Vertical Order Traversal of a Binary Tree

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.

Examples

Example 1:

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:

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

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

Explanation:

• Column -2: Only node 4.
• Column -1: Only node 2.
• Column 0: Nodes 1, 5, and 6. Nodes 5 and 6 are at the same position (row 2, col 0), so they are sorted by value: [5, 6].
• Column 1: Only node 3.
• Column 2: Only node 7.

Example 3:

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

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

Explanation: Same as Example 2 but nodes 5 and 6 are swapped in the tree. They still end up at position (row 2, col 0) and are sorted by value.

Constraints

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