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Published byMeredith Lapping Modified over 2 years ago

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CSCI Linked lists

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CSCI Definitions l (linked) list is a data structure for efficient dynamic data storage l node - element of a list n data part - holds information contained in the list n pointer (reference) part - a pointer to type(class) node l nodes are allocated dynamically l list is formed by having the reference part of one node point to the next node l head (node) - first node in the list l tail (node) - last node in the list n the reference part of the tail points to NULL abcd NULL b (linked) list data part pointer part node head (node)tail (node)

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CSCI List manipulation l since head points to the next node and (transitively) to all the other nodes, all the information necessary to get the list data is a pointer to the head l list traversal - going through list elements to collect information on the lists structure or data stored l to traverse 1. allocate pointer variable for traversal ( ptr ) 2. assign address of head (from pointer to head) to ptr 3. look up the pointer part of node and assign it to ptr 4. Repeat step 3 until NULL is encountered l since nodes are allocated dynamically, they can be removed and added to the list with only minimum modifications required abcd NULL head (node)tail (node) pointer to head ptr

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CSCI Review l what is a list? l what is a node? l what does data part of node contain? l what does the reference part of node contain? l what is the head of a list? l what is the tail of a list? l what does the reference part of the tail of the list points to? l what is list traversal? why would you want to traverse a list?

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CSCI Linked Lists Definition of Linked Lists Examples of Linked Lists Operations on Linked Lists Linked List as a Class Linked Lists as Implementations of Stacks, Sets, etc.

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CSCI Definition of Linked Lists A linked list is a sequence of items (objects) where every item is linked to the next. Graphically: data head_ptr

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CSCI Definition Details Each item has a data part (one or more data members), and a link that points to the next item One natural way to implement the link is as a pointer; that is, the link is the address of the next item in the list It makes good sense to view each item as an object, that is, as an instance of a class. We call that class: Node The last item does not point to anything. We set its link member to NULL. This is denoted graphically by a slash in the link.

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CSCI Examples of Linked Lists (A Waiting Line) A waiting line of customers: John, Mary, Dan, Sue (from the head to the tail of the line) A linked list of strings can represent this line: JohnMaryDanSue head_ptr

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CSCI Examples of Linked Lists (A Stack of Numbers) A stack of numbers (from top to bottom): 10, 8, 6, 8, 2 A linked list of ints can represent this stack: head_ptr 8

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CSCI Examples of Linked Lists ( A Set of Non-redundant Elements ) A set of characters: a, b, d, f, c A linked list of chars can represent this set: abdc head_ptr f

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CSCI Examples of Linked Lists ( A Sorted Set of Non-redundant Elements ) A set of characters: a, b, d, f, c The elements must be arranged in sorted order: a, b, c, d, f A linked list of chars can represent this set: abcf head_ptr d

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CSCI Examples of Linked Lists ( A Polynomial ) A polynomial of degree n is the function P n (x)=a 0 +a 1 x+a 2 x 2 +…+a n x n. The a i s are called the coefficients of the polynomial The polynomial can be represented by a linked list ( 2 data members and a link per item ): a 0,0a 1,1a 2,2a n,n head_ptr

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CSCI Operations on Linked Lists Insert a new item –At the head of the list, or –At the end of the list, or –Inside the list, in some designated position Search for an item in the list –The item can be specified by position, or by some value Delete an item from the list –Search for and locate the item, then remove the item, and finally adjust the surrounding pointers size( ); isEmpty( )

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CSCI Insert– At the Head Insert a new data A. Call new: newPtr List before insertion: After insertion to head: data head_ptr Adata head_ptr A The link value in the new item = old head_ptr The new value of head_ptr = newPtr

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CSCI Insert – at the Tail Insert a new data A. Call new: newPtr List before insertion After insertion at end: data head_ptr Adata head_ptr A The link value in the new item = NULL The link value of the old last item = newPtr

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CSCI Insert – inside the List Insert a new data A. Call new: newPtr List before insertion: After insertion in 3 rd position: data head_ptr data A head_ptr data The link-value in the new item = link-value of 2 nd item The new link-value of 2 nd item = newPtr

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CSCI Delete – the Head Item List before deletion: List after deletion of the head item: data head_ptr data head_ptr data The new value of head_ptr = link-value of the old head item The old head item is deleted and its memory returned data

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CSCI Delete – the Tail Item List before deletion: List after deletion of the last item: data head_ptr data head_ptr New value of link value of the next to last item New link value of new last item = NULL. data

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CSCI Delete – an inside Item List before deletion: List after deletion of the 2 nd item: data head_ptr data head_ptr New link-value of the item located before the deleted one = the link-value of the deleted item data

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CSCI size() and isEmpty() We need to scan the items in the list from the head_ptr to the last item marked by its link-value being NULL Count the number of items in the scan, and return the count. This is the size(). Alternatively, keep a counter of the number of item, which gets updated after each insert/delete. The function size( ) returns that counter If head_ptr is NULL, isEmpty() returns true; else, it returns false.

