 # Print the Bottom View of the Binary Tree.

Objec­tive: Given a binary tree, print it in Bottom View of it.

What is Bottom View: Bottom view means when you look the tree from the bottom the nodes you will see will be called the bottom view of the tree. See the exam­ple below. as you can see in the example above,8, 4, 9, 5, 3, 7 is the bottom view of the given binary tree.

Approach:

This Approach is quite sim­i­lar to the Print the Binary Tree in Ver­ti­cal Order Path.
and Print The Top View of a Binary Tree. Just mod­i­fied the code so that it will print only the last ele­ment it will encounter in the ver­ti­cal order. That will be the bottom view.

How will you know that you are vis­it­ing the last node at every level(Vertically)?

• Take a variable called level, whenever you go left, do level++ AND whenever you go right do level–.
• With step above we have separated out the levels vertically.
• Now you need to store the ele­ments of each level, so cre­ate a TreeMap and the (key,value) pair will be (level,element at that level).
• Now all we need to do the level order tra­ver­sal and store only recent visited node at each level(vertically), this way you will be storing only the last element at each level.
• We will use sim­ple queue tech­nique for level order tra­ver­sal or BFS.
• we will cre­ate a class QueuePack, this will store the objects con­tain­ing node and its level.
• At the end traverse through TreeMap and print all the values in it, it will be the bottom view of a tree.
• See the code for bet­ter understanding.

Code:

```Output:
4 6 5 7 8
```

### 6 thoughts on “Print the Bottom View of the Binary Tree.”

1. how would the tpre-order traverse guarantee most recent visited node would be at “bottom” of a vertical level?
Would following sequence work?
Node root = new Node(1);
root.left = new Node(2);
root.right = new Node(3);
root.left.left = new Node(4);
root.left.right = new Node(5);
root.left.right.left = new Node(6);
root.left.right.right = new Node(7);
root.left.right.right.right = new Node(9); ==> add another right node, which will be at same vertical level of node(8) but lower.
root.right.right = new Node(8);
We should get 4 6 5 7 9 as bottom view, but my guess is the code will return 4 6 5 7 8 (wrong result)

• Hi Xiaozhen,

Code is correct and will return 4 6 5 7 9, don’t concentrate on preorder traversal, we are storing the node at each vertical level in a hash map ( in fact we are updating it so hash map will contain the last node visited at that level) See the diagram.

2. 3. Can you please explain how 5 and 6 both being at level -0 are printed using the code ?

4. Print In-Order nodes where either left or right child is NULL

private static void printBottomView(Tree tree) {

if(tree==null)
return;
printBottomView(tree.leftChild);
if(tree.leftChild==null||tree.rightChild==null)
System.out.println(“===”+tree.data+”===”);
printBottomView(tree.rightChild);
}

5. 