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
Radix sort Radix sort is a fast stable sorting algorithm which can be used to sort keys in integer representation order. Keys may be a string of characters, or numerical digits in a given 'radix'. The processing of the keys begins at the least significant digit (i.e., the rightmost digit), and proceeds to the most significant digit (i.e., the leftmost digit). The sequence in which digits are processed by an LSD radix sort is the opposite of the sequence in which digits are processed by a most significant digit (MSD) radix sort. An LSD radix sort operates in O("nw") time, where "n"