Binary tree and BST tool

The tree

Traversals

Preorder (root, left, right)

50 30 20 40 70 60 80

Inorder (left, root, right)

20 30 40 50 60 70 80

Postorder (left, right, root)

20 40 30 60 80 70 50

Level order

50 30 70 20 40 60 80

About the tree

Root

50

Number of nodes (size)

7

Height = depth (edges from the root to the deepest leaf)

2

Levels (the root is at level 0)

3

Leaves (external nodes)

20, 40, 60, 80

Internal nodes (not the root)

30, 70

Full binary tree (every node has 0 or 2 children)

Yes

Complete binary tree

Yes

Binary search tree (inorder is in order)

Yes

Inserting, one value at a time

Each value starts at the root and goes left if smaller, right if larger, until there is a free place.

1. 50: the first value is the root
2. 30: 30 < 50: go left → left of 50
3. 70: 70 > 50: go right → right of 50
4. 20: 20 < 50: go left; 20 < 30: go left → left of 30
5. 40: 40 < 50: go left; 40 > 30: go right → right of 30
6. 60: 60 > 50: go right; 60 < 70: go left → left of 70
7. 80: 80 > 50: go right; 80 > 70: go right → right of 70