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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 solutions to the sub-problems are then combined to give a solution to the original problem. The divide-and-conquer technique is the basis of efficient algorithms for many problems, such as sorting (e.g., quicksort , merge sort ), multiplying large numbers (e.g., the Karatsuba algorithm ), finding the closest pair of points , syntactic ...
In array languages, operations are generalized to apply to both scalars and arrays. Thus, a+b expresses the sum of two scalars if a and b are scalars, or the sum of two arrays if they are arrays. An array language simplifies programming but possibly at a cost known as the abstraction penalty.
Every solution submitted by a contestant is run on the judge against a set of (usually secret) test cases. Normally, contest problems have an all-or-none marking system, meaning that a solution is "Accepted" only if it produces satisfactory results on all test cases run by the judge, and is rejected otherwise.
The nearest neighbour algorithm was one of the first algorithms used to solve the travelling salesman problem approximately. In that problem, the salesman starts at a random city and repeatedly visits the nearest city until all have been visited.
Procedural programming languages are based on the concept of the unit and scope (the data viewing range) of an executable code statement. A procedural program is composed of one or more units or modules, either user coded or provided in a code library; each module is composed of one or more procedures, also called a function, routine ...
c = a + b 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 ...
This change gives the following algorithm (for a zero-based array). -- To shuffle an array a of n elements (indices 0..n-1): for i from n−1 down to 1 do j ← random integer such that 0 ≤ j ≤ i exchange a[j] and a[i] An equivalent version which shuffles the array in the opposite direction (from lowest index to highest) is: