Trees 5 May 2016 OSU CSE 1 A New Math Type: tree A ubiquitous - - PowerPoint PPT Presentation

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Trees 5 May 2016 OSU CSE 1 A New Math Type: tree A ubiquitous concept in computing is that of a tree Often we are interested in a binary tree , a special case of a tree in which each node has at most two children An informal

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Trees

5 May 2016 OSU CSE 1

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A New Math Type: tree

A ubiquitous concept in computing is that
f a tree

– Often we are interested in a binary tree, a special case of a tree in which each node has at most two children

An informal introduction (“node”?,

“children”?) follows, using pictures rather than any new mathematical notation

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Recursive Structure

A tree is made up of:

– A root node – A string of zero or more child nodes of the root, each of which is the root of its own tree

Since a tree may contain other trees, its

structure is recursive

Note: the following explanation of trees is

adequate for present purposes but is not technically complete; details later…

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B R K A C T L G S H E P

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Nodes

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B R K A C T L G S H E P ?

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Edges or Branches

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B R K A C T L G S H E P

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B R K A C T L G S H E P root node (node B)

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B R K A C T L G S H E P children of root node (or,

f node B)

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B R K A C T L G S H E P parent of node S (for example)

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B R K A C T L G S H E P siblings of node S

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B R K A C T L G S H E P leaf nodes

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B R K A C T L G S H E P root leaf Yes, it’s drawn upside down!

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B R K A C T L G S H E P size of a tree is its total number of nodes; here, it is 12

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Your Turn!

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Q G H R C T L D What’s the size of each

f these 4

trees? C A Y W K P B

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B R K A C T L G S H E P path from node B to node L; its length is 3

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B R K A C T L G S H E P height of a tree is the length of the longest path from its root; here, it is 4

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Your Turn!

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Q G H R C T L D What’s the height of each of these 4 trees? C A Y W K P B

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A Tricky One?

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N What’s the height of this tree? D A Y L K P Q B

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B R K A C T L G S H E P tree rooted at node B

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B R K A C T L G S H E P subtree 0

f tree

rooted at node B (or,

f node B)

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B R K A C T L G S H E P subtree 1

f tree

rooted at node B (or,

f node B)

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B R K A C T L G S H E P subtree 2

f tree

rooted at node B (or,

f node B)

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B R K A C T L G S H E P Notice the recursive structure: a root plus its subtrees.

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Resources

Wikipedia: Tree structure

– http://en.wikipedia.org/wiki/Tree_structure

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