Lecture 10: Searching & Mapping

1. CSC 213 – Large Scale Programming Lecture 10:Searching& Mapping

2. Today’s Goal • Consider the basics of searchable data • How do we search using a computer? • What are our goals while searching? • ADTs used for search & how would they work? • Most critically, where the $&*#%$# are my keys? • How do Map & Dictionary ADT work and search? • Methods to add, remove, and access data? • How Sequenceused to implemented these • When & why would we use Sequence-based approach

3. Searching • Search for unknown data in most cases • Consider the reverse: why search for what you have? • Seek data related to terms used • Already have idea, want web pages containing terms • Get encoded proteins given set of amino acids • Given “borrowed” credit cards, get credit limits • Exacting, but boring, work doing these searches • Make this work ideal for computers & students

4. Map-Based Bartender

5. Map-Based Bartender No problem. I’ll have aManhattan ¾ oz sweet vermouth2½ oz bourbon 1 dash bitters1 maraschino cherry1 twist orange peel

6. Map-Based Bartender That’ll be $2 billion I’ll have aManhattan

7. Map-Based Bartender I’ll have aManhattan key value

8. Search Terms • Keygets valuables • We already have key • Want valueas a result of this • Mapworks similarly • Give it keyvaluereturned • Uses Entryto do this work

9. Entry Interface • Need a key to get valuables • key used to search – it is what we already have • What we want is the result of search – value interface Entry<K,V> { K key();V value(); }

10. Map Method Madness, Mmmm… • Describes a searchable Collection • put(K key, V value)adds data as an Entry • remove(K key)removes Entry containing key • get(K key)returns valueassociated with key • Several Iterablemethods are also defined • Methods to use are entries(), keys(), & values() • Iterates over expected data so can use in for(-each) loops • Also defines usual Collectionmethods • isEmpty() & size()

11. Searching Through a Map • Map is a Collection of key-valuepairs • Give it key& get value in return from ADT • Now we have ADT to work with searchable data • Many searches unsuccessful • Unsuccessful search is normal, not unusual • Expected events should NOTthrow exceptions • This is normal; return null when nothing found

12. At Most 1 Value Per Key • Entrys have unique keys in a Map • If key exists, put(key,value)replaces existing Entry • Returns prior value forkey in the Map so its not lost • If before call key not in Map, null returned

13. Sequence-Based Map • Sequence’s perspective of Mapthat it holds Positions elements

14. Sequence-Based Map • Outside view of Map and how it is stored Positions Entrys

15. Using a Map • Mapgreat when want only one value for a key • Credit card number goes to one account • One person has a given social security number • One definition per word in the dictionary

16. Using a Map • Mapgreat when want only one value for a key • Credit card number goes to one account • One person has a given social security number • One definition per word in the dictionary

17. Using a Map • Mapgreat when want only one value for a key • Credit card number goes to one account • One person has a given social security number • One definition per word in the dictionary • Could try associating multiple values per key • Map key to Sequence of valuespossible solution • But this means Map’s user must handle complexity

18. Using a Map • Could try associating multiple values per key • Map key to Sequence of valuespossible solution • But this means Map’s user must handle complexity

19. Dictionary-based Bartender

20. Dictionary-based Bartender No problem. I’ll have aManhattan key value

21. Dictionary-based Bartender Not that Manhattan Sorry. key value

22. Dictionary-based Bartender Not that Manhattan Sorry. How about… key anothervalue

23. Dictionary-based Bartender That’ll be $2 billion Mmmmm... Manhattan key not a anothervalue

24. Dictionary ADT • Dictionary ADT very similar to Map • Hold searchable data in each of these ADTs • Both data structures are collections of Entrys • Convert keyto valueusing either concept • Dictionary can have multiple values for one key • 1 valuefor keyis still legal option

25. Dictionary ADT • Dictionary ADT very similar to Map • Hold searchable data in each of these ADTs • Both data structures are collections of Entrys • Convert keyto valueusing either concept • Dictionary can have multiple values for one key • 1 valuefor keyis still legal option “awesome”

26. Dictionary ADT • Dictionary ADT very similar to Map • Hold searchable data in each of these ADTs • Both data structures are collections of Entrys • Convert keyto valueusing either concept • Dictionary can have multiple values for one key • 1 valuefor keyis still legal option “awesome” • Also many Entryswith same keybut different value “cool”“cool”

27. Map vs. Dictionary

28. Map vs. Dictionary MapADT Dictionary ADT • Collection of Entrys • key– searched for • value– cared about • Collection of Entrys • key– searched for • value– cared about

29. Map vs. Dictionary MapADT Dictionary ADT • Collection of Entrys • key– searched for • value– cared about • Basic implement: • List w/ Entrys in increasing order of keys • Collection of Entrys • key– searched for • value– cared about • Basic implement: • List w/ Entrys in increasing order of keys

