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Using transistors instead of vacuum tubes in computers resulted in machines that were much smaller and cheaper, and that required considerably less electricity to operate The transistor is one of the most important inventions in the 20th century While computer companies such as IBM and Honeywell focused on the development of mainframe computers, Digital Equipment Corporation (DEC) focused on the development of smaller computers DEC s PDP series of computers were small and designed to serve the computing needs of laboratories The PDP-8 was one of the first computers purchased by end users Because of their low cost and portability, these machines could be purchased to fill a specific need The PDP-8 is generally regarded as the first minicomputer The invention of the integrated circuit caused the trend toward smaller, cheaper, and faster computers to accelerate.

hash(Rad) = 3, load = 9% hash(Uhr) = 4, load = 18% hash(Ohr) = 2, load = 27% hash(Tor) = 8, load = 36% hash(Hut) = 5, load = 45% 3, 4, hash(Tag) = 7, load = 54% 5, hash(Eis) = 6, load = 63% 3, 4, 7, hash(Ast) = 1, load = 72% hash(Zug) = 9, load = 81%

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The essential difference here is in the sequence of index numbers probed within the while loop when a collision occurs. Instead of searching linearly, it uses a squared increment. For example, when the insertion of "Ast" collides at index 3, linear probing continued probing at indexes 4, 5, 6, 7, 8, and 9 (in Example 8.6). But with quadratic probing, only indexes 3, 4, 7, and 1 ( = 12 mod 11) are probed, using successive jumps of 1, 4, and 9 (12, 22, and 32). Linear probing required 50 percent more probes.

Popular Electronics featured an article on a kit that home hobbyists could purchase that would enable them to build a computer at home This machine, offered first in 1974, was the Altair 8800, manufactured by a company named MITS It ushered in the personal computer era These initial machines were designed to be built at home, which was fine for the home hobbyist but limited the availability of the machine The first programming language for the Altair was Altair BASIC, the first product of a little company called Microsoft In 1981 IBM introduced its personal computer, or PC, which changed the face of computing forever It was now possible for individuals to simply purchase these machines and use them at home..

The price that the quadratic probing algorithm pays for its improved performance is that it is more likely to result in an infinite loop. That happens in Example 8.7 with the next insertion. The string "Hof" hashes initially to index 3. After eight collisions, the linear probing algorithm found a free cell at index 0 ( = 11 mod 11). But the probe sequence used on this item by the quadratic probing algorithm is the same as for "Ast": 3, 4, 7, 1, 8, 6, 6, 8 1, 7, 4, 3, 4, . . . . This is computed from the unmodulated quadratic sequence 3, 4, 7, 12, 19, 28, 39, 52, 67, 84, 103, 124, 147, . . . . This continues indefinitely, probing only the six indexes 3, 4, 7, 1, 8, and 6, all of which have already been used. So even though the table is only 81% full, the insertion fails. That can t happen with linear probing. SEPARATE CHAINING Instead of devising a more effective collision resolution algorithm, we can avoid collisions altogether by allowing more than one item per table component. This method is called separate chaining, because is uses linked lists ( chains ) to hold the multiple items. In this context, the table components are usually called buckets. EXAMPLE 8.8 Separate Chaining

Here is how part of a definition for a HashTable class might look, using separate chaining:

If lock is not true (!lock), then make lock true, and return the value true to the calling program Otherwise, return the value false to the calling program Some boolean variable called lock is used to lock or unlock the resource If the resource is not locked at the time of the call, the instruction will lock it and return true meaning, It s OK to proceed If the resource is locked at the time of the call, the instruction will return false meaning, You must wait If such an instruction is part of the machine instruction set, code like this can take advantage of it: boolean thisLock; while( !testAndSet( thisLock ) ) { /* Do nothing */ } /* Now do whatever needs to be done in isolation */ /* Now free the lock */ thisLock = false; /* Carry on */ .

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public class HashTable { private static final int MASK = 0x7FFFFFFF; // 2^32-1

CHAP. 8]

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