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In this case, the array from which samples are taken is [2, 3, -1, -20, 5, 10]. In computer science, the maximum sum subarray problem, also known as the maximum segment sum problem, is the task of finding a contiguous subarray with the largest sum, within a given one-dimensional array A[1...n] of numbers.
The list ranking problem was posed by Wyllie (1979), who solved it with a parallel algorithm using logarithmic time and O(n log n) total steps (that is, O(n) processors).). Over a sequence of many subsequent papers, this was eventually improved to linearly many steps (O(n/log n) processors), on the most restrictive model of synchronous shared-memory parallel computation, the exclusive read ...
Note that some of the numbers may be marked more than once (e.g., 15 will be marked both for 3 and 5). As a refinement, it is sufficient to mark the numbers in step 3 starting from p 2, as all the smaller multiples of p will have already been marked at that point. This means that the algorithm is allowed to terminate in step 4 when p 2 is ...
The input to the algorithm is a set S of numbers, and a parameter k. The required output is a partition of S into k subsets, such that the sums in the subsets are as nearly equal as possible. The main steps of the algorithm are: Order the numbers from large to small. Replace the largest and second-largest numbers by their difference.
Algorithm LargestNumber Input: A list of numbers L. Output: The largest number in the list L. if L.size = 0 return null largest ← L[0] for each item in L, do if item > largest, then largest ← item return largest "←" denotes assignment. For instance, "largest ← item" means that the value of largest changes to the value of item.
The Art of Computer Programming, Volume 3: Sorting and Searching, Third Edition. Addison–Wesley, 1997. ISBN 0-201-89685-0. Pages 138–141 of Section 5.2.3: Sorting by Selection. Anany Levitin. Introduction to the Design & Analysis of Algorithms, 2nd Edition. ISBN 0-321-35828-7. Section 3.1: Selection Sort, pp 98–100. Robert Sedgewick.
Graphs of functions commonly used in the analysis of algorithms, showing the number of operations versus input size for each function. The following tables list the computational complexity of various algorithms for common mathematical operations.
The greedy algorithm for maximum coverage chooses sets according to one rule: at each stage, choose a set which contains the largest number of uncovered elements. It can be shown that this algorithm achieves an approximation ratio of 1 − 1 e {\displaystyle 1-{\frac {1}{e}}} .