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HASH TABLE PERFORMANCE A hash table of size 101 that contain six elements will perform very well. It is very unlikely to have any collisions, so the access functions are immediate, running in constant time O(1). This is direct access, just like an array. But a hash table of size 101 that contains 100 elements is likely to perform very poorly because there will have been many collisions in the process of storing its elements. For example, if the string "Lob" had 60 collisions before a free component was found for it, then each time it is accessed, it will take 60 probes to find it. That kind of performance is close to O(n) not much better than a linked list. The solution to the problem described here is to prevent the hash table from becoming too full. This is done by resizing it whenever it reaches a threshold size. The measure of fullness depends upon two parameters: The size of the hash table is the actual number of elements in the table; the capacity of the table is the number of components that it has. The ratio of these two parameters is called the load factor. In the first example cited in this section, the size was 6 and the capacity was 101, resulting in a load factor of 6/101 = 5.94 percent. In the second example, the size was 100, resulting in a load factor of 100/101 = 99.01 percent. The HashMap class automatically resizes its hash table when the load factor reaches a specific threshold value. This threshold value can be set when the hash table is created, using the constructor

such an application will almost always limit the number of elements in the list so that a flood of requests will not simply swamp the computer and leave no time or memory for processing requests So the server thread will also include a check to see if the number of pending requests is already at its maximum value; if so, the server thread will wait until the worker thread can complete at least one of the tasks On the other side, imagine the worker thread taking tasks off the list Again, removing a task from the list will require multiple machine instructions The worker thread will also be checking to see if the list is empty, for there may be no work to do In that case, the worker thread will wait until some task is added to the list by the server thread.

public HashMap(int initialCapacity, float loadFactor)

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which also allows the initial capacity to be set. If you use a constructor that does not take one or the other of these two arguments, then the default values of capacity 101 and load threshold 75 percent will be used.

Since an interrupt can occur between any two machine instructions, and since the operating system may choose to execute any ready thread at any moment, it is possible that the server thread will be interrupted as it adds a task to the list, and that the worker thread will be scheduled to execute next Without some control to insure that items are added to and removed from the list at appropriate times and as whole items, it s possible that the coordination will fail For instance, suppose the server thread finds the address of the last element of the list and then is interrupted After the OS services the interrupt, the OS schedules the worker thread, which removes a task from the list and completes processing In fact, the worker may continue to execute and remove several tasks from the list before the OS intervenes to schedule another thread.

COLLISION RESOLUTION ALGORITHMS The collision resolution algorithm used in the previous examples is called linear probing. When a new item hashes to a table component that is already in use, the algorithm specifies to increment the index until an empty component is found. This may require a wraparound back to the beginning of the hash table. EXAMPLE 8.6 Linear Probing

When the server thread eventually regains the CPU, it will continue from the point it was interrupted, and store a reference to a new task in the location it previously computed Now, however, the address is incorrect Depending on the situation, one of several possible errors will occur, but the application will surely fail, and it will fail in a way that cannot be reliably reproduced Such errors can be devilish to debug The section of code that must be executed in isolation in order to avoid corruption is called the critical section Guaranteeing correct execution of the critical sections requires that mutual exclusion be enforced when the critical sections are executing The code of a cooperating thread that is not in the critical section (and often most of the code is not in the critical section) is called the remainder section.

This program extends the program in Example 8.4. It keeps track of which table components are used and the load factor after each hashing.

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