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Vertical Order Traversal of a Binary Tree

Understand how to solve the vertical order traversal problem for binary trees by applying breadth-first search techniques. This lesson guides you to return node values from top to bottom within each column, ensuring nodes on the same row and column are ordered left to right. Gain practical experience implementing and reasoning about this traversal approach.

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Statement

Find the vertical order traversal of a binary tree when the root of the binary tree is given. In other words, return the values of the nodes from top to bottom in each column, column by column from left to right. If there is more than one node in the same column and row, return the values from left to right.

Constraints:

  • The number of nodes in the tree is in the range [1, 500].
  • 0≤0 \leq Node.data ≤1000\leq 1000

Examples

In the slides below, the input parameter is a list that represents the level order traversal of the binary tree.

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Understand the problem

Let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

Vertical Order Traversal of a Binary Tree

1.

What should be the output if the following tree is given as input?

tree = [25, 14, 35, -1, 15, null, 200, null, 10, null, null, 90, 350]

          __ 25 _ 
         |       |
      __ 14 _    35 _ 
     |       |       |
     -1 _    15   __ 200 _ 
         |       |        |
         10      90       350
A.

[[25], [14, 35], [-1, 15, 200], [10, 90, 350]]

B.

[[-1], [14, 10], [25, 15], [35, 90], [200], [350]]

C.

[[-1], [14], [10], [25], [15], [35], [90], [200], [350]]

D.

[[25, 14, -1], [10], [14, 15], [200, 90], [125, 35, 200, 350]]

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Figure it out!

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Sequence - Vertical
Drag and drop the cards to rearrange them in the correct sequence.
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Try it yourself

Implement your solution in the following coding playground.

Java
usercode > Solution.java
// Definiton of a binary tree node class

// class TreeNode<T> {

//     T data;

//     TreeNode<T> left;

//     TreeNode<T> right;



//     TreeNode(T data) {

//         this.data = data;

//         this.left = null;

//         this.right = null;

//     }

// }



import java.util.*;

import ds_v1.BinaryTree.TreeNode;



public class Solution{



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



        // Replace this placeholder return statament with your code

        return new ArrayList<List<Integer>>();

  }

}
Vertical Order Traversal of a Binary Tree