# 987. Vertical Order Traversal of a Binary Tree

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: [,[3,15],,]
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: [,,[1,5,6],,]
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-&gt;val = \$value; }
* }
*/
class Solution {

/**
* @param TreeNode \$root
* @return Integer[][]
*/
function verticalTraversal(\$root) {
\$result = [];
\$this-&gt;traversalHelper(\$root,0,0,\$result);
// Sort by col, from left to right
ksort(\$result);
foreach(\$result as &amp;\$rs){
\$new_sub = [];
// foreach col, sort by depth from top to bottom
ksort(\$rs);
foreach(\$rs as &amp;\$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, &amp;\$result) {
if(\$root !== null){
if(!isset(\$result[\$pos])){
\$result[\$pos] = [];
}
if(!isset(\$result[\$pos][\$depth])){
\$result[\$pos][\$depth] = [];
}
\$result[\$pos][\$depth][] = \$root-&gt;val;

\$this-&gt;traversalHelper(\$root-&gt;left, \$pos - 1,\$depth+1, \$result);
\$this-&gt;traversalHelper(\$root-&gt;right, \$pos + 1,\$depth+1, \$result);
}
}
}```