Lecture08

Tree

• A Tree is a hierarchical collection
  • supports one-to-many relationship between elements:
    • ONE unique predecessor element
    • MANY successor elements
• Trees are graphs
• Trees can be rooted:
  • they have one dediated node that serves as a root
• We will be talking about binary trees for now

m-ary|k-ary|k-way Tree

• An m-ary tree is a rooted tree in which each node has no more than m successors(children).

Binary Tree(m=2 m-ary Tree)

• An binary tree is a rooted tree in which each nodes has no more than TWO successors(children).

Terminology

Nodes and Edges

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Root/ Internal / Leaf

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Parent / Child Node

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Siblings

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Predecessor / Successor

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Path / Path Length

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Ancestor / Descendant

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Node Depth

• Node depth: length of a path( number of edges it contains) from the root to the node(in some books: number of nodes it contains + root node depth is 1)

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Node Height

• Node height: length of the longest path(number of edges it contains) from the node to its leaf descendant.( in some books: number of nodes it contains + root node depth is 1)

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Tree Height

• Tree height: maximum node depth in the tree OR height of the root.
  • Here: tree height H=2

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Tree Width

• Tree width: number of nodes in its widest level.
  • Here : tree width W=4

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Subtrees

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Tree size

• Tree size: number of all nodes in a tree
  • Here: N= 2⁰+ 2¹+ 2²=7(but this is very ”neat“ tree)
    
    image-20210325162226551.png

Trees and Object-Orientation

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