0 and 1000
Approach:
Respect: Beautifully explained here, found it intuitive than the official solution -
https://leetcode.com/problems/vertical-order-traversal-of-a-binary-tree/discuss/231327/PYTHON-solution-with-explanation
> Root node is considered as 0 horizontal distance.
->As we move left hd is decreased by 1 and is increased by 1 as we move right.
->vd is used to get the top to bottom series.
->comparison in each dic is done based on vd value
-> if vd comes out to be same then node value is compared.
"""
from collections import defaultdict, deque
from typing import List


# Definition for a binary tree node.
class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right


class Solution:
    def verticalTraversal(self, root: TreeNode) -> List[List[int]]:
        if not root:
            return []
        q = deque()
        q.append([root, 0, 0])
        dic = defaultdict(list)
        while q:
            for _ in range(len(q)):
                node, hd, vd = q.popleft()
                dic[hd].append([vd, node.val])
                if node.left:
                    q.append([node.left, hd - 1, vd - 1])
                if node.right:
                    q.append([node.right, hd + 1, vd - 1])
        res = []
        for i in sorted(dic.keys()):
            level = [x[1] for x in sorted(dic[i], key=lambda x: (-x[0], x[1]))]
            res.append(level)
        return res