# Bottom View of a Binary Tree

Given a Binary Tree, we need to print the bottom view from left to right. A node x is there in output if x is the bottommost node at its horizontal distance. Horizontal distance of left child of a node x is equal to horizontal distance of x minus 1, and that of right child is horizontal distance of x plus 1.

Examples:

```                      20
/    \
8       22
/   \      \
5      3      25
/ \
10    14

```

For the above tree the output should be 5, 10, 3, 14, 25.

If there are multiple bottom-most nodes for a horizontal distance from root, then print the later one in level traversal. For example, in the below diagram, 3 and 4 are both the bottom-most nodes at horizontal distance 0, we need to print 4.

```
20
/    \
8       22
/   \    /   \
5      3 4     25
/ \
10    14 ```

For the above tree the output should be 5, 10, 4, 14, 25.

## Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

Method 1 – Using Queue

The following are steps to print Bottom View of Binary Tree.
1. We put tree nodes in a queue for the level order traversal.
2. Start with the horizontal distance(hd) 0 of the root node, keep on adding left child to queue along with the horizontal distance as hd-1 and right child as hd+1.
3. Also, use a TreeMap which stores key value pair sorted on key.
4. Every time, we encounter a new horizontal distance or an existing horizontal distance put the node data for the horizontal distance as key. For the first time it will add to the map, next time it will replace the value. This will make sure that the bottom most element for that horizontal distance is present in the map and if you see the tree from beneath that you will see that element.

A Java based implementation is below :

## C++

 `// C++ Program to print Bottom View of Binary Tree ` `#include ` `using` `namespace` `std; ` ` `  `// Tree node class ` `struct` `Node ` `{ ` `    ``int` `data; ``//data of the node ` `    ``int` `hd; ``//horizontal distance of the node ` `    ``Node *left, *right; ``//left and right references ` ` `  `    ``// Constructor of tree node ` `    ``Node(``int` `key) ` `    ``{ ` `        ``data = key; ` `        ``hd = INT_MAX; ` `        ``left = right = NULL; ` `    ``} ` `}; ` ` `  `// Method that prints the bottom view. ` `void` `bottomView(Node *root) ` `{ ` `    ``if` `(root == NULL) ` `        ``return``; ` ` `  `    ``// Initialize a variable 'hd' with 0 ` `    ``// for the root element. ` `    ``int` `hd = 0; ` ` `  `    ``// TreeMap which stores key value pair ` `    ``// sorted on key value ` `    ``map<``int``, ``int``> m; ` ` `  `    ``// Queue to store tree nodes in level ` `    ``// order traversal ` `    ``queue q; ` ` `  `    ``// Assign initialized horizontal distance ` `    ``// value to root node and add it to the queue. ` `    ``root->hd = hd; ` `    ``q.push(root);  ``// In STL, push() is used enqueue an item ` ` `  `    ``// Loop until the queue is empty (standard ` `    ``// level order loop) ` `    ``while` `(!q.empty()) ` `    ``{ ` `        ``Node *temp = q.front(); ` `        ``q.pop();   ``// In STL, pop() is used dequeue an item ` ` `  `        ``// Extract the horizontal distance value ` `        ``// from the dequeued tree node. ` `        ``hd = temp->hd; ` ` `  `        ``// Put the dequeued tree node to TreeMap ` `        ``// having key as horizontal distance. Every ` `        ``// time we find a node having same horizontal ` `        ``// distance we need to replace the data in ` `        ``// the map. ` `        ``m[hd] = temp->data; ` ` `  `        ``// If the dequeued node has a left child, add ` `        ``// it to the queue with a horizontal distance hd-1. ` `        ``if` `(temp->left != NULL) ` `        ``{ ` `            ``temp->left->hd = hd-1; ` `            ``q.push(temp->left); ` `        ``} ` ` `  `        ``// If the dequeued node has a right child, add ` `        ``// it to the queue with a horizontal distance ` `        ``// hd+1. ` `        ``if` `(temp->right != NULL) ` `        ``{ ` `            ``temp->right->hd = hd+1; ` `            ``q.push(temp->right); ` `        ``} ` `    ``} ` ` `  `    ``// Traverse the map elements using the iterator. ` `    ``for` `(``auto` `i = m.begin(); i != m.end(); ++i) ` `        ``cout << i->second << ``" "``; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``Node *root = ``new` `Node(20); ` `    ``root->left = ``new` `Node(8); ` `    ``root->right = ``new` `Node(22); ` `    ``root->left->left = ``new` `Node(5); ` `    ``root->left->right = ``new` `Node(3); ` `    ``root->right->left = ``new` `Node(4); ` `    ``root->right->right = ``new` `Node(25); ` `    ``root->left->right->left = ``new` `Node(10); ` `    ``root->left->right->right = ``new` `Node(14); ` `    ``cout << ``"Bottom view of the given binary tree :\n"` `    ``bottomView(root); ` `    ``return` `0; ` `} `

