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CSE 326: Data Structures Lists

CSE 326: Data Structures Lists. Lecture 5: Wednesday, Jan 15, 2003. Outline. Finish lists Stacks and queues Begin trees Remember: reading assignment Chapter 3 this week (including weekend). Iterators. Introduce a new public class to explicitly represent a position in a list Then:.

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CSE 326: Data Structures Lists

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  1. CSE 326: Data Structures Lists Lecture 5: Wednesday, Jan 15, 2003

  2. Outline • Finish lists • Stacks and queues • Begin trees Remember: reading assignment Chapter 3 this week (including weekend)

  3. Iterators • Introduce a new public class to explicitly represent a position in a list • Then: public class LinkedListItr {ListNode current; public Object retrieve() { return current.element; } public void advance() { current = current.next; } public boolean pastEnd() { return current == NULL; } LinkedListItr i; for (i = mylist.first(); !i.pastEnd(); i.advance){ do something on each v.retrieve() }

  4. Abstract Iterators • Iterators can also be defined for an array implementation of lists: • We can create an abstract iterator that works for both linked list and array implements of List public class ArrayListItr { Object [] data; integer current; public Object retrieve() { return data[current]; } public void advance() { current = current+1; public boolean pastEnd() {return current>size;}}

  5. Abstract Iterator • Why do this? abstract class ListItr { abstract Object retrieve(); abstract void advance(); abstract boolean pastEnd(); } class LinkedListItr extends ListItr { … } class ArrayListItr extends ListItr { … }

  6. Another Array Implementation of Linked Lists 1 7 9 2 3 4 5 6 8 10 Data F O A R N R T Next 3 8 6 4 -1 10 5 First = 2 • How do we implement • Delete(position) ? • Insert(element, position)?

  7. Free Cell Management 1 7 9 2 3 4 5 6 8 10 Data F O A R N R T Next 7 9 0 3 8 6 4 -1 10 5 First = 2 Free = 1 When an item is removed from the list, must “reclaim” the unused cell for later use Can use same array to manage a second list of unused cells

  8. Memory Management • Keeping a free cell list is an example of a memory management strategy • How is memory managed in C? • C++? • Java?

  9. ( 5 2 3 ) 5 + 2x + 3x2 ( 7 8 ) 7 + 8x ( 3 0 2 ) 3 + x2 List ADT Polynomial ADT Possible linked list implementation: Ai is the coefficient of the xi-1 term: Problem?

  10. 4 + 3x2001 ( 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 )

  11. 4 0 3 2001 Sparse Vector Data Structure:4 + 3x2001 (<4 0> <2001 3>)

  12. Addition of Two Polynomials? Complexity? 15+10x50+3x1200 p 15 0 10 50 3 1200 5+30x50+4x100 q 5 0 30 50 4 100

  13. Addition of Two Polynomials • One pass down each list: (n+m) 15+10x50+3x1200 p 15 0 10 50 3 1200 5+30x50+4x100 q 5 0 30 50 4 100 r 20 0 40 50 4 100 3 1200

  14. Sparse Matrices • How could we represent this compactly? ( <row (<column data> <column data> …)> <row (<column data> <column data> …)> … ) ( <1 (<1 18> <2 33>)> <4 (<4 99>)> <5 (<5 27>) )

  15. a b c a b c Various List Implementations • Without header: • With header: • Variation: a b c Advantage of the header: easier to insert/delete at the beginning/end

  16. b a c Various List Implementations • Simply linked: • Double linked: a b c Advantage of double linked: delete is easier; also: traverse backwards

  17. Various List Implementations • Open: • Circular: a b c a b c Advantage: none, really, but circular lists are popular

  18. Old list 2 5 8 Newlist 2 5 6 Copy semantics v.s. destructive semantics Example: insert x in a sorted list: • Copy semantics (assume no header) public ListNode insert(int x, ListNode l) { if (l==null || l.element > x) /* insert here */ return new ListNode(x, l); else /* copy here */ return new ListNode(l.element, insert(x,l.next))

  19. Copy semantics v.s. destructive semantics • Destructive semantics (assume header now) public void insert(int x, LinkList h) { if (h.header==null || h.header.element > x) header = new ListNode(x, h.header); else { ListNode l = h.header; while (l.next != null && l.next.element < x) l = l.next; l.next = new ListNode(x, l.next); } 2 5 8 6

  20. Summary: Some Complexities

  21. The Stack ADT Mathematical definition: • The operators: • The axioms: newStack :  stackpush: stack  element  stack top : stack  element pop : stack  stack isEmpty : stack  boolean constructors top(newStack) = error top(push(s, x)) = x pop(newStack) = error pop(push(s,x)) = s isEmpty(newStack) = true isEmpty(push(s, x)) = false Express eachoperator in terms ofthe constructors

  22. Stack Implementations • Implementation with arrays: • newStack, push, pop, top, isEmpty = O(1) • Issue: size of the array is a limitation • Solution: make it stretchy ! top

  23. a b c Stack Implementations • Implementation with linked list: • newStack, push, pop, top, isEmpty = O(1) Where is the top of the stack ?

  24. Applications of Stacks • Tree traversals, graph traversals • Will see in coming lectures • Parsing expressions • Read the book !

  25. The Queue ADT Mathematical definition: • Operators: • The axioms: newQueue :  queueenqueue: queue  element  queue front : queue  element dequeue : queue  stack isEmpty : queue  boolean constructors front(newQueue) = error front(enqueue(q, x) = if isEmpty(q) then x else front(q) dequeue(newQueue) = error dequeue(enqueue(q, x) = if isEmpty(q) then q else dequeue(q) isEmpty(newQueue) = true isEmpty(enqueue) = false Express eachoperator in terms ofthe constructors

  26. Queue Implementations • Implementation with “circular” arrays: • newQueue, enqueue, dequeue, front, isEmpty = O(1) • Stretchy arrays, of course  front rear

  27. Queue Implementations • Implementation with linked list: • newQueue, enqueue, dequeue, front, isEmpty = O(1) a b c Where is the front and where is the rear ?

  28. Applications of Queues • Tree traversals, graph traversals • Will see in coming lectures • Wherever fairness is needed: • Printer queues • Packets in a network • http requests at a web server • Etc.

  29. Trees Material: Weiss Chapter 4 • N-ary trees • Binary Search Trees • AVL Trees • Splay Trees

  30. Tree Jargon • Nodes: A, B, …, F • Root node: A • Leaf nodes: B, E, F, D • Edges: (A,B), (A,C), …, (C, F) • Path: sequence of nodes connected by edges. • Path examples: (B), (A,B),(A,C), (A,C,E), (A,C,F), (C), etc A C D B F E Questions. A tree has N nodes.How many edges does it have ? How many paths ?

  31. Tree Jargon • Length of a path = number of edges • Depth of a node x = length of path from root to x • Height of node x = length of longest path from x to a leaf • Depth and height of tree = height of root • The label of a node: A, B, C, … depth=0, height = 2 A C D B F depth = 2, height=0 E

  32. Definition and Tree Trivia Graph-theoretic definition of a Tree: A tree is a graph for which there exists a node, called root, such that: -- for any node x, there exists exactly one path from the root to x Recursive Definition of a Tree: A tree is either: a. empty, or b. it has a node called the root, followed by zero or more trees called subtrees

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