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-valued polynomial Integer-valued polynomial In mathematics, an integer-valued polynomial (also known as a numerical polynomial) "P"("t") is a polynomial whose value "P"("n") is an integer for every integer "n". Every polynomial with integer coefficients is integer-valued, but the converse is not true. For example, the polynomial takes on integer values whenever "t" is an integer. That is because one of "t" and "t" + 1 must be an even number. (The values this polynomial takes are the triangular numbers.) Integer-valued polynomials are objects of study in their own right in algebra, and frequently appear in algebraic topology. The class of integer-valued polynomials