In this article, we will discuss the merge sort Algorithm. Merge sort is the sorting technique that follows the divide and conquer approach. This article will be very helpful and interesting to students as they might face merge sort as a question in their examinations. In coding or technical interviews for software engineers, sorting algorithms are widely asked. So, it is important to discuss the topic.
Merge sort is similar to the quick sort algorithm as it uses the divide and conquer approach to sort the elements. It is one of the most popular and efficient sorting algorithm. It divides the given list into two equal halves, calls itself for the two halves and then merges the two sorted halves. We have to define the merge() function to perform the merging.
The sub-lists are divided again and again into halves until the list cannot be divided further. Then we combine the pair of one element lists into two-element lists, sorting them in the process. The sorted two-element pairs is merged into the four-element lists, and so on until we get the sorted list.
So, first compare 12 and 31, both are in sorted positions. Then compare 25 and 8, and in the list of two values, put 8 first followed by 25. Then compare 32 and 17, sort them and put 17 first followed by 32. After that, compare 40 and 42, and place them sequentially.
The merge sort in c is a sorting algorithm that follows the divide and conquers technique to sort an array in C in ascending order. The merge sort program in C divides an array into two halves and then merges the two halves in sorted order. The merge sort is a stable sorting algorithm.
Now that we have individual arrays of unit size, the arrays will be merged in a manner that the items in the merged array at every step are in sorted order. The merging of arrays will occur in the opposite order of the way the arrays were divided, i.e. firstly the unit arrays will be merged into the size of 2, then the arrays of the size of two will be merged into the size of 4 and so on and eventually we will have two halves of the original array which will together be merged into one sorted array.
In the first step the arrays  and  will be merged into array [6, 8]. Now the unit array  will be merged with the array [6, 8] and end up in an array [2, 6, 8]. Similarly the arrays  and  will be merged into the array [1, 4] and the arrays [1, 4] and  will merge into [1, 3, 4].
Now in the final step, we will merge [2, 6, 8] and [1, 3, 4] such that it stores items in a sorted manner. Thus we will have [1, 2, 3, 4, 6, 8]. In this way, the merge sort program in c will sort the given array.
The following is the code implementation of the merge_sort function. In this function, we will find the mid-point, and then we will call the merge_sort function for array elements from left to mid-point and from index next to mid-point to rightmost index. Then we will call the merge function to merge the array.
The function will first calculate the mid value using l + (right - left) / 2 then it will recursively call the mergesort function for values from left to mid and mid+1 to right respectively. It will call the merge function at the end to merge the portion ranging from left to right.
The base case: The merge_sort function will work until we have an array of unit sizes, this will operate only until the (left < right) condition holds