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This algorithm finds the greedy (LPT) solution first, but then proceeds to look for better solutions. Several additional heuristics can be used to improve the runtime: [ 2 ] In a node in which the current sum-difference is at least the sum of all remaining numbers, the remaining numbers can just be put in the smallest-sum subset.
Another example is attempting to make 40 US cents without nickels (denomination 25, 10, 1) with similar result — the greedy chooses seven coins (25, 10, and 5 × 1), but the optimal is four (4 × 10). A coin system is called "canonical" if the greedy algorithm always solves its change-making problem optimally.
In computer science and software engineering, busy-waiting, busy-looping or spinning is a technique in which a process repeatedly checks to see if a condition is true, such as whether keyboard input or a lock is available. Spinning can also be used to generate an arbitrary time delay, a technique that was necessary on systems that lacked a ...
Kleinberg, J., and Tardos, E. (2005) Algorithm Design, Chapter 1, pp 1–12. See companion website for the Text Archived 2011-05-14 at the Wayback Machine. Knuth, D. E. (1996). Stable Marriage and Its Relation to Other Combinatorial Problems: An Introduction to the Mathematical Analysis of Algorithms. CRM Proceedings and Lecture Notes.
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.
In 1955, mathematician John Nash wrote a letter to the NSA, speculating that cracking a sufficiently complex code would require time exponential in the length of the key. [5] If proved (and Nash was suitably skeptical), this would imply what is now called P ≠ NP, since a proposed key can be verified in polynomial time.
In mathematics, economics, and computer science, the Gale–Shapley algorithm (also known as the deferred acceptance algorithm, [1] propose-and-reject algorithm, [2] or Boston Pool algorithm [1]) is an algorithm for finding a solution to the stable matching problem.
The generator polynomial of the BCH code is defined as the least common multiple g(x) = lcm(m 1 (x),…,m d − 1 (x)). It can be seen that g(x) is a polynomial with coefficients in GF(q) and divides x n − 1. Therefore, the polynomial code defined by g(x) is a cyclic code.