Counting Sort is an efficient sorting algorithm that works by determining the frequency of each unique element in an array and then placing them in the correct order. Unlike comparison-based algorithms like QuickSort or MergeSort, Counting Sort has a linear time complexity.

Time Complexity

The time complexity of Counting Sort is O(n + k), where n is the number of elements in the input array and k is the range of the input values.

Since Counting Sort does not involve any comparisons, it is not affected by the number of elements being sorted. It simply counts the occurrences of each element in the input array, which can be done in linear time.

Space Complexity

Counting Sort requires additional space to store the count of each element. The space complexity of Counting Sort is O(k), where k is the range of the input values.

The size of the counting array used in Counting Sort is equal to the range of the input values. The elements in the counting array store the count of each unique element. Therefore, the space required is proportional to the range of the input values.

Usage and Considerations

Counting Sort is best suited for sorting arrays with a small range of input values. If the range is significantly larger than the number of elements in the array, Counting Sort might not be the most efficient choice.

It is important to note that Counting Sort is a stable sorting algorithm. This means that if there are two elements with the same value, the algorithm will preserve their relative order in the sorted output.

Counting Sort is often used as a subroutine in other complex algorithms and in combination with other sorting techniques, such as Radix Sort.

#CountingSort #TimeComplexity