1. More Linking Up with Linked Lists
Chapter 11
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

2. Chapter Contents 11.1 Some Variants of Singly-Linked Lists
11.2 Linked Implementation of Sparse Polynomials
11.3 Doubly-Linked Lists and the Standard C++ list
11.4 Case Study: Larger-Integer Arithmetic
11.5 Other Multiply-Linked Lists
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

3. Chapter Objectives
Survey common variants of linked lists and why they are used
Study in detail an application of linked lists to implement sparse polynomials
Describe doubly-linked lists and how they are used to implement C++ STL list container
Build a class that makes it possible to do arithmetic with large integers
Look briefly at some other applications of multiply-linked lists
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

4. Linked Lists with Head Nodes
Consider linked lists from Chapter 6
First node is different from others
Has no predecessor
Thus insertions and deletions must consider two cases
First node or not first node
The algorithm is different for each
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

5. Linked Lists with Head Nodes
Dual algorithms can be reduced to one
Create a "dummy" head node
Serves as predecessor holding actual first element
Thus even an empty list has a head node
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

6. Linked Lists with Head Nodes
For insertion at beginning of list
Head node is predecessor for new node newptr->next = predptr->next; predptr->next = newptr;
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

7. Linked Lists with Head Nodes
For deleting first element from a list with a head node
Head node is the predecessor predptr->next = ptr->next; delete ptr;
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

8. Circular Linked Lists Set the link in last node to point to first node
Each node now has both predecessor and successor
Insertions, deletions now easier
Special consideration required for insertion to empty list, deletion from single item list
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

9. Circular Linked Lists
Traversal algorithm must be adjusted if (first != 0) // list not empty { ptr = first; do { // process ptr->data ptr = ptr->next; } while (ptr != first); }
A do-while loop must be used instead of a while loop
Why is this required?
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

10. Linked Implementation of Sparse Polynomials
Consider a polynomial of degree n
Can be represented by a list
For a sparse polynomial this is not efficient
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

11. Linked Implementation of Sparse Polynomials
We could represent a polynomial by a list of ordered pairs
{ (coef, exponent) … }
Fixed capacity of array still problematic
Wasted space for sparse polynomial
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

12. Linked Implementation of Sparse Polynomials
Linked list of these ordered pairs provides an appropriate solution
Each node has form shown
Now whether sparse or well populated, the polynomial is represented efficiently
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

13. Linked Implementation of Sparse Polynomials
Note start of Polynomial class template
Type parameter CoefType
Term and Node are inner classes
Addition operator
Adds coefficients of like degrees
Must traverse the two addend polynomials
Requires temporary pointers for each polynomial (the addends and the resulting sum)
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

14. Addition Operator
Requires temporary pointers for each polynomial (the addends and the resulting sum)
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

15. Addition Operator As traversal takes place Compare exponents
If different, node with smaller exponent and its coefficient attached to result polynomial
If exponents same, coefficients added, new corresponding node attached to result polynomial
View source code
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

16. Doubly-Linked Lists Bidirectional lists
Nodes have data part, forward and backward link
Facilitates both forward and backward traversal
Requires pointers to both first and last nodes
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

17. Doubly-Linked Lists To insert a new node
Set forward and backward links to point to predecessor and successor
Then reset forward link of predecessor, backward link of successor
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

18. Doubly-Linked Lists To delete a node
Reset forward link of predecessor, backward link of successor
Then delete removed node
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

19. The STL list<T> Class Template
A sequential container
Optimized for insertion and erasure at arbitrary points in the sequence.
Implemented as a circular doubly-linked list with head node.
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

20. Comparing List<t> With Other Containers
Property Array vector<T> deque<T> list<T>
Direct/random access ([]) + (exclnt) +  (good) X
Sequential access + +  +
Insert/delete at front -(poor) - + +
Insert/delete in middle
Insert/delete at end
Overhead lowest low low/medium high
Note : list<T> does not support direct access
does not have the subscript operator [ ].
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

