Bottom view of a Binary Tree

The bottom view of a binary tree is the number of nodes visible when viewed from the bottom. At every horizontal distance, there would be exactly one node that will appear in the bottom view. The horizontal distance is measured with the root serving as a reference; then, we measure each node’s left and right deviations.

Here, the nodes four, eight, six, nine, and seven are viewed from the bottom hence they will come in the bottom view of a tree.

Approach

Do a level order traversal of the tree.
Assign horizontal distance to each node of Binary Tree and replace the same horizontal distance node in a map with key as the distance to obtain the Bottom View.
Make key as distance and data as value for the map.
Perform it for every node in the tree.

C++ code:

 #include <bits/stdc++.h>
 using namespace std;
 #define mkp make_pair // macro
 struct Node  // Tree structure
 {
     int data;
     int distance;
     Node *left, *right;
     Node(int val)
     {
         data = val;
         left = NULL;
         right = NULL;
     }
 };
 // Function to print Bottom View of Binary Tree
 void BottomView(Node *root)
 {
     if (root == NULL)
         return;
     // initialising variables
     queue<Node *> q;
     q.push(root);
     root -> distance = 0;
     map<int, int> mp;
     // variable to store distance of nodes
     int distance;
     // assigning horizontal distance to each node of Binary Tree
     // and replacing nodes of the same horizontal distance in a map with
     // key as the distance to obtain the Bottom View
     while (!q.empty())
     {
         // extract the node at the front of queue
         Node *temp = q.front();
         distance = temp -> distance;
         // make key as distance and data as value for map
         mp[distance] = temp -> data;
         // remove the extract node from queue
         q.pop();
         // when left child exists, assign horizontal distance to it,
         // and push it to the queue
         if (temp -> left != NULL)
         {
             temp -> left -> distance = distance - 1;
             q.push(temp -> left);
         }
         // when right child exists, assign horizontal distance to it,
         // and push it to the queue
         if (temp -> right != NULL)
         {
             temp -> right -> distance = distance + 1;
             q.push(temp -> right);
         }
     }
     /*
         Map mp contains:
         [-2] -> 4
         [-1] -> 8
         [0] -> 6
         [1] -> 9
         [2] -> 7
     */
     cout << "Bottom View of Binary Tree: " << endl;
     map<int, int> :: iterator it;
     // Iterate over the map keys i.e -2, -1, 0, 1, 2
     for (it = mp.begin(); it != mp.end(); it++)
         cout << it -> second << " ";
 }
 // Driver Function
 int main()
 {
     map<int, Node *> m;
     // Input number of edges
     int n;
     cin >> n;
     Node *root = NULL;
     /*
         Input Format:
             Input:
                     3
                     1 2 L
                     1 3 R
                     2 4 L
                     This means there are 3 edges
                     2 is the left child of 1,
                     3 is the right child of 1,
                     4 is the left child of 2.
     */
     for (int i = 0; i < n; i++)
     {
         int node1, node2;
         char direction;
         cin >> node1 >> node2 >> direction;
         Node *parent, *child;
         if (m.find(node1) == m.end())
         {
             parent = new Node(node1);
             m[node1] = parent;
             if (root == NULL)
                 root = parent;
         }
         else
             parent = m[node1];
         child = new Node(node2);
         if (direction == 'L')
             parent -> left = child;
         else
             parent -> right = child;
         m[node2] = child;
     }
     // call to BottomView function
     BottomView(root);
     return 0;
 }

Input:

1 2 L

1 3 R

2 4 L

2 5 R

3 6 L

3 7 R

5 8 L

6 9 R

Visualization of the tree

/ \

2 3

/ \ / \

4 5 6 7

/ \

8 9

Output:

Bottom View of Binary Tree:

4 8 6 9 7

DAA: Bottom view of a Binary Tree