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CSCI Searching for an Item Suppose you want to find the item whose data value is A You have to search sequentially starting from the head item rightward until the first item whose data member is equal to A is found. At each item searched, a comparison between the data member and A is performed.

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CSCI Time of the Operations Time to search() is O(L) where L is the relative location of the desired item in the List. In the worst case. The time is O(n). In the average case it is O(N/2)=O(n). Time for remove() is dominated by the time for search, and is thus O(n). Time for insert at head or at tail is O(1). Time for insert at other positions is dominated by search time, and thus O(n). Time for size() is O(1), and time for isEmpty() is O(1)

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CSCI Implementation of an Item Each item is a collection of data and pointer fields, and should be able to support some basic operations such as changing its link value and returning its member data Therefore, a good implementation of an item is a class The class will be called Node

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CSCI Class Node Design for Item The member variables of Node are: –The data field(s) –The link pointer, which will be called next The functions are: FunctionActionWhy Needed getNext( )returns the link.for navigation getData( )returns the datafor search setNext( Node *ptr) sets link to ptrfor insert/delete setData (type x) sets data to x.to modify data contents

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CSCI Class Node Type class Node { private: int data; // different data type for other apps Node *next; // the link pointer to next item public: Node(int x=0;Node * ptr=NULL); // constructor int getData( ); Node *getNext( ); void setData(int x); void setNext(Node *ptr); };

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CSCI Class Node Implementation Node::Node(int x, Node *p){ data=x; next=p;}; int Node::getData( ){return data;}; Node * Node::getNext( ){return next;}; void Node::setData(int x) {data=x;}; void Node::setNext(Node *ptr){next=ptr;};

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CSCI Implementation of Linked List A linked list is a collection of Node objects, and must support a number of operations Therefore, it is sensible to implement a linked list as a class The class name for it is List

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CSCI Class Design for List The member variables are: –Node *head_ptr; Member functions –Node * search(int x); Node * itemAt(int position); –void removeHead(); void removeTail(); void remove(int x); –void insertHead(int x); void insertTail(int x); void insert(Node *p, int x) // inserts item after the item // pointed to by p –int size( ); Node *getHead( ); Node getTail( ); –bool isEmpty( );

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CSCI Class List Type class List { private: Node *head_ptr; public: List( ); // constructor int size( ); Node *getHead( ); Node *getTail( ); bool isEmpty( ); Node *search(int x); Node *itemAt(int position); void removeHead(); void removeTail(); void remove(int x); // delete leftmost item having x void insertHead(int x); void insertTail(int x); void insert(Node *p, int x); };

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CSCI Implementation of Class List List::List( ){head_ptr= NULL}; int List::size( ){return numOfItems;}; Node * List::getHead( ) {return head_ptr;}; Node * List::getTail( ) {……..}; bool List::isEmpty() {return (!head_ptr);};

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CSCI Implementation of search( ) Node *List::search(int x){ Node * currentPtr = getHead( ); while (currentPtr != NULL){ if (currentPtr->getData( ) == x) return currentPtr; else currentPtr = currentPtr->getNext(); } return NULL;// Now x is not, so return NULL };

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CSCI Implementation of itemAt( ) Node *List::itemAt(int position){ …………………… return currentPtr; };

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CSCI Implementation of removeHead( ) void List::removeHead( ){ …..what if head is null…..??? Node * currentPtr = head_ptr( ); head_ptr=head_ptr->getNext( ); delete currentPtr; };

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CSCI Implementation of removeTail( ) void List::removeTail( ){ ………………. };

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CSCI Implementation of remove( ) void List::remove(int x){ ………………… };

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CSCI Implementation of insertHead( ) void List::insertHead(int x){ Node * newHead = new Node(x,head_ptr); head_ptr= newHead; };

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CSCI Implementation of insertTail( ) void List::insertTail(int x){ ……………… };

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CSCI Implementation of insert( ) // inserts item x after the item pointed to by p void List::insert(Node *p, int x){ ……………………….. };

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