21. list<t> Iterators
list<T>'s iterator is "weaker" than that for vector<T>.
vector<T>: random access iterators
list<T>: bidirectional iterators
Operations in common
++ Move iterator to next element (like ptr = ptr-> next)
-- Move iterator to preceding element (like ptr = ptr-> prev)
* dereferencing operator (like ptr-> data)
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

22. list<t> Iterators
Operators in common
= assignment (for same type iterators) it1 = it2 makes it1 positioned at same element as it2
== and != (for same type iterators) checks whether iterators are positioned at the same element
See basic list operations, Table 11-2, pg 621
View demonstration of list operations, Fig. 11-1
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

23. Example: Internet Addresses
Consider a program that stores IP addresses of users who make a connection with a certain computer
We store the connections in an AddressCounter object
Tracks unique IP addresses and how many times that IP connected
View source code, Fig. 11.2
Note uses of STL list and operators
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

24. The STL list<T> Class Template
Node structure
struct list_node
{ pointer next, prev; T data; }
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

25. The STL list<T> Class Template
But it's allo/deallo-cation scheme is complex
Does not simply using new and delete operations.
Using the heap manager is inefficient for large numbers of allo/deallo-cations
Thus it does it's own memory management.
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

26. The STL list<T> Memory Management
When a node is allocated
If there is a node on the free list, allocate it.
This is maintained as a linked stack
If the free list is empty:
Call the heap manager to allocate a block of memory (a "buffer", typically 4K)
Carve it up into pieces of size required for a node of a list<T>.
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

27. The STL list<T> Memory Management
When a node is deallocated
Push it onto the free list.
When all lists of this type T have been destroyed
Return it to the heap
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

28. Case Study: Large-Integer Arithmetic
Recall that numeric representation of numbers in computer memory places limits on their size
32 bit integers, two's complement max
We will design a BigInt class
Process integers of any size
For simplicity, nonnegative integers only
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

29. BigInt Design First step : select a storage structure
We choose a linked list
Each node sores a block of up to 3 consecutive digits
Doubly linked list for traversing in both directions
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

30. BigInt Design Input in blocks of 3 integers, separated by spaces
As each new block entered, node added at end
Output is traversal, left to right
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

31. BigInt Design Addition adds the groupings right to left
Keeping track of carry digits
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

32. BigInt Implementation
Standard list type provides all the tools we need
Note class declaration, Fig. 11.3A
View class definition, Fig. 11.3B
Driver program to demonstrate use of the class, Fig 11.4
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

33. Multiply-Ordered Lists
Ordered linked list
Nodes arranged so data items are in ascending/descending order
Straightforward when based on one data field
However, sometimes necessary to maintain links with a different ordering
Possible solution
Separate ordered linked lists – but wastes space
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

34. Multiply-Ordered Lists
Better approach
Single list
Multiple links
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

35. Sparse Matrices Usual storage is 2D array or 2D vector
If only a few nonzero entries
Can waste space
Stored more efficiently with linked structure
Similar to sparse polynomials
Each row is a linked list
Store only nonzero entries for the row
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

36. Sparse Matrices For we represent with A =
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

37. Sparse Matrices This still may waste space Alternative implementation
Consider if many rows were all zeros
Alternative implementation
Single linked list
Each node has row, column, entry, link
Resulting list
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

38. Sparse Matrices However … this loses direct access to rows
Could replace array of pointers with
Linked list of row head nodes
Each contains pointer to non empty row list
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

39. Sparse Matrices If columnwise processing is desired
Use orthogonal list
Each node stores row, column, value, pointer to row successor, pointer to column successor
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

40. Sparse Matrices Note the resulting representation of the matrix A =
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

41. This is an example of a generalized list
Generalized Lists
Examples so far have had atomic elements
The nodes are not themselves lists
Consider a linked list of strings
The strings themselves can be linked lists of characters
This is an example of a generalized list
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

42. Generalized Lists Commonly represented as linked lists where
Nodes have a tag field along with data and link
Tag used to indicate whether data field holds
Atom
Pointer to a list
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved

43. Generalized Lists Lists can be shared
To represent (2, (4,6), (4,6))
For polynomials in two variables P(x,y) = 3 + 7x + 14y2 + 25y7 – 7x2y7 + 18x6y7
Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved