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Variations on Linked Lists Ellen Walker CPSC 201 Data Structures Hiram College

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Linked List (review) Each element contains two parts: –Value of this element –Pointer to the next element class string_node { Private: string val; string_node *next; }

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Inserting into a Linked List (Review) /* Assume item is a reference to the node that contains “Barry”*/ Node newNode = new Node (“Carol”); newNode.next = aNode.next; aNode.next = newitem;

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Printing a Linked List (Review) //print elements, starting at the node called head; // Uses a for loop for(Node current=head; current!=null; current=current.next){ System.out.println(current.data); }

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Printing Using Iterator (Review) //prints the list, one item per line //returns iterator pointing before the list… Iterator itr = aList.iterator(); while(itr.hasNext()){ String name = itr.next(); System.out.println(name); }

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LinkedList Implementation (Review) public class LinkedList { private Node head; //first element or null private int size; //list length … private static class Node { //inner class private E data; private node next; } //methods go here }

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Implementing toString Writes elements of list into a string Use either traversal from before (iterator version shown) String toString(){ StringBuilder result = new StringBuilder(); Iterator itr = iterator(); while(itr.hasNext()){ result.append(itr.next()); result.append(‘\n’); }

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Dummy Nodes simplify implementation An empty list has one node (the dummy node) There is no longer a special case for adding the first element of the node! What changes need to be made to… –Constructor? –Find / Retrieve ? –Insert / Delete? Sometimes a dummy node can have a useful value (e.g. smallest possible element for sorted list)

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Changes to the implementation for a dummy node Constructor –Head is a new (dummy) node instead of NULL indexOf / get –indexOf is unchanged (assume value not otherwise in list) –get(k) will return value at node (k+1) Insert / Delete –Begin by locating the predecessor node –No special cases for first node (it has a predecessor)

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Circular List Circular List: The tail of the list points back to the head There is no NULL pointer to “end” the list.

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Issues with circular list How do you know when you’re done? –Make sure you save the head pointer. –When (cur.next == head) you’ve reached the end How are insertion and deletion handled? –No special cases! –Predecessor to head node is the last node in the list.

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The Josephus Problem (One of many variations…) The founder of a startup is forced to lay off all but one employee. Not having any better way to decide, he arranges all employees in a circle and has them count off. The 10th employee in the circle is laid off, and the count begins again. The last person is not laid off. If there are N employees, where should you sit to avoid being laid off?

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Solution Model the circle of employees as a circular linked list Implement the counting off process, and delete the 10th employee each time After N-1 people are deleted, there should be only one employee left. That employee’s original position number is the solution to the problem.

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Doubly Linked List Each node has prev and next pointer List can be traversed forward or backward To insert a node after “cur” –Node tmp = new Node (newItem); –tmp.next = cur.next; –cur.next=tmp; –tmp.prev=cur; –tmp.next.prev = tmp; Reverse the process to delete!

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Which list implementation? Array –Can jump into the middle easily (random access) –Inserting & deleting can require time-consuming shifting –Must allocate block of memory at once (can resize later with new) Linked –No random access –Insert & delete are fixed cost, once you decide where. –Nodes allocated one at a time.

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Linked List Choices Plain vanilla –Simple, small Dummy header –Eliminates special cases (chance for error) Circular –No defined start position in sequence –Can find the node before, though it takes N steps Doubly linked –Easy to find the node before –Larger Node; twice as many special cases Circular and doubly linked

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Linked Lists and Recursion Recursive definition of a list –Null (empty list) is a list(base case) –A list consists of one item (the head) followed by a list (next) Example: –A->B->C-| is a list –Head = A, next = B->C-|

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Recursive Function on Lists Base case for the recursive function is the empty list (base case for the definition) Other cases - –“Take a step” = do something to the head –Recurse = call function for the rest of the list –May or may not build up a solution

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Recursive List Search Node recFind (Node head, E x){ //x is not in an empty list! If (head == null) return null; //x is found at the beginning Else if (head.item == x) return head; //Recursive case: search the rest of the list Return recFind(head.next, x); }

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Recursive functions are private! A recursive function uses Node references. Node references are private –Implementation detail –Not every implementation of List has Nodes Most recursive functions have a public “starter” and a private internal function

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Public Caller for recFind boolean isIn(E x){ //call Find on the head of the list //if Find does not return null, the item is in // the list. return (recFind(head,x) != null); }

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Recursive CountItem This function counts the number of occurrences of the item x in the list Int CountItem (Node * head, ItemType x){ }

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Public Caller for CountItem int List::howMany(ListItemType x){ }

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