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maps - Computer Science 211 Data Structures Mount Holyoke...

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Computer Science 211 Data Structures Mount Holyoke College Fall 2009 Topic Notes: Maps and Hashing Maps/Dictionaries A map or dictionary is a structure used for looking up items via key-value associations. We have seen this idea several times so far: Way back at the beginning of the semester, when we used a dictionary of Harry Potter spells. We stored symbol tables in maps for the postscript lab. We stored our vertices in maps in the graph implementations we just looked at. Both Java and the structure package define an interface called Map that we can use for this. See Structure Source: /home/jteresco/shared/cs211/src/structure5/Map.java This interface include the kinds of things we are used to seeing in our structures, so we won’t spend too much time looking at it. There are a lot of implementations of a Map possible. We can use a linked list of Association s. See Structure Source: /home/jteresco/shared/cs211/src/structure5/MapList.java We can use a MapList to simplify the Spells example. See Example: /home/jteresco/shared/cs211/examples/Spells/SpellsMapList.java This provides a convenient implementation, but doesn’t improve efficiency over our previous meth- ods. If our keys are comparable, we might keep our map contents sorted for more efficient lookups with a sorted array, or a binary search tree. See Structure Source: /home/jteresco/shared/cs211/src/structure5/Table.java In fact, there are many possible implementations of maps. If we think abstractly about a few variants, we can consider their time complexity on common opertions and space complexity. In the table below, n denotes the actual number of elements in the map, and N denote the maximum number of elements it could contain (where that restriction makes sense).
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CS 211 Data Structures Fall 2009 Structure Search Insert Delete Space Linked List O ( n ) O (1) O ( n ) O ( n ) Sorted Array O (log n ) O ( n ) O ( n ) O ( N ) Balanced BST O (log n ) O (log n ) O (log n ) O ( n ) Array[KeyRange] of EltType O (1) O (1) O (1) KeyRange That last line is very interesting. If we know the range of keys (suppose they’re all integers between 0 and KeyRange-1) we can use the key as the index directly into an array. And have constant time access! Hashing The map implementation of an array with keys as the subscripts and values as contents makes a lot of sense. However, there are some important restrictions on the use of this representation. This implementation assumes that the data has a key which is of a restricted type (some enumerated type in Pascal, integers in Java), which is not always the case. What if we’re trying to store strings or doubles or something more complex? Moreover, the size requirements for this implementation could be prohibitive. Suppose we wanted to store 2000 student records indexed by social security number. We would need an array with 1 billion elements!
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