Trees are collection of Nodes(Vertices) and Edges. Among them 1 Node is considered as ROOT. If there are N nodes, there will be N-1 vertices.
Terminology
- Root
- Parent
- Children
- Siblings: Children of same parent.
- Descendents: All Nodes coming out of parent.
- Ancestors:
- Degree of a Node: No. of Direct Children a Node is having
- Internal/External Nodes: Internal Nodes = Non Leaf Nodes = Non Terminal Nodes. External Nodes = Terminal Nodes = Nodes with Degree 0
- Level: Root at Level 1 and then it goes down. Each Level has No. of Nodes.
- Height: Level-1 is Height. 0,1,2,3,4
- Forest: Collection of Trees is called as Forest.
Binary Tree:
Every Node can have MAX 2 children.
2 Types of Nodes in BT.
- Unlabelled Nodes: For a given no. of Nodes n, The No. of Binary Trees that can be formed is
CATALAN’s FORMULA T(n) = 2nCn/n+1.
T(n) = sigma[T(i-1)*T(n-i)]
- Labelled Nodes: T(n) = (2nCn/n+1)*(n!)
- deg(T) = 2
- It can have {0,1,2} children max for each Node.
- Left Skewed, Right Skewed
- Height of BT = log(n+1)-1 ≤h≤n-1
- No. of Nodes in BT = h+1≤n≤2^(h+1)-1
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