Sorted

1
Sorted Unsorted List as Linked Structures

• CSC 2110 - Data Structures Abstraction
• Spring/Summer 2001
• Wayne State University
• Instructor Anne-Marie Bosneag

2
Content

• Definition of unsorted list
• Specification of an unsorted list as a linked
  structure
• Implementation of an unsorted list as a linked
  structure
• Definition of the sorted list
• Specification of a sorted list as a linked
  structure
• Implementation of a sorted list as a linked
  structure

3
What is a List?

• A list is a homogeneous collection of elements,
  with a linear relationship between elements.
• That is, each list element (except the first) has
  a unique predecessor, and each element (except
  the last) has a unique successor.

4
ADT Unsorted List Operations

• Transformers
• MakeEmpty
• InsertItem
• DeleteItem
• Observers
• IsFull
• LengthIs
• RetrieveItem
• Iterators
• ResetList
• GetNextItem

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5

• include ItemType.h // unsorted.h
• . . .
• template ltclass ItemTypegt
• class UnsortedType
• public // LINKED LIST IMPLEMENTATION
• UnsortedType ( )
• UnsortedType ( )
• void MakeEmpty ( )
• bool IsFull ( ) const
• int LengthIs ( ) const
  
• void RetrieveItem ( ItemType item,
  bool found )
• void InsertItem ( ItemType item )
• void DeleteItem ( ItemType item )
• void ResetList ( )
• void GetNextItem ( ItemType item )
  
• private
• NodeTypeltItemTypegt listData
• int length

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6

class UnsortedTypeltchargt
UnsortedType
Private data length
3 listData currentPos
MakeEmpty
UnsortedType
RetrieveItem
InsertItem
DeleteItem . .
GetNextItem
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• // LINKED LIST IMPLEMENTATION ( unsorted.cpp )
• include itemtype.h
• template ltclass ItemTypegt
• UnsortedTypeltItemTypegtUnsortedType ( ) //
  constructor
• // Pre None.
• // Post List is empty.
• length 0
• listData NULL
• template ltclass ItemTypegt
• int UnsortedTypeltItemTypegtLengthIs ( ) const
• // Post Function value number of items in the
  list.
• return length

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• template ltclass ItemTypegt
• void UnsortedTypeltItemTypegtRetrieveItem(
  ItemType item, bool found )
• // Pre Key member of item is initialized.
• // Post If found, items key matches an
  elements key in the list and a copy
• // of that element has been stored in item
  otherwise, item is unchanged.
• bool moreToSearch
• NodeTypeltItemTypegt location
• location listData
• found false
• moreToSearch ( location ! NULL )
• while ( moreToSearch !found )
• if ( item location-gtinfo )
  // match here
• found true
• item location-gtinfo
• else // advance pointer
• location location-gtnext
• moreToSearch ( location ! NULL )

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• template ltclass ItemTypegt
• void UnsortedTypeltItemTypegtInsertItem (
  ItemType item )
• // Pre list is not full and item is not in
  list.
• // Post item is in the list length has been
  incremented.
• NodeTypeltItemTypegt location
• // obtain and fill a node
• location new NodeTypeltItemTypegt
• location-gtinfo item
• location-gtnext listData
• listData location
• length

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Inserting B into an Unsorted List
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Inserting B into an Unsorted List
location new NodeTypeltItemTypegt
item location
B
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Inserting B into an Unsorted List
location-gtinfo item
item location
B
B
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Inserting B into an Unsorted List
location-gtnext listData
B
item location
B
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Inserting B into an Unsorted List
listData location
item location
B
B
Private data length
3 listData currentPos
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length
item location
B
B
Private data length
4 listData currentPos
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class SortedTypeltchargt
SortedType
Private data length 3 listData curren
tPos
MakeEmpty
SortedType
RetrieveItem
InsertItem
DeleteItem . .
GetNextItem
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InsertItem algorithm for Sorted Linked List

• Find proper position for the new element in the
  sorted list using two pointers predLoc and
  location, where predLoc trails behind location.
• Obtain a node for insertion and place item in it.
• Insert the node by adjusting pointers.
• Increment length.

