Mastering Algorithms with C

Description of Counting Sort

Counting sort is an efficient, linear-time sorting algorithm that works by counting how many times each element of a set occurs to determine how the set should be ordered. By avoiding the comparisons that have been a part of the sorting methods presented thus far, counting sort improves on the O (n lg n) runtime bound of comparison sorts.

Counting sort does have some limitations. The most significant is that it works only with integers or data that can be expressed in some integer form. This is because counting sort makes use of an array of counts indexed by the integer elements themselves to keep track of how many times each one occurs. For example, if the integer 3 occurs in the data four times, 4 will be stored initially at position 3 in the array of counts. Also, we must know the largest integer in the set in order to allocate enough space for the counts.

Aside from being fast, an important virtue of counting sort is that it is stable. Stable sorts leave elements that have equal values in the same order as they appear in the original set. This is an important attribute in some cases, as we will see with radix sort.