tinyHiker / trees_binary_BST

Using python to work with binary trees and binary search trees

Tree Terminology and Types of Binary Trees

Tree Terminology

• Root: The top node without a parent.
• Edge: A link between a parent and a child node.
• Leaf: A node which does not have children.
• Sibling: Children of the same parent.
• Ancestor: A parent, grandparent, great-grandparent, etc., of a node.
• Depth of a Node: The length of the path from the root to the node, measured in the number of edges.
• Height of a Node: The length of the path from the node to the deepest node connected to it. This length is measured by the number of edges.
• Depth of the Tree: The depth of the root node, which is always zero.
• Height of the Tree: The height of the root node.

Types of Binary Trees

Full Binary Tree

• Each node has either 0 or 2 children. No node has exactly 1 child.

Perfect Binary Tree

• Every node other than leaf nodes has exactly two children.
• All leaf nodes are at the same level.
• The tree has exactly 2^(h+1) - 1 nodes, where h is the height of the tree.
• The number of leaf nodes is (n+1)/2 for a tree with n nodes.

Complete Binary Tree

• Every level, except possibly the last, is completely filled.
• If the last level is not filled, nodes are as far left as possible.

Balanced Binary Tree

• A tree where all leaf nodes are at the same distance from the root.

Deepest Node in a Binary Tree

• The deepest node is the last node reached in a level order traversal.

Tree Search Techniques

Depth First Search (DFS)

1. Preorder Traversal: Visit the root node, then the left subtree, followed by the right subtree.
2. Inorder Traversal: Visit the left subtree, then the root node, and finally the right subtree.
3. Postorder Traversal: Visit the left subtree, the right subtree, and then the root node.

Breadth First Search (BFS)

• Level Order Traversal: Visit each level from left to right.