Python Short Code - Counting Sort

Counting Sort is a linear-time sorting algorithm that works by counting the number of occurrences of each element in the input array and using this information to determine the position of each element in the output array. It is a non-comparative algorithm, meaning it doesn't compare the elements directly to sort them, rather it uses the properties of the elements themselves to place them in order.

The Counting Sort algorithm works as follows:

Find the range of values in the input array and create a counting array of size k, where k is the range of values.

Traverse the input array and increment the count of each element in the counting array.

Modify the counting array to reflect the correct positions of each element in the output array. This is done by summing the current count with the count of the previous element in the counting array.

Traverse the input array in reverse order and place each element in its correct position in the output array based on the current count of its value in the counting array.

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 values. Because k is a constant for integer data types, the time complexity can be simplified to O(n). Counting Sort is very efficient for sorting arrays with a limited range of values, but it can be less efficient for arrays with a large range of values or with many repeated values.

One potential downside of Counting Sort is that it requires extra memory to store the counting array and the output array, which can make it less efficient for large arrays with limited memory. However, in many cases, the benefits of its time complexity can outweigh this downside. Counting Sort is often used as a subroutine in other sorting algorithms, such as Radix Sort, to sort specific digit positions in the input array.

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