this tends to be too costlyand methods that offer compromise by being simple to compute and still superior to the linear function are preferred one of them consists of using quadratic function such that the sequence of indices for probing is (khi ( mod ni > note that computation of the next index need not involve the operation of squaringif we use the following recurrence relations for hi and di hi+ di+ hi di di > with and this is called quadratic probingand it essentially avoids primary clusteringalthough practically no additional computations are required very slight disadvantage is that in probing not all table entries are searchedthat isupon insertion one may not encounter free slot although there are some left in factin quadratic probing at least half the table is visited if its size is prime number this assertion can be derived from the following deliberation if the -th and the -th probes coincide upon the same table entrywe can express this by the equation mod mod ( (modulo nsplitting the differences up into two factorswe obtain ( )( (modulo nand since jwe realize that either or have to be at least / in order to yield + * with being an integer in practicethe drawback is of no importancesince having to perform / secondary probes and collision evasions is extremely rare and occurs only if the table is already almost full as an application of the scatter storage techniquethe cross-reference generator procedure shown in sect is rewritten the principal differences lie in the procedure search and in the replacement of the pointer type node by the global hash table of words the hash function is the modulus of the table sizequadratic probing was chosen for collision handling note that it is essential for good performance that the table size be prime number although the method of key transformation is most effective in this case -actually more efficient than tree organizations -it also has disadvantage after having scanned the text and collected the wordswe presumably wish to tabulate these words in alphabetical order this is straightforward when using tree organizationbecause its very basis is the ordered search tree it is nothoweverwhen key transformations are used the full significance of the word hashing becomes apparent not only would the table printout have to be preceded by sort process (which is omitted here)but it even turns out to be advantageous to keep track of inserted keys by linking them together explicitly in list hencethe superior performance of the hashing method considering the process of retrieval only is partly offset by additional operations required to complete the full task of generating an ordered cross-reference index const (*primetable size*wordlen (*max length of keys*noc (*max no of items per word*type word array wordlen of chartable pointer to array of record keywordnintegerlnoarray noc of integer end(adens _crossref *