By Richard E. Klima, Neil Sigmon, Ernest Stitzinger
As well as conventional themes, this finished compendium of algorithms, info constructions, and concept of computation covers:oapplications parts the place algorithms and information structuring ideas are of specific significance ograph drawingorobot algorithmsoVLSI layoutovision and snapshot processing algorithmsoschedulingoelectronic cashodata compressionodynamic graph algorithmsoon-line algorithmsomultidimensional facts structuresocryptographyoadvanced subject matters in combinatorial optimization and parallel/distributed computingUnique insurance of Algorithms and idea of Computation instruction manual makes it a necessary reference for researchers and practitioners in those purposes parts.
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Additional resources for Algorithms and Theory of Computation Handbook
This process continues until the queue contains a single item, the optimum tree. Reasonable implementations of priority queues will yield O(n log n) implementations of Huffman’s greedy algorithm. The idea of making greedy choices, facilitated with a priority queue, works to ﬁnd optimum solutions to other problems too. For example, a spanning tree of a weighted, connected, undirected graph G = (V , E) is a subset of |V | − 1 edges from E connecting all the vertices in G; a spanning tree is minimum if the sum of the weights of its edges is as small as possible.
2 Also when linked lists are an internal component of other algorithms, like hashing with chaining, which is explained later. 3 Sorted Array Search In the off-line case we can search faster if we allow some time to preprocess the set and the elements can be ordered. Certainly, if we sort the set (using O(n log n) comparisons in the worst-case) and we store it in an array, we can use the well-known binary search. Binary search uses divide and conquer to quickly discard half of the elements by comparing the searched key with the element in the middle of the array, and if not equal, following the search recursively either on the ﬁrst half or the second half (if the searched key was smaller or larger, respectively).
Consider the element uniqueness problem, the problem of determining if there are any duplicate numbers in a set of n numbers, x1 , x2 , . . , xn . Since there are only two possible outcomes, yes or no, the information theoretic lower bound says that a single comparison should be sufﬁcient to answer the question. 4) 1≤i