Assuming that the set of possible list values [a,b,c,d] , so…

Assuming that the set of possible list values [a,b,c,d] , sort the following list in alphabetical order by the distribution counting algorithm: b,c,d,c,b,a,a,b Purchase the answer to view it Purchase the answer to view it Purchase the answer to view it Purchase the answer to view it

Answer

The distribution counting algorithm is a sorting algorithm that can be used to sort a list of values in linear time complexity. It works by counting the occurrences of each value in the list and then placing them in sorted order based on their counts.

In this case, we are given the list [b,c,d,c,b,a,a,b] and we want to sort it in alphabetical order based on the set of possible values [a,b,c,d].

To use the distribution counting algorithm, we need to first determine the counts of each value in the given list. We can do this by iterating through the list and keeping track of the number of occurrences for each value.

Let’s create a count array with the length equal to the number of possible values in the set [a,b,c,d]. In this case, the count array will have a length of 4. We initialize all the count array elements to zero.

Next, we iterate through the given list and for each value we encounter, we increment the corresponding count array element by one. After iterating through the entire list, the count array will have the counts of each value.

For the given list [b,c,d,c,b,a,a,b], the count array will be [2, 4, 2, 1], representing the counts of [a,b,c,d] respectively.

Now that we have the counts of each value, we can create a sorted list by iterating through the count array. For each count array element, we append the corresponding value to the sorted list the number of times specified by the count.

In this case, the sorted list will be [a,a,b,b,b,c,c,c,c,d,d].

The distribution counting algorithm works by taking advantage of the fact that the values in the set of possible values are consecutive and have a fixed order. It uses an auxiliary count array to keep track of the occurrences of each value, and then constructs a sorted list based on these counts.

One advantage of the distribution counting algorithm is that it has a linear time complexity of O(n+k), where n is the number of elements in the given list and k is the number of possible values in the set. This makes it efficient for sorting large lists, especially when the number of possible values is small.

However, one limitation of the distribution counting algorithm is that it requires the values in the list to be non-negative integers. If the values are not integers or if they are negative, the algorithm may need to be modified or another sorting algorithm should be used.