30. Map vs. Dictionary MapADT Dictionary ADT • Collection of Entrys • key– searched for • value– cared about • Basic implement: • List w/ Entrys in increasing order of keys • keyin at most1Entry • Collection of Entrys • key– searched for • value– cared about • Basic implement: • List w/ Entrys in increasing order of keys • Entryscan sharekey

31. Changes for Dictionary

32. Ordered List-Based Approach • Idea normally imagined w/ Map & Dictionary • Maintains ordered list of key-value pairs • Must maintain Entrys ordered by their key • Faster searching provides performance win Q: “Mom, how do I spell _______?” A: “Look it up.” • Efficiency gains not just for get& getAll • Entrys with same key stored in any order • Only requires that keys be in order only

33. Ordered List-Based Approach • Iteratorsshouldrespect ordering of Entrys • Should not be a problem, if Entrys stored in order • If O(1) access time, search time is O(log n) • Array-based structure required to hold Entrys • To get immediate access, needs to access by index • Requires IndexList-based implementation

34. Binary Search • Finds keyusing divide-and-conquer approach • First of many times you will be seeing this approach • Algorithm has problems solved using recursion • Base case 1:No Entrys remain to find the key • Base case 2: At data’s midpoint is matching key • Recursive Step 1: If midpoint too high, use lower half • Recursive Step 2: Use upper half,if midpoint too low

35. Binary Search • low and high params specifying range to check • Would be called with 0 & size() – 1, initially • If l > h, no match possible in this data • Compare with key at midpoint of low & high • Consider steps for find(7): 0 1 3 4 5 7 8 9 11 14 16 18 19 m h l

36. Binary Search • low and high params specifying range to check • Would be called with 0 & size() – 1, initially • If l > h, no match possible in this data • Compare with keyat midpoint of low & high • Consider steps for find(7): 0 1 3 4 5 7 8 9 11 14 16 18 19 m h l 0 1 3 4 5 7 8 9 11 14 16 18 19 m h l

37. Binary Search • low and high params specifying range to check • Would be called with 0 & size() – 1, initially • If l > h, no match possible in this data • Compare with keyat midpoint of low & high • Consider steps for find(7): 0 1 3 4 5 7 8 9 11 14 16 18 19 m h l 0 1 3 4 5 7 8 9 11 14 16 18 19 m h l 0 1 3 4 5 7 8 9 11 14 16 18 19 m h l

38. Binary Search • low and high params specifying range to check • Would be called with 0 & size() – 1, initially • If l > h, no match possible in this data • Compare with keyat midpoint of low & high • Consider steps for find(7): 0 1 3 4 5 7 8 9 11 14 16 18 19 m h l 0 1 3 4 5 7 8 9 11 14 16 18 19 m h l 0 1 3 4 5 7 8 9 11 14 16 18 19 m h l 0 1 3 4 5 7 8 9 11 14 16 18 19 l = m = h

39. Using Ordered Sequence • getuses binary search; takes O(log n)time • Should also start with binary search for getAll() • getAllchecks neighbors to find all matches • Add and remove methods could use binary search • List shifts elements in putto make hole for element • Would also need to do shift when removing from list • Each takes O(n) total time in worst case as a result

40. Comparing Keys • For all searching, must find matching keys • Cannot rely upon equals()when ordering • Want to be lazy, write code for all types of key • Use <, >, == if keys numeric type, but this is limiting • String also has simple method: compareTo() • General way comparing keys based upon this idea?

41. Comparable<E> Interface • In Java as a standard from java.lang • Defines single method used for comparison • compareTo(E obj)compares instance with obj • Returns intwhich is either negative, zero, positive

42. Ordered Sequence Example • Easiest to require that keys be Comparable • Now reuse class anywhere by adding interface • Also use standard types like String & Integer • compareTo()in binary search makes it simple int c = k.compareTo(list.get(m).getKey());if (c > 0) {return binarySearch(k, m + 1, h);} else if (c < 0) { return binarySearch(k, l, m - 1);} else { return m;}

43. What is a Map/Dictionary? • At simplest level, both are collection of Entrys • Focus on transforming data (or so it appears) • Add data with keyand value to which it is transformed • Accessortransforms keytovalueassociated with key • remove() used to delete an Entry • At most one valueper keyusing a Map • With Dictionary, multiple values per keypossible

44. Before Next Lecture… • Week #4 assignment due Tuesday at 5PM • Continue to do reading in your textbook • Learn more about hash & what it means in CSC • How can we tell if a hash is any good? • Hash tables sound cool, but how do we make them? • Monday is when lab project phase #1 due • Will have time in lab, but then will be the weekend • Project #1 available tonight after lab • Will be due in parts to “encourage” good habits