CPCS 204: Data Structures

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CPCS 204 Data Structures AlgorithmsChapter 7
Trees

• Instructor Nouf Ghanimi

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overview

• 7.1 General Trees
• 7.2  Tree Traversal Algorithms

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Trees

• non-linear Data Structures
• Tree is a set of nodes and edges that connect
  them.
• Between each node there exactly one path between
  nodes.
• A path is connected sequence of edges.

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Rooted tree

• Rooted tree one distinguished node is called the
  root.
• Every node c, except the root, has one parent
  called p. where p is the first node on the path
  from c to the root.
• Since p is the parent of c then c is ps child

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Rooted tree

• Root has no parent.
• A node can have any of children.
• Example.

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Rooted tree

• Leaf node with no children (external), opposite
  is internal.
• Sibling nodes with same parent.
• Ancestor of node d nodes on the path from d to
  the root, including d, ds parent , ds grand
  parent, , root.
• If a is ancestor of d , then d is descendant of
  a.

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Rooted tree

• Length of path edges in path (Example).
• Depth of node n length of path from n to root,
  ex depth of root is zero.
• Height of node n length of path from n to its
  deepest descendant.

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Rooted tree

• Ex height of any leaf is zeroheight of tree
  height of the root
• Sub tree rooted at n tree formed by n its
  descendants.
• Binary tree no node has gt 2 children
• Every child is a left or right child, even if
  its the only child.

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Web page example
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Representing rooted trees

• Each node has three references
• Item
• Parent
• Children stored in a list

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Tree Traversal

• A traversal is a manner of visiting each node in
  a tree once.

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1) Preorder traversal

• Visit each node before recursively visiting its
  children, left to right. Root is visited first.
• Each node visited only once.
• It takes O(n) time , where n is of nodes in
  tree.
• It is natural way to print the structure of
  directories

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1) Preorder Traversal
Algorithm preOrder(v) visit(v) for each child w
of v preOrder (w)
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Make Money Fast!
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1. Motivations
References
2. Methods
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2.1 StockFraud
2.2 PonziScheme
2.3 BankRobbery
1.1 Greed
1.2 Avidity
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2) Postorder traversal

• Visited each node children ,left to right, before
  the node itself.
• Natural way to sum the disk space in directories.

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Postorder Traversal
Algorithm postOrder(v) for each child w of
v postOrder (w) visit(v)
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cs16/
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todo.txt1K
homeworks/
programs/
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1
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DDR.java10K
Stocks.java25K
h1c.doc3K
h1nc.doc2K
Robot.java20K
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3) In order traversal

• This is only with binary tree.
• Visit left child, then visit the node itself,
  then you visit the right child.

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Inorder Traversal
Algorithm inOrder(v) if hasLeft (v) inOrder (left
(v)) visit(v) if hasRight (v) inOrder (right (v))
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Expression tree

• You can generate a formula of expression called
  postfix, prefix, infix expressions.
• In order 3 7 4 2
• Preorder 3 7 4 2
• Postorder 3 7 4 2

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4) Level-order traversal

• Visit the root, then visit all depth-1 nodes
  (left to right), then all depth -2 nodes, etc.
• 3 7 4 2 (means nothing)

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4) Level-order traversal

• Implementation not recursive.
• Use a queue which initially contains only the
  root.
• Repeat, dequeue a node from the list
• , visit it
• ,enqueue its children (left to right)
• Until queue is empty