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Implementing SortedType member function
InsertItem

// LINKED LIST IMPLEMENTATION
(sorted.cpp) include ItemType.h template
ltclass ItemTypegt void SortedTypeltItemTypegt
InsertItem ( ItemType item ) // Pre List has
been initialized. List is not full. item is not
in list. // List is sorted by key member. //
Post item is in the list. List is still
sorted. . . .
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Inserting S into a Sorted List
predLoc location
Private data length
3 listData currentPos
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Finding proper position for S
predLoc location
NULL
Private data length 3 listData current
Pos
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Finding proper position for S
predLoc location
Private data length 3 listData curren
tPos
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Finding proper position for S
predLoc location
Private data length
3 listData currentPos
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Inserting S into proper position
predLoc location
Private data length
4 listData currentPos
C L X
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Inserting an element into SortedType

• template ltclass ItemTypegt
• void SortedTypeltItemTypegtInsertItem(ItemType
  item)
• NodeTypeltItemTypegt newNode, predLoc,
  location
• bool moreToSearch true
• location listData predLoc NULL
• while (moreToSearch)
• if (location-gtinfo lt item)
• predLoc location
• location location-gtnext
• moreToSearch (location ! NULL)
• else
• moreToSearch false

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Inserting an element into SortedType

• newNode new NodeTypeltItemTypegt
• newNode-gtinfo item
• if (predLoc NULL)
• newNode-gtnext listData
• listData newNode
• else
• newNode-gtnext location
• predLoc-gtnext newNode
• length

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What is a Circular Linked List?

• A circular linked list is a list in which every
  node has a successor the last element is
  succeeded by the first element.

B C L
listData
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Finding a List Item into a Circular Sorted List

• template ltclass ItemTypegt
• void FindItem (NodeTypeltItemType listData,
  ItemType item,
• NodeTypeltItemTypegt location,
• NodeTypeltItemTypegt predLoc, bool found)
• //Pre List not empty
• //Post If there is an element in the list, whose
  key matches the items key, then found true,
  location contains the address of the found
  element and predLoc contains the address of the
  successor. If not found, found false and
  predLoc and location point to predecessor and
  succesor, respectively.

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Finding a List Item - cont.

• bool moreToSearch
• location listData-gtnext
• predLoc listData
• found false
• while (moreToSearch !found)
• if (item lt location-gtinfo)
• moreToSearch false
• else if (item location-gtinfo)
• found true
• else predLoc location
• location location-gtnext
• moreToSeach (location !
  listData-gtnext)

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Inserting an Item into a Circular Sorted List

• template ltclass ItemTypegt
• void SortedTypeltItemTypegtInsertItem (ItemType
  item)
• NodeTypeltItemTypegt newNode, predLoc,
  location
• bool found
• newNode new NodeTypeltItemTypegt
• newNode-gtinfo item
• if (listData ! NULL)
• FindItem(listData, item, location, predLoc,
  found)
• newNode-gtnext predLoc-gtnext
• predLoc-gtnext newNode
• //if last node, reassign listData
• if (listData-gtinfo lt item)
• listData newNode

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Inserting an Item - cont

• else
• listData newNode
• newNode-gtnext newNode
• length

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Deleting an Item from a Circular Sorted List

• template ltclass ItemTypegt
• void SortedTypeltItemTypegtDeleteItem (ItemType
  item)
• NodeTypeltItemTypegt location, predLoc
• bool found
• FindItem(listData, item, location, predLoc,
  found)
• if (predLoc location) //the only node in the
  list
• listData NULL
• else predLoc-gtnext location-gtnext
• if (location listData)
• listData predLoc
• delete location
• length--

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What is a Doubly Linked List?

• A doubly linked list is a list in which each node
  is linked to both its successor and its
  predecessor.

A C F
T Z
listData
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Each node contains two pointers
templatelt class ItemType gt struct NodeType
ItemType info //Data member
NodeTypeltItemTypegt back //Pointer to
predecessor NodeTypeltItemTypegt next
//Pointer to successor
3000 A NULL
. back . info . next
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Finding an Item into a Doubly-linked Sorted List

• template ltclass ItemTypegt
• void FindItem (NodeTypeltItemTypegt listData,
  ItemType item,
• NodeTypeltItemTypegt location, bool found)
• bool moreToSearch true
• location listData found false
• while (moreToSearch !found)
• if (item lt location-gtinfo)
• moreToSearch false
• else if (item location-gtinfo)
• found true
• else location location-gtnext
• moreToSearch (location ! NULL)

35
What are Header and Trailer Nodes?

• A Header Node is a node at the beginning of a
  list that contains a key value smaller than any
  possible key.
• A Trailer Node is a node at the end of a list
  that contains a key larger than any possible key.
• Both header and trailer are placeholding nodes
  used to simplify list processing.

INT_MIN 5 8
13 INT_MAX
listData