Types of Views & Binary Trees

In binary trees, the views and types refer to different perspectives and classifications of the tree structure.

Types of Views in Binary Tree are :

                     1
                   /   \
                 2       3
                / \     / \
               4   5   6   7
              / \   \     /
             8   9   10  11

• Horizontal View: The horizontal view of a binary tree shows the nodes from left to right at each level. Nodes at the same level are listed in the order of their appearance, from left to right.

1 2 3 4 5 6 7 8 9 10 11

• Vertical View: The vertical view of a binary tree shows the nodes from top to bottom, where nodes in the same vertical line are displayed in the order of their occurrence from top to bottom.

8
4
2 9 10
1 5 6 11
3 7

• Left View: The left view of a binary tree shows the leftmost node at each level. It represents the visible nodes when looking at the tree from the left side.

1 2 4 8

• Right View: The right view of a binary tree shows the rightmost node at each level. It represents the visible nodes when looking at the tree from the right side.

1 3 7 11

• Top View: The top view of a binary tree displays the nodes visible when viewing the tree from the top. It shows the nodes on the vertical lines that intersect the topmost node at each horizontal distance.

8 4 2 1 3 7 11

• Bottom View: The bottom view of a binary tree displays the nodes visible when viewing the tree from the bottom. It shows the nodes on the vertical lines that intersect the bottom-most node at each horizontal distance.

8 9 10 5 6 11 7

Time & Space complexity for each type of view in a binary tree:

View Type	Time Complexity	Space Complexity
Horizontal View	O(n)	O(n)
Vertical View	O(n log n)	O(n)
Left View	O(n)	O(n)
Right View	O(n)	O(n)
Top View	O(n log n)	O(n)
Bottom View	O(n)	O(n)

Types of Binary Trees:

• Full Binary Tree: A binary tree in which every node has either 0 or 2 children.

        1
       / \
      2   3
     / \
    4   5

• Complete Binary Tree: A binary tree in which all levels, except possibly the last one, are completely filled, and all nodes are as left as possible.

        1
       / \
      2   3
     / \  /
    4   5 6

• Perfect Binary Tree: A binary tree in which all internal nodes have two children, and all leaf nodes are at the same level.

        1
       / \
      2   3
     / \ / \
    4  5 6  7

• Balanced Binary Tree: A binary tree in which the heights of the left and right subtrees of every node differ by at most one.

        1
       / \
      2   3
     /     \
    4       5

• Binary Search Tree (BST): A binary tree in which for every node, all values in its left subtree are less than its value, and all values in its right subtree are greater than its value.

        4
       / \
      2   5
     / \   \
    1   3   6

• Skewed Binary Tree: is a special type of binary tree in which all the nodes are either in the left subtree or the right subtree.

         1
        /
       2
      /
     3
    /
   4

OR

   1
    \
     2
      \
       3
        \
         4

Binary Tree Type	Time Complexity	Space Complexity
Full Binary Tree	O(n)	O(n)
Complete Binary Tree	O(n)	O(n)
Perfect Binary Tree	O(log n)	O(log n)
Balanced Binary Tree	O(log n)	O(log n)
Binary Search Tree (BST)	Average Case: O(log n)	O(n)

Note: also read about Binary Trees: Structure & Tree travels

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