/**

 * Definition for a binary tree node.

 * public class TreeNode {

 *     int val;

 *     TreeNode left;

 *     TreeNode right;

 *     TreeNode(int x) { val = x; }

 * }

 */

class Solution {

    int min = Integer.MAX_VALUE;

    int max = Integer.MIN_VALUE;

    public List<List<Integer>> verticalOrder(TreeNode root) {

        List<List<Integer>> res = new ArrayList<>();

        if (root == null) {

            return res;

        }

        dfs(root, 0);

        for (int i = min; i <= max; i++) {

            res.add(new ArrayList<>());

        }

        Queue<TreeNode> queue = new LinkedList<>();

        Queue<Integer> indexQ = new LinkedList<>();

        queue.offer(root);

        // map the leftmost to 0, so that root is -min

        indexQ.offer(-min);

        while (!queue.isEmpty()) {

            TreeNode cur = queue.poll();

            int curIndex = indexQ.poll();

            res.get(curIndex).add(cur.val);

            if (cur.left != null) {

                queue.offer(cur.left);

                indexQ.offer(curIndex - 1);

            }

            if (cur.right != null) {

                queue.offer(cur.right);

                indexQ.offer(curIndex + 1);

            }

        }

        return res;

    }

    private void dfs(TreeNode root, int num) {

        if (root == null) {

            return;

        }

        min = Math.min(min, num);

        max = Math.max(max, num);

        dfs(root.left, num - 1);

        dfs(root.right, num + 1);

    }

}