Search results
Results from the WOW.Com Content Network
List comprehension is a syntactic construct available in some programming languages for creating a list based on existing lists. It follows the form of the mathematical set-builder notation (set comprehension) as distinct from the use of map and filter functions.
Here, the list [0..] represents , x^2>3 represents the predicate, and 2*x represents the output expression.. List comprehensions give results in a defined order (unlike the members of sets); and list comprehensions may generate the members of a list in order, rather than produce the entirety of the list thus allowing, for example, the previous Haskell definition of the members of an infinite list.
[1]: 226 Since this function is generally difficult to compute exactly, and the running time for small inputs is usually not consequential, one commonly focuses on the behavior of the complexity when the input size increases—that is, the asymptotic behavior of the complexity. Therefore, the time complexity is commonly expressed using big O ...
At recursion level k = 0, badsort merely uses a common sorting algorithm, such as bubblesort, to sort its inputs and return the sorted list. That is to say, badsort(L, 0) = bubblesort(L). Therefore, badsort's time complexity is O(n 2) if k = 0. However, for any k > 0, badsort(L, k) first generates P, the list of all permutations of L.
There exist methods with lower complexity, [3] which often depend on the length of the LCS, the size of the alphabet, or both. The LCS is not necessarily unique; in the worst case, the number of common subsequences is exponential in the lengths of the inputs, so the algorithmic complexity must be at least exponential. [4]
Strand sort is a recursive sorting algorithm that sorts items of a list into increasing order. It has O(n 2) worst-case time complexity, which occurs when the input list is reverse sorted. [1] It has a best-case time complexity of O(n), which occurs when the input is already sorted. [citation needed]
Therefore, the time complexity, generally called bit complexity in this context, may be much larger than the arithmetic complexity. For example, the arithmetic complexity of the computation of the determinant of a n × n integer matrix is O ( n 3 ) {\displaystyle O(n^{3})} for the usual algorithms ( Gaussian elimination ).
The running time can be improved by iteratively merging the first with the second, the third with the fourth, and so on. As the number of arrays is halved in each iteration, there are only Θ(log k) iterations. In each iteration every element is moved exactly once. The running time per iteration is therefore in Θ(n) as n is the number of elements.