Vertical Order Traversal of a Binary Tree

Tested Python solution for LeetCode 987 with 19 pytest cases. Generate a practice environment with lcpy.

LeetCode 987, Hard. Topics: Hash Table, Tree, Depth-First Search, Breadth-First Search, Sorting, Binary Tree. View on LeetCode.

Generate this problem as a practice environment: tested reference solution, 19 parametrized pytest cases, and a playground notebook:

lcpy gen -n 987   # by problem number
lcpy gen -s vertical_order_traversal_of_a_binary_tree   # by problem name

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Problem

Given the root of a binary tree, calculate the vertical order traversal of the binary tree.

For each node at position (row, col), its left and right children will be at positions (row + 1, col - 1) and (row + 1, col + 1) respectively. The root of the tree is at (0, 0).

The vertical order traversal of a binary tree is a list of top-to-bottom orderings for each column index starting from the leftmost column and ending on the rightmost column. There may be multiple nodes in the same row and same column. In such a case, sort these nodes by their values.

Return the vertical order traversal of the binary tree.

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Examples

Input: root = [3,9,20,null,null,15,7]
Output: [[9],[3,15],[20],[7]]

Column -1: Only node 9 is in this column. Column 0: Nodes 3 and 15 are in this column in that order from top to bottom. Column 1: Only node 20 is in this column. Column 2: Only node 7 is in this column.

Input: root = [1,2,3,4,5,6,7]
Output: [[4],[2],[1,5,6],[3],[7]]

Column -2: Only node 4 is in this column. Column -1: Only node 2 is in this column. Column 0: Nodes 1, 5, and 6 are in this column. 1 is at the top, so it comes first. 5 and 6 are at the same position (2, 0), so we order them by their value, 5 before 6. Column 1: Only node 3 is in this column. Column 2: Only node 7 is in this column.

Input: root = [1,2,3,4,6,5,7]
Output: [[4],[2],[1,5,6],[3],[7]]

This case is the exact same as example 2, but with nodes 5 and 6 swapped. Note that the solution remains the same since 5 and 6 are in the same location and should be ordered by their values.

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Constraints

• The number of nodes in the tree is in the range [1, 1000]
• 0 <= Node.val <= 1000

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Solution

Reference implementation from solution.py on GitHub, full suite in test_solution.py:

from leetcode_py import TreeNode


class Solution:
    # Time: O(n log n)
    # Space: O(n)
    def vertical_traversal(self, root: TreeNode[int] | None) -> list[list[int]]:
        nodes: list[tuple[int, int, int]] = []

        def dfs(node: TreeNode[int] | None, row: int, col: int) -> None:
            if node is None:
                return
            nodes.append((col, row, node.val))
            dfs(node.left, row + 1, col - 1)
            dfs(node.right, row + 1, col + 1)

        dfs(root, 0, 0)
        nodes.sort()

        columns: dict[int, list[int]] = {}
        for col, _row, val in nodes:
            columns.setdefault(col, []).append(val)
        return [columns[col] for col in sorted(columns)]

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Complexity

Time	Space
O(n log n)	O(n)

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