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For example, for the array of values [−2, 1, −3, 4, −1, 2, 1, −5, 4], the contiguous subarray with the largest sum is [4, −1, 2, 1], with sum 6. Some properties of this problem are: If the array contains all non-negative numbers, then the problem is trivial; a maximum subarray is the entire array.
The earliest description of the bubble sort algorithm was in a 1956 paper by mathematician and actuary Edward Harry Friend, [4] Sorting on electronic computer systems, [5] published in the third issue of the third volume of the Journal of the Association for Computing Machinery (ACM), as a "Sorting exchange algorithm".
In computer science, a jagged array, also known as a ragged array [1] or irregular array [2] is an array of arrays of which the member arrays can be of different lengths, [3] producing rows of jagged edges when visualized as output.
In addition to support for vectorized arithmetic and relational operations, these languages also vectorize common mathematical functions such as sine. For example, if x is an array, then y = sin (x) will result in an array y whose elements are sine of the corresponding elements of the array x. Vectorized index operations are also supported.
For that reason, the elements of an array data structure are required to have the same size and should use the same data representation. The set of valid index tuples and the addresses of the elements (and hence the element addressing formula) are usually, [3] [5] but not always, [2] fixed while the array is in use.
An array language simplifies programming but possibly at a cost known as the abstraction penalty. [3] [4] [5] Because the additions are performed in isolation from the rest of the coding, they may not produce the optimally most efficient code. (For example, additions of other elements of the same array may be subsequently encountered during the ...
Moreover, for each number of cities there is an assignment of distances between the cities for which the nearest neighbour heuristic produces the unique worst possible tour. (If the algorithm is applied on every vertex as the starting vertex, the best path found will be better than at least N/2-1 other tours, where N is the number of vertices.) [1]
Illustration of the dining philosophers problem. Each philosopher has a bowl of spaghetti and can reach two of the forks. In computer science, the dining philosophers problem is an example problem often used in concurrent algorithm design to illustrate synchronization issues and techniques for resolving them.