nyhoff, adts, data structures and problem solving with c++, second edition, 2005 pearson education,...

Nyhoff, ADTs, Data Structures and Problem Solving with C++, Second Edition, © 2005 Pearson Education, Inc. All rights reserved. 0-13-140909-3

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More Linking Up with Linked Lists

Chapter 11


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Chapter Contents

11.1 Some Variants of Singly-Linked Lists11.2 Linked Implementation of Sparse

Polynomials11.3 Doubly-Linked Lists and the Standard C+

+ list11.4 Case Study: Larger-Integer Arithmetic11.5 Other Multiply-Linked Lists


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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


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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


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• 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


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• For insertion at beginning of list– Head node is predecessor for new nodenewptr->next = predptr->next;predptr->next = newptr;


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• For deleting first element from a list with a head node– Head node is the predecessorpredptr->next = ptr->next;delete ptr;


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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


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Circular Linked Lists

• Traversal algorithm must be adjustedif (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?


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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


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• We could represent a polynomial by a list of ordered pairs– { (coef, exponent) … }

• Fixed capacity ofarray still problematic– Wasted space for

sparse polynomial


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• 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


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• 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)


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Addition Operator

• Requires temporary pointers for each polynomial (the addends and the resulting sum)


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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


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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


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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


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Doubly-Linked Lists

• To delete a node– Reset forward link of predecessor, backward link

of successor– Then delete removed node


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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.


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Comparing List<t> With Other Containers

• Note : list<T> does not support direct access – does not have the subscript operator [ ].

Property Array vector<T> deque<T> list<T>Direct/random access ([]) (exclnt)(good)XSequential access

Insert/delete at front (poor)

Insert/delete in middle

Insert/delete at end

Overhead lowest low low/mediumhigh


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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)


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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


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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


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Node structure

struct list_node{ pointer next,

prev;T data; }


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• 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.


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The STL list<T> Memory Management

When a node is allocated1. If there is a node on the free list, allocate it.

• This is maintained as a linked stack

2. If the free list is empty:a) Call the heap manager to allocate a block of

memory (a "buffer", typically 4K)b) Carve it up into pieces of size required for a

node of a list<T>.


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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


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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

2147483647• We will design a BigInt class

– Process integers of any size– For simplicity, nonnegative integers only


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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


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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


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BigInt Design

• Addition adds the groupings right to left– Keeping track of carry digits


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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


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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


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Multiply-Ordered Lists

• Better approach– Single list– Multiple links


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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


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• For

we represent with

Sparse Matrices

A =


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Sparse Matrices

• This still may waste space– Consider if many rows were all zeros

• Alternative implementation– Single linked list– Each node has row, column,

entry, link• Resulting list


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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


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Sparse Matrices

• If columnwise processing is desired– Use orthogonal list– Each node stores row, column, value, pointer to

row successor, pointer to column successor


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Sparse Matrices• Note the resulting

representation of the matrix

A =


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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

charactersThis is an

example of a generalized list


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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


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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,...

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