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An algorithm is fundamentally a set of rules or defined procedures that is typically designed and used to solve a specific problem or a broad set of problems.. Broadly, algorithms define process(es), sets of rules, or methodologies that are to be followed in calculations, data processing, data mining, pattern recognition, automated reasoning or other problem-solving operations.
Divide and conquer divides the problem into multiple subproblems and so the conquer stage is more complex than decrease and conquer algorithms. [citation needed] An example of a decrease and conquer algorithm is the binary search algorithm. Search and enumeration Many problems (such as playing chess) can be modelled as problems on graphs.
For example, if at each step the median is chosen as the pivot then the algorithm works in O(n log n). Finding the median, such as by the median of medians selection algorithm is however an O( n ) operation on unsorted lists and therefore exacts significant overhead with sorting.
Specific applications of search algorithms include: Problems in combinatorial optimization, such as: . The vehicle routing problem, a form of shortest path problem; The knapsack problem: Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as ...
A stack (LIFO queue) will yield a depth-first algorithm. A best-first branch and bound algorithm can be obtained by using a priority queue that sorts nodes on their lower bound. [3] Examples of best-first search algorithms with this premise are Dijkstra's algorithm and its descendant A* search. The depth-first variant is recommended when no ...
For examples of this specification-method applied to the addition algorithm "m+n" see Algorithm examples. An example in Boolos-Burgess-Jeffrey (2002) (pp. 31–32) demonstrates the precision required in a complete specification of an algorithm, in this case to add two numbers: m+n. It is similar to the Stone requirements above.
Since algorithms are platform-independent (i.e. a given algorithm can be implemented in an arbitrary programming language on an arbitrary computer running an arbitrary operating system), there are additional significant drawbacks to using an empirical approach to gauge the comparative performance of a given set of algorithms. Take as an example ...
It puts a median into A[hi] first, then that new value of A[hi] is used for a pivot, as in a basic algorithm presented above. Specifically, the expected number of comparisons needed to sort n elements (see § Analysis of randomized quicksort ) with random pivot selection is 1.386 n log n .