Extension of linked list

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Extension of linked list

• Zhen Jiang
• West Chester University
• zjiang_at_wcupa.edu

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Outline

• Double Cyclic Linked List
• Queue Stack
• Binary Tree
• Expression Tree
• Networks

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(Single) Linked list
node
NULL
4
Double Cyclic Linked List
node
NULL
5
Queue
node
Delete an item from the tail
NULL
Insert a new item at the head
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Stack
node
NULL
Insert a new item at the head
Delete an item from the head
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• Implementation of stack with template
• http//www.cs.wcupa.edu/zjiang/csc513_template.pp
  t

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• Use of Stack
• Project 5
• Reading information via file
• http//www.cs.wcupa.edu/zjiang/530_proj5_file.pdf
  
• Three stacks, one for each , (), and .
• Left gt push/insert
• Right gt pop/delete the closest left symbol
• Evaluation of (postfix) expression

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• (5 4) 3
• 5 (4 3)
• 5 4 3
• 5 (4 3)

• 5 4 3
• 5 4 3
• 5 4 3
• 5 4 3

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• Read the formula from left to right
• Number gt push
• Binary operator gt 2 pops
• Right number popped first
• Then, left number popped.
• Calculate result ltsecondgt op ltfirstgt
• Push (result)
• Until expression reading finishes and only one
  (final) result is left in stack

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Disorder of the link connection
node
NULL
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Tree

• Definition
• Each node u has n(u) children
• Considering the parent-child relationship is
  undirected, there is no cycle in a tree
• There is only one node called the root in the
  entire tree. It has children only but no parent.

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Binary Tree

• Definition
• Definition of tree (3)
• For each node u, n(u)lt3
• LltSltR
• lt is a relation between any two nodes in the tree

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• Constructor
• Assume each node has a number value so that we
  have the relation lt
• Given a sequence n1, n2, n3, , ni,
• n1 -gt set root unit (node)
• ni -gt call insertion(node, ni)

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• Insertion(p, n)
• If (p-gtv lt n)
• If p-gtR not empty
• Insertion (p-gtR, n)
• else
• Set p-gtR
• If (p-gtv gt n)
• Similar to the case (p-gtv lt n)

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• Travel (print out all node values)
• Infix travel, L-gtS-gtR
• Postfix travel, L-gtR-gtS
• Prefix travel, S-gtL-gtR

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• Infix travel
• If node is not empty, Infix_print (node)
• Infix_print (p)
• If (p-gtL) infix_print(p-gtL)
• Cout ltlt p-gtv
• If(p-gtR) infix_print (p-gtR)

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• Search
• If node is not empty, Search (node, n)
• Search (p, n)
• If (p-gtv n) return true
• If (p-gtv lt n) return Search (p-gtR, n)
• If (p-gtv gt n) return Search (p-gtL, n)
• Terminating condition if (!p) return false

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• Deletion
• Delete the root node
• If node is empty
• If node-gtL (or node-gtR) is empty
• tmp node-gtR (or node-gtL)
• Delete node
• node tmp

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• If neither node-gtL nor node-gtR is empty
• If node-gtL-gtR is empty
• node -gt v node-gtL-gtv
• tmp node-gtL-gtL
• Delete node-gtL
• node-gtL tmp
• Else
• tmp node-gtL
• While (tmp-gtR-gtR) tmp tmp-gtR
• node-gtv tmp-gtR-gtV
• tmp2 tmp-gtR-gtL
• Delete tmp-gtR
• tmp-gtR tmp2

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• See if you can find a certain value in the tree
  and delete it!
• Delete (n)
• If (node-gtv n) delete node
• If (node-gtv lt n)
• deletion (node, node-R, n, 1)
• If (node-gtv gt n)
• deletion (node, node-L, n, 0)

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• Deletion (parent, start, value, flag)
• If start is empty // not found, done!
• If start-gtv lt value
• If start-gtv gt value
• Else //start-gtv value
• If both start-gtL and start-gtR are empty
• Delete start
• If (flag)Parent -gtR NULL
• Else Parent -gt L NULL
• If start-gtL (or start-gtR) is empty

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• Deletion (parent, start, value, flag)
• Else //start-gtv value
• If start-gtL (or start-gtR) is empty
• If (flag) Parent-R Start-gtR (or start-gtL)
• Else Parent-gtL Start-gtR
• Delete start
• If neither start-gtL nor start-gtR is empty

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• If start-gtL-gtR is empty
• start -gt v start-gtL-gtv
• tmp start-gtL-gtL
• Delete start-gtL
• start-gtL tmp
• Else
• tmp start-gtL
• While (tmp-gtR-gtR) tmp tmp-gtR
• start-gtv tmp-gtR-gtV
• tmp2 tmp-gtR-gtL
• Delete tmp-gtR
• tmp-gtR tmp2

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Expression Tree

• Definition
• Definition of binary tree (5)
• All leaves are numbers, and all intermediate
  nodes are operators
• To simplify the discussion in this class, we use
  binary operators only.

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• Evaluation
• If node is not empty, R_E(node)
• R_E(p)
• If p-gtv is not digit
• Lvalue R_E(p-gtL)
• Rvalue R_E(p-gtR)
• Return Lvalue ltp-gtvgt Rvalue
• Else
• Return p-gtv

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• Print
• Postfix
• Construction
• From infix format
• http//www.cs.wcupa.edu/zjiang/csc530_expressionT
  ree.htm

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Network

• Graph table
• http//www.cs.wcupa.edu/zjiang/csc530_graph_table
  .pdf
• Depth first search
• http//www.cs.wcupa.edu/zjiang/csc530_depth.pdf
• Width first search
• http//www.cs.wcupa.edu/zjiang/csc530_width.pdf
• Shortest path construction
• http//www.cs.wcupa.edu/zjiang/csc530_shortestpat
  h.pdf

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• Spanning (travel)
• Project 7