Hash Tables Versus Binary Search Trees in Java

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Use a hash table instead of a binary search tree if you do not need order statistics and are worried about nonrandom inputs
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We can also use binary search trees to implement i n s e r t and f i n d operations Although the resulting average time bounds are O(1og N), binary search trees also support routines that require order and thus are more powerful Using a hash table we cannot efficiently find the minimum element or extend the table to allow computation of an order statistic We cannot search
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efficiently for a string unless the exact string is known A binary search tree could quickly find all items in a certain range, but this capability is not supported by a hash table Furthermore, the O(1og N ) bound is not necessarily that much more than 0(1), especially since no multiplications or divisions are required by search trees The worst case for hashing generally results from an implementation error, whereas sorted input can make binary search trees perform poorly Balanced search trees are quite expensive to implement Hence, if no ordering information is required and there is any suspicion that the input might be sorted, hashing is the data structure of choice
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Hashing applications are abundant Compilers use hash tables to keep track of declared variables in source code The data structure is called a symbol table Hash tables are the ideal application for this problem because only insert and find operations are performed Identifiers are typically short, so the hash function can be computed quickly In this application, most searches are successful Another common use of hash tables is in game programs As the program searches through different lines of play, it keeps track of positions that it has encountered by computing a hash function based on the position (and storing its move for that position) If the same position recurs, usually by a simple transposition of moves, the program can avoid expensive recomputation This general feature of all game-playing programs is called the rransposition table We discussed this feature in Section 112, where we implemented the tic-tac-toe algorithm A third use of hashing is in online spelling checkers If misspelling detection (as opposed to correction) is important, an entire dictionary can be prehashed and words can be checked in constant time Hash tables are well suited for this purpose because the words do not have to be alphabetized Printing out misspellings in the order they occurred in the document is acceptable
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Hash tables can be used to implement the insert and find operations in constant average time Paying attention to details such as load factor is especially important in the use of hash tables; otherwise, the constant time bounds are not meaningful Choosing the hash function carefully is also important when the key is not a short string or integer You should pick an easily computable function that distributes well
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For separate chaining hashing, the load factor is typically close to 1, although performance does not significantly degrade unless the load factor becomes very large For quadratic probing, the table size should be prime and the load factor should not exceed 05 Rehashing should be used for quadratic probing to allow the table to grow and maintain the correct load factor This approach is important if space is tight and it is not possible just to declare a huge hash table This completes the discussion of basic searching algorithms In 21 we examine the binary heap, which implements the priority queue and thus supports efficient access of the minimum item in a collection of items
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