Data Organization

1
Data Organization

• Example 1 Heap storage management
• Keep track of free chunks of memory
• Example 2 A simple text editor
• Maintain a sequence of lines
• Example 3 Stable matching problem
• Maintain the set of currently free men
• Keep track of each person's preferences
• Quickly find the highest-ranked woman to whom a
  man has not proposed yet
• Quickly find whether a woman is engaged and to
  whom

2
Data Organization

• All these examples have a common organizational
  model
• A sequence of similar items
• (memory blocks, lines, men/women)
• Certain desired operations
• find, insert, delete

3
The list ADT

• Data
• A collection of homogeneous elements arranged in
  a sequence
• Operations
• Insert
• Delete
• Find
• Update
• Retrieve
• Length

4
The list ADT

• Most operations refer to a certain position in
  the list. How will this be designed?
• Maintain a "current" position?
• Specify an index?
• Specify a pointer to an element?
• Specify a generalized pointer to an element?

5
The list data structure

• Implementation 1 Contiguous memory
• Use a dynamic array
• How is each operation implemented?
• How efficient is each operation?
• Random access capability is good for retrieval if
  we use an index for element access
• Important The list ADT does not provide random
  access.
• We need to shift elements every time we insert or
  delete
• We need to reallocate whenever the array fills up.

6
The list data structure

• Implementation 2 Linked memory
• Use a node structure to store the data and a
  pointer to the next node, to create a chain of
  nodes.
• Uses more space than the array (due to the
  pointers) but insert/delete do not require
  shifting.
• However, deleting requires us to traverse the
  whole list in order to access the predecessor of
  the node to be deleted.
• Easy solution keep in mind the abstract image of
  a linked list!
• Move the next node's contents into the one to be
  deleted, and then physically remove the next
  node.
• We can use a similar trick for the insert
  operation
• Does this work in all cases?

7
Other list flavors

• Doubly-linked list
• Each node has a pointer to its successor and its
  predecessor.
• Faster insert/delete, but more space.
• Circular list
• The last node points back to the head.
• Sorted list
• Items stored in sorted order.
• Which implementation provides faster operations?
  Array or linked memory?

8
Other list flavors

• XOR list
• A space saving list
• Instead of both a previous and next pointer,
  store the XOR of the predecessor and successor.
• Node B stores A XOR C
• If you are at B and know the address of A, you
  can compute the address of C.
• The list can be traversed in any direction,
  provided you know where you came from.
• Interesting, but not very useful...

9
Other list flavors

• Unrolled linked list
• A space saving list
• Store k data items in each node
• It's a list of arrays
• Reduces cache misses
• Each node should be at least half-full
• If a node is too empty after a delete, merge it
  with a neighbor.
• If a node overflows after an insert, split it.

10
Other list flavors

• Satellite list
• An easily reversible list
• Developed for use in TSP algorithms
• Imagine each node as having two "satellites",
  north and south. A chain of pointers links all
  the northern satellites and another chain links
  all the southern ones.
• Reversing part of the list requires changing only
  4 pointers.
• Compare this to reversing a doubly-linked list.