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.

My notes.

Mind the case.

[0,8,1,null,null,3,2,null,4,5,null,null,7,6]

          0
     8         1
          3         2
              4,5
          6         7

Rendered by Leetcode, with my lines added



My Solution

/**
 * Definition for a binary tree node.
 * class TreeNode {
 *     public $val = null;
 *     public $left = null;
 *     public $right = null;
 *     function __construct($value) { $this->val = $value; }
 * }
 */
class Solution {

    /**
     * @param TreeNode $root
     * @return Integer[][]
     */
    function verticalTraversal($root) {
        $result = [];
        $this->traversalHelper($root,0,0,$result);
        // Sort by col, from left to right
        ksort($result);
        foreach($result as &$rs){
            $new_sub = [];
            // foreach col, sort by depth from top to bottom
            ksort($rs);
            foreach($rs as &$r){
                // Same depth, sort by value asc, according to spec
                asort($r);
                $new_sub = array_merge($new_sub,$r);
            }
            $rs = $new_sub;
        }
        return $result;
    }
    
    // Recursion, go through the tree
    function traversalHelper($root, $pos,$depth, &$result) {
        if($root !== null){
            if(!isset($result[$pos])){
                $result[$pos] = [];
            } 
            if(!isset($result[$pos][$depth])){
                $result[$pos][$depth] = [];
            }
            $result[$pos][$depth][] = $root->val;
            
            $this->traversalHelper($root->left, $pos - 1,$depth+1, $result);
            $this->traversalHelper($root->right, $pos + 1,$depth+1, $result);
        }
    }
}