Tags: "leetcode", "hashmap", "dfs", access_time 2-min read

Vertical Order Traversal of a Binary Tree

Created: February 27, 2020 by [lek-tin]

Last updated: February 27, 2020

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

1. The tree will have between 1 and 1000 nodes.
2. Each node’s value will be between 0 and 1000.

Solution

Time: O(NlogN)
Space: O(N)
Nodes stored into list: lookup[col][row]

class Solution:
    def verticalTraversal(self, root: TreeNode) -> List[List[int]]:
        def dfs(node, lookup, col, row):
            if not node:
                return
            lookup[col][row].append(node)
            dfs(node.left, lookup, col-1, row+1)
            dfs(node.right, lookup, col+1, row+1)

        # lookup shape:
        # {
        #     int: {
        #         int: []
        #     }
        # }
        lookup = collections.defaultdict(lambda: collections.defaultdict(list))
        dfs(root, lookup, 0, 0)

        result = []
        for col in sorted(lookup):
            vertical = []
            for row in sorted(lookup[col]):
                print("col:", col, "row:", row)
                # find which node comes above vertically
                vertical.extend(sorted(node.val for node in lookup[col][row]))
            result.append(vertical)
            print("------")
        return result