By Mikhail J. Atallah, Marina Blanton
Algorithms and conception of Computation instruction manual, moment variation: normal suggestions and methods presents an updated compendium of basic laptop technological know-how issues and strategies. It additionally illustrates how the subjects and methods come jointly to carry effective options to special useful difficulties. in addition to updating and revising a number of the latest chapters, this moment version comprises 4 new chapters that disguise exterior reminiscence and parameterized algorithms in addition to computational quantity idea and algorithmic coding conception.
This best-selling guide maintains to aid laptop pros and engineers locate major details on quite a few algorithmic issues. The specialist members sincerely outline the terminology, current uncomplicated effects and strategies, and provide a few present references to the in-depth literature. additionally they offer a glimpse of the key examine concerns about the appropriate topics.
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Additional info for Algorithms and theory of computation handbook, - General concepts and techniques
2 Sequential Search Consider the simplest problem: search for a given element in a set of n integers. If the numbers are given one by one (this is called an online problem), the obvious solution is to use sequential search. That is, we compare every element, and, in the worst case, we need n comparisons (either it is the last element or it is not present). Under the traditional RAM model, this algorithm is optimal. This is the algorithm used to search in an unsorted array storing n elements, and is advisable when n is small or when we do not have enough time or space to store the elements (for example in a very fast communication line).
If the hash function distributes the elements uniformly over the table, the number of collisions cannot be too large on the average (after all, the expected number of elements per slot is α), but the well-known birthday paradox makes it very likely that there will be at least one collision, even for a lightly loaded table. There are two basic methods for handling collisions in a hash table: chaining and open addressing. 1 Chaining The simplest chaining method stores elements in the table as long as collisions do not occur.
Can we speed up binary search? First, we have to deﬁne how the memory is accessed in a concurrent way. The most used model is concurrent read but exclusive write (CREW) (otherwise it is diﬃcult to know the ﬁnal value of a memory cell after a writing operation). In a CREW PRAM, we can use the following simple parallel binary search. We divide the sorted set into p + 1 segments (then, there are p internal segment boundaries). Processor i compares the key to the element stored in the ith boundary and writes in a variable ci a 0, if it is greater or a 1 if it is smaller (in case of equality, the search ends).