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Vertical Order Traversal

A
P
package com.thealgorithms.datastructures.trees;

import java.util.ArrayList;
import java.util.HashMap;
import java.util.LinkedList;
import java.util.Map;
import java.util.Queue;

/* The following class implements a vertical order traversal
in a tree from top to bottom and left to right, so for a tree :
           1
          / \
         2   3
        / \   \
       4   5   6
        \     / \
         7   8   10
          \
           9
 the sequence will be :
 4 2 7 1 5 9 3 8 6 10
 */
public class VerticalOrderTraversal {

    public static void main(String[] args) {
        BinaryTree tree = new BinaryTree();
        tree.put(5);
        tree.put(6);
        tree.put(3);
        tree.put(1);
        tree.put(4);
        BinaryTree.Node root = tree.getRoot();
        ArrayList<Integer> ans = verticalTraversal(root);
        for (int i : ans) {
            System.out.print(i + " ");
        }
    }

    /*Function that receives a root Node and prints the tree 
	in Vertical Order.*/
    private static ArrayList<Integer> verticalTraversal(BinaryTree.Node root) {
        /*Queue to store the Nodes.*/
        Queue<BinaryTree.Node> queue = new LinkedList<>();

        /*Queue to store the index of particular vertical 
		 column of a tree , with root at 0, Nodes on left 
		 with negative index and Nodes on right with positive
		 index. */
        Queue<Integer> index = new LinkedList<>();

        /*Map of Integer and ArrayList to store all the 
		 elements in a particular index in a single arrayList
		 that will have a key equal to the index itself. */
        Map<Integer, ArrayList<Integer>> map = new HashMap<>();

        /* min and max stores leftmost and right most index to
		 later print the tree in vertical fashion.*/
        int max = 0, min = 0;
        queue.offer(root);
        index.offer(0);

        while (!queue.isEmpty()) {

            if (queue.peek().left != null) {
                /*Adding the left Node if it is not null
				and its index by subtracting 1 from it's 
				parent's index*/
                queue.offer(queue.peek().left);
                index.offer(index.peek() - 1);
            }
            if (queue.peek().right != null) {
                /*Adding the right Node if it is not null
				and its index by adding 1 from it's 
				parent's index*/
                queue.offer(queue.peek().right);
                index.offer(index.peek() + 1);
            }
            /*If the map does not contains the index a new
			 ArrayList is created with the index as key.*/
            if (!map.containsKey(index.peek())) {
                ArrayList<Integer> a = new ArrayList<>();
                map.put(index.peek(), a);
            }
            /*For a index, corresponding Node data is added
			 to the respective ArrayList present at that
			 index. */
            map.get(index.peek()).add(queue.peek().data);
            max = (int) Math.max(max, index.peek());
            min = (int) Math.min(min, index.peek());
            /*The Node and its index are removed 
			 from their respective queues.*/
            index.poll();
            queue.poll();
        }
        /*Finally map data is printed here which has keys
		from min to max. Each ArrayList represents a 
		vertical column that is added in ans ArrayList.*/
        ArrayList<Integer> ans = new ArrayList<>();
        for (int i = min; i <= max; i++) {
            for (int j = 0; j < map.get(i).size(); j++) {
                ans.add(map.get(i).get(j));
            }
        }
        return ans;
    }
}