package 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;
	}
}