## Java

 `// Java Program to print Bottom View of Binary Tree ` `import` `java.util.*; ` `import` `java.util.Map.Entry; ` ` `  `// Tree node class ` `class` `Node ` `{ ` `    ``int` `data; ``//data of the node ` `    ``int` `hd; ``//horizontal distance of the node ` `    ``Node left, right; ``//left and right references ` ` `  `    ``// Constructor of tree node ` `    ``public` `Node(``int` `key) ` `    ``{ ` `        ``data = key; ` `        ``hd = Integer.MAX_VALUE; ` `        ``left = right = ``null``; ` `    ``} ` `} ` ` `  `//Tree class ` `class` `Tree ` `{ ` `    ``Node root; ``//root node of tree ` ` `  `    ``// Default constructor ` `    ``public` `Tree() {} ` ` `  `    ``// Parameterized tree constructor ` `    ``public` `Tree(Node node) ` `    ``{ ` `        ``root = node; ` `    ``} ` ` `  `    ``// Method that prints the bottom view. ` `    ``public` `void` `bottomView() ` `    ``{ ` `        ``if` `(root == ``null``) ` `            ``return``; ` ` `  `        ``// Initialize a variable 'hd' with 0 for the root element. ` `        ``int` `hd = ``0``; ` ` `  `        ``// TreeMap which stores key value pair sorted on key value ` `        ``Map map = ``new` `TreeMap<>(); ` ` `  `         ``// Queue to store tree nodes in level order traversal ` `        ``Queue queue = ``new` `LinkedList(); ` ` `  `        ``// Assign initialized horizontal distance value to root ` `        ``// node and add it to the queue. ` `        ``root.hd = hd; ` `        ``queue.add(root); ` ` `  `        ``// Loop until the queue is empty (standard level order loop) ` `        ``while` `(!queue.isEmpty()) ` `        ``{ ` `            ``Node temp = queue.remove(); ` ` `  `            ``// Extract the horizontal distance value from the ` `            ``// dequeued tree node. ` `            ``hd = temp.hd; ` ` `  `            ``// Put the dequeued tree node to TreeMap having key ` `            ``// as horizontal distance. Every time we find a node ` `            ``// having same horizontal distance we need to replace ` `            ``// the data in the map. ` `            ``map.put(hd, temp.data); ` ` `  `            ``// If the dequeued node has a left child add it to the ` `            ``// queue with a horizontal distance hd-1. ` `            ``if` `(temp.left != ``null``) ` `            ``{ ` `                ``temp.left.hd = hd-``1``; ` `                ``queue.add(temp.left); ` `            ``} ` `            ``// If the dequeued node has a left child add it to the ` `            ``// queue with a horizontal distance hd+1. ` `            ``if` `(temp.right != ``null``) ` `            ``{ ` `                ``temp.right.hd = hd+``1``; ` `                ``queue.add(temp.right); ` `            ``} ` `        ``} ` ` `  `        ``// Extract the entries of map into a set to traverse ` `        ``// an iterator over that. ` `        ``Set> set = map.entrySet(); ` ` `  `        ``// Make an iterator ` `        ``Iterator> iterator = set.iterator(); ` ` `  `        ``// Traverse the map elements using the iterator. ` `        ``while` `(iterator.hasNext()) ` `        ``{ ` `            ``Map.Entry me = iterator.next(); ` `            ``System.out.print(me.getValue()+``" "``); ` `        ``} ` `    ``} ` `} ` ` `  `// Main driver class ` `public` `class` `BottomView ` `{ ` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``Node root = ``new` `Node(``20``); ` `        ``root.left = ``new` `Node(``8``); ` `        ``root.right = ``new` `Node(``22``); ` `        ``root.left.left = ``new` `Node(``5``); ` `        ``root.left.right = ``new` `Node(``3``); ` `        ``root.right.left = ``new` `Node(``4``); ` `        ``root.right.right = ``new` `Node(``25``); ` `        ``root.left.right.left = ``new` `Node(``10``); ` `        ``root.left.right.right = ``new` `Node(``14``); ` `        ``Tree tree = ``new` `Tree(root); ` `        ``System.out.println(``"Bottom view of the given binary tree:"``); ` `        ``tree.bottomView(); ` `    ``} ` `} `

Output:

