Day 29 - Vertical Order Traversal of a Binary Tree
Tags: leetcode, python, challenge
Published: 2021-01-31 16:41:30

>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.

__Example 1:__

![Alt Text](https://dev-to-uploads.s3.amazonaws.com/i/kcx9eumqbqg9zs78d7i3.jpg)

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

__Example 2:__

![Alt Text](https://dev-to-uploads.s3.amazonaws.com/i/hyg1bnl23x9xjpwk2svi.jpg)

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

__Example 3:__

![Alt Text](https://dev-to-uploads.s3.amazonaws.com/i/gcf2u454gal3yo0zktx0.jpg)

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

## Solution

```python
from collections import deque, OrderedDict
from typing import List
from .util import TreeNode


class TravesalItem:
    def __init__(self, node, row, col):
        self.node = node
        self.row = row
        self.col = col


class Solution:
    def verticalTraversal(self, root: TreeNode) -> List[List[int]]:
        grid_items = []
        traversal = {}

        traversal_queue = deque([TravesalItem(root, 0, 0)])
        while traversal_queue:
            ti = traversal_queue.popleft()
            if ti.node is not None:
                grid_items.append((ti.col, ti.row, ti.node.val))
                traversal_queue.append(
                    TravesalItem(ti.node.left, ti.row + 1, ti.col - 1)
                )
                traversal_queue.append(
                    TravesalItem(ti.node.right, ti.row + 1, ti.col + 1)
                )

        for col, row, val in sorted(grid_items):
            if col not in traversal:
                traversal[col] = []
            traversal[col].append(val)

        return traversal.values()
```

## Analysis

![Alt Text](https://dev-to-uploads.s3.amazonaws.com/i/8d21obw16wsu6720b7g7.png)