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Wikidata item; Appearance. move to sidebar hide In ... The following Python source code tests a sequence of numbers to determine if it is superincreasing:
The classic merge outputs the data item with the lowest key at each step; given some sorted lists, it produces a sorted list containing all the elements in any of the input lists, and it does so in time proportional to the sum of the lengths of the input lists. Denote by A[1..p] and B[1..q] two arrays sorted in increasing order.
In order to find the value associated with a given key, a sequential search is used: each element of the list is searched in turn, starting at the head, until the key is found. Associative lists provide a simple way of implementing an associative array, but are efficient only when the number of keys is very small.
If the running time (number of comparisons) of merge sort for a list of length n is T(n), then the recurrence relation T(n) = 2T(n/2) + n follows from the definition of the algorithm (apply the algorithm to two lists of half the size of the original list, and add the n steps taken to merge the resulting two lists). [5]
algorithm merge(A, B) is inputs A, B : list returns list C := new empty list while A is not empty and B is not empty do if head(A) ≤ head(B) then append head(A) to C drop the head of A else append head(B) to C drop the head of B // By now, either A or B is empty.
Pick a random number k between one and the number of unstruck numbers remaining (inclusive). Counting from the low end, strike out the kth number not yet struck out, and write it down at the end of a separate list. Repeat from step 2 until all the numbers have been struck out.
Note how the use of A[i][j] with multi-step indexing as in C, as opposed to a neutral notation like A(i,j) as in Fortran, almost inevitably implies row-major order for syntactic reasons, so to speak, because it can be rewritten as (A[i])[j], and the A[i] row part can even be assigned to an intermediate variable that is then indexed in a separate expression.
In computer science, an associative array, map, symbol table, or dictionary is an abstract data type that stores a collection of (key, value) pairs, such that each possible key appears at most once in the collection. In mathematical terms, an associative array is a function with finite domain. [1] It supports 'lookup', 'remove', and 'insert ...