Week 12: Priority queues Heaps and heap operations

Transcription

1 Week 12: Priority queues Heaps and heap operations Comp 271 Spring, 2012 Mr. Weisert The queues we studied in week 6 were FIFO Many real-world situations consider other criteria for choosing which object in the queue to serve next. Urgency Resource requirement Examples? Where people are being served it's often easier to establish separate queues for certain categories. Why? Examples? But machines are more flexible than people Priority is often determined by a formula Age (or timeofarrival) may get more weight as time passes, so that even the least urgent most demanding service eventually gets performed. We won't worry about the formula now. Just assume that each object in the queue has an assigned priority. compareto (or compare) ranks priority A common but sometimes confusing convention for designating priority Low numbers often represent high priority. "Priority 1" often denotes absolute top priority; i.e. a dire emergency Nothing is more important Fortunately the class designer can control ranking by the way compareto (or compare) is implemented. COMP 271, Springl, copyright Conrad Weisert

2 WARNING! The Student example (p. 556) is both seriously flawed in several ways (See errata sheet entries for that page) poorly motivated ("priority" usually implies the order in which elements (customers) will be served, not just a ranking for sorting.) Nevertheless it shows how a priority queue works: We can use it to learn about siftup (p ) and other operations on a priority queue. But don't ever develop anything like that yourself. Heap Structure A complete binary tree in which The root is the first (smallest, largest, etc.) according to compareto (or compare) The left and right subtrees are heaps See example, p. 554 How is that different from a binary search tree? What use is it? Question When we remove the root (highest priority) element from a heap, how many possiblities are there for the new root (the next highest priority item)? Underlying structure for a heap For a TreeMap we used a linked list of nodes (Entry) For a heap, however, because the binary tree is complete, (how do we know?) we can use an array That allows access to any element in constant time. COMP 271, Springl, copyright Conrad Weisert

3 Reminder Don't ever do what the Student class (p. 556) does. In particular: Don't decompose a String argument in a constructor (with or without Scanner) Why not? What should we do instead? More questions Why is the internal array underlying a heap a built-in Java array (see ) instead of an ArrayList collection? What is modcount (p ) used for? How does the grow(int k) method (called from the add method, p. 559) work? Don't use compareto for a non-natural ordering, esp. when an accessor function could easily provide the needed data. Heap operations (methods) T element() (p. 563) Returns (but doesn't remove) the root element, which is the smallest (or highest priority) T remove() (p. 564) Returns (and removes) the root element and does any rearrangements needed to preserve the heap property. How does the performance differ? boolean add(t element) (p. 559) Adds element to the prirority queue, preserving the heap property. Auxliary (fix-up) methods siftup(int K, T element) (page 560) Used by add(int K, T element) siftdown(int k, T element) (page 566) Used by remove() They maintain the heap property Follow the diagrams to help understand what they do COMP 271, Springl, copyright Conrad Weisert

4 Heap sort See section 13.4 for full explanation. Two new words (for most of us) heapify (verb, p. 567) heapity (noun. p. 570) What's your reaction to this (p. 567)? "After all of the swaps and fix downs the elements in the array queue will be in reverse order, so by reversing the order of the elements, the array will be in order" (p. 567) We shall examine this algorithm Thursday Message compression Text messages are usually composed of a string of character codes, which may be: Unicode (16 bits, full international support) ASCII (7 or 8 bits, English with punctuation) BCI (6 bits, upper case only -- obsolete) EBCDIC (8 bits, IBM extension of BCI) But some characters (E in English) appear much more frequently than others (!). Therefore, we can usually compress a message by using short codes for frequently occurring characters and longer codes for infrequent ones. That may have a significant impact on performance, expecially involving input-output or long-distance transmission. Huffman codes To compress a message using variable-length character coding, we could either: a. use the known frequencies of characters in English (or another language) or b. derive custom encoding for a specific message A risk with variable-length codes What happens if a bit is lost in transmission? What are the advantages and disadvantages of each? COMP 271, Springl, copyright Conrad Weisert

5 Other compression techniques Summarize repeated characters, especially blanks (50)' 'Hello, there!(50)' ' Use shift instead of separate individual codes for upper & lower case N OW IS THE TIME. But those aren't what this chapter is about. COMP 271, Springl, copyright Conrad Weisert