```Bottom view of the given binary tree:
5 10 4 14 25```

Method 2- Using HashMap()
This method is contributed by Ekta Goel.
Approach:
Create a map like, map where key is the horizontal distance and value is a pair(a, b) where a is the value of the node and b is the height of the node. Perform a pre-order traversal of the tree. If the current node at a horizontal distance of h is the first we’ve seen, insert it in the map. Otherwise, compare the node with the existing one in map and if the height of the new node is greater, update in the Map.

Below is the implementation of the above:

 `// C++ Program to print Bottom View of Binary Tree ` `#include < bits / stdc++.h >  ` `#include < map > ` `using` `namespace` `std; ` ` `  `// Tree node class ` `struct` `Node  ` `{ ` `    ``// data of the node ` `    ``int` `data; ` `     `  `    ``// horizontal distance of the node ` `    ``int` `hd;  ` `     `  `    ``//left and right references ` `    ``Node * left, * right;  ` `     `  `    ``// Constructor of tree node ` `    ``Node(``int` `key)  ` `    ``{ ` `        ``data = key; ` `        ``hd = INT_MAX; ` `        ``left = right = NULL; ` `    ``} ` `}; ` ` `  `void` `printBottomViewUtil(Node * root, ``int` `curr, ``int` `hd, map <``int``, pair <``int``, ``int``>> & m) ` `{ ` `    ``// Base case ` `    ``if` `(root == NULL) ` `        ``return``; ` `     `  `    ``// If node for a particular  ` `    ``// horizontal distance is not ` `    ``// present, add to the map. ` `    ``if` `(m.find(hd) == m.end())  ` `    ``{ ` `        ``m[hd] = make_pair(root -> data, curr); ` `    ``}  ` `    ``// Compare height for already  ` `    ``// present node at similar horizontal ` `    ``// distance ` `    ``else`  `    ``{ ` `        ``pair < ``int``, ``int` `> p = m[hd]; ` `        ``if` `(p.second <= curr) ` `        ``{ ` `            ``m[hd].second = curr; ` `            ``m[hd].first = root -> data; ` `        ``} ` `    ``} ` `     `  `    ``// Recur for left subtree ` `    ``printBottomViewUtil(root -> left, curr + 1, hd - 1, m); ` `     `  `    ``// Recur for right subtree ` `    ``printBottomViewUtil(root -> right, curr + 1, hd + 1, m); ` `} ` ` `  `void` `printBottomView(Node * root)  ` `{ ` `     `  `    ``// Map to store Horizontal Distance, ` `    ``// Height and Data. ` `    ``map < ``int``, pair < ``int``, ``int` `> > m; ` `     `  `    ``printBottomViewUtil(root, 0, 0, m); ` `     `  `     ``// Prints the values stored by printBottomViewUtil() ` `    ``map < ``int``, pair < ``int``, ``int` `> > ::iterator it; ` `    ``for` `(it = m.begin(); it != m.end(); ++it) ` `    ``{ ` `        ``pair < ``int``, ``int` `> p = it -> second; ` `        ``cout << p.first << ``" "``; ` `    ``} ` `} ` ` `  `int` `main()  ` `{ ` `    ``Node * root = ``new` `Node(20); ` `    ``root -> left = ``new` `Node(8); ` `    ``root -> right = ``new` `Node(22); ` `    ``root -> left -> left = ``new` `Node(5); ` `    ``root -> left -> right = ``new` `Node(3); ` `    ``root -> right -> left = ``new` `Node(4); ` `    ``root -> right -> right = ``new` `Node(25); ` `    ``root -> left -> right -> left = ``new` `Node(10); ` `    ``root -> left -> right -> right = ``new` `Node(14); ` `    ``cout << ``"Bottom view of the given binary tree :\n"``; ` `    ``printBottomView(root); ` `    ``return` `0; ` `} `

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