The counting sort algorithm will be discussed in this article. The counting sort is a sorting method based on the keys that connect certain ranges. Sorting algorithms are frequently asked in coding or technical interviews for software professionals. As a result, it is critical to debate the subject.

This sorting method does not compare elements to sort them. Sorting is accomplished by counting objects with separate key values, similar to hashing. Following that, it does some arithmetic operations to determine the index position of each object in the output sequence. Counting sort isn't commonly used as a sorting algorithm.

When the range of objects to be sorted is not bigger than the number of objects to be sorted, counting sort is effective. It's useful for sorting negative input values.

There is no particular syntax for counting sort, as C is a type of language where we will be using some conditions and loops to perform counting sort.

Counting sort works exactly like a hashtag; users calculate the max value of the array to be sorted.

Then the occurrences of each element in the array from 0 to length 1 are assigned to an auxiliary array. And this is used to retrieve a sorted version of the array.

This algorithm has linear time complexity, but it also has space complexity which is way too high and only is used in cases where the array element range is closer to the size of the array.

Algorithm/Pseudo Code of Counting Sort in C

First, we need to iterate the input array and find a maximum value present in the array.

Then declare a new array with size max_value + 1 with 0 values.

Count each of the elements in the array and increment these values by the corresponding index.

Find the cumulative sum of the auxiliary array by adding current and previous frequency.

And now, this cumulative array value signifies the location of an element in the sorted array.

We need to iterate the auxiliary array from 0 to maximum.

Having 0 at the corresponding index and reducing the count by 1 signifies the element’s second position if it exists in the input array.

Now this actual received array to the input array.

The algorithm is based on three types of array:

Output Array: Stores the sorted data values.

Temporary Array: Data storage temporarily.

void countsorting(int arr[], int n, int n1)

// creating an integer array of size n for sorted array

// creating an integer array of size n1, initialized by zero

// Using the value of each item in an input array as index,

// Calculating starting index for each integer

// Copying to output array, and preserving order of inputs with equal keys

// copying output array back to the input array

int arr[] = { 4, 5, 2, 2, 1, 5, 4, 5, 6, 10, 10, 9, 10, 3, 10 };

void countingSort(int Array[], int n1, int n)

In this tutorial, you will learn about the counting sort algorithm and its implementation C.

Counting Sort in C

Merge sort is a sorting method that uses the divide and conquers method. This essay will be highly useful and fascinating to students who may be asked about merge sort in their exams. Sorting algorithms are frequently asked in coding or technical interviews for software professionals. As a result, it is critical to debate the subject.

Merge sort is similar to the rapid sort algorithm in that it sorts the elements using a divide and conquer strategy. It's one of the most widely used and effective sorting algorithms. It splits the given list into two halves, then calls itself for each half and merges the two sorted parts. To perform the merging, we must define the merge() function.

Merge sort in C does not have any particular syntax, but still, it follows some kind of steps and algorithm at the time of implementation, which is represented as follows:

The merge sort consists of some keys for the comparison of elements within the arrays:

1. Let the two divided arrays be arr [k….o] and arr [o+1…y] and let the merge key include (arr, o, k, y).

2. The key include (arr, o, k, y) is the merge key which is used for comparison and merging into two halves.

3. Now, some of the scenarios are followed to make the comparisons, including the entire key and the parameters defined so far.

4. If key > 1, then that algorithm will work in a way where the middle point will be searched for, and then the array will get divided into two halves after comparison with the key using the below formula.

5. Call for the mergesort() function for the first half of the array from the bifurcated array.

6. Call for the mergeSort() function for the next half of the array within the bifurcated array.

As previously stated, the Merge sort is a sorting algorithm that uses the divide and conquers concept. So, let's take a look at the divide and conquer strategy. In the divide and conquer technique, the problem must be recursively divided into sub-problems, then dug and divided into the next set or subset of problems, and finally made final by backtracking and combining the subset with the solution one layer above or below. One thing to remember about the divide and conquer algorithm is that the division and sub-structure that follows the division should not cause the divided sub-problem to modify the original problem that was stated and delivered at the start.

The main emphasizing and important steps to be followed are the three steps starting from divide conquer and then combining it so that it has to be from bottom to top fashion for the final result. Merge sort has some advantages associated with it regarding efficiency, and it is very important to get the merge sort in C in terms of time complexity. Merge sort will comprise one entire array, containing all the elements and its associated key, value pairs into it for comparison and manipulation with other sets of elements in the array. The associated subset available with the merge function has to be proper for further division and combination into final results. Merge sort is one of the algorithms which include playing around with the elements and indexing.

Merge sort also adheres to the following time complexity, making the complete algorithm efficient and fast as required by the requirement and implementation:

If we try to estimate the worst-case time complexity, then it will be O (n*logn)

If we try to estimate the best case time complexity, then It will be O (n*logn)

If we try to estimate the Average time complexity, then it will be O (n*logn)

Then merge sort algorithm can be applied to sort the elements, and in an entire program, only the merge sort function can be used for any other work.

We shall see the implementation of merge sort in C programming language here −

int a[11] = { 10, 14, 19, 26, 27, 31, 33, 35, 42, 44, 0 };

void merging(int low, int mid, int high) {

   for(l1 = low, l2 = mid + 1, i = low; l1 <= mid && l2 <= high; i++) {

If we compile and run the above program, it will produce the following result −

Merge sort is quite a useful algorithm in terms of efficiency as it follows the divide and conquer paradigm. This divide and conquer way is efficient because it helps in making the entire problem into sub-problems, making the computation and sorting process easy while keeping the original problem the same. Furthermore, it helps programmers to adopt this sorting because of its easy and simplified nature in terms of understanding.

In this tutorial, you will learn about the merge sort algorithm and its implementation in C.

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