Counting sort initialization of the output array, each take time. Therefore, the time for the whole algorithm is the sum of the times for these steps, . Because it uses arrays of length and , the total space usage of the algorithm is also . For problem instances in which the maximum key value is significantly smaller than the number of items, counting sort can be highly space-efficient, as the only storage it uses other than its input and output arrays is the Count array which uses space . If each item to be sorted is itself an integer, and used as
Integer sequence explicit definition. Alternatively, an integer sequence may be defined by a property which members of the sequence possess and other integers do not possess. For example, we can determine whether a given integer is a perfect number, even though we do not have a formula for the "n"th perfect number. Integer sequences which have received their own name include: An integer sequence is a computable sequence if there exists an algorithm which, given "n", calculates "a", for all "n" > 0. The set of computable integer sequences is countable. The set of all integer sequences is uncountable (with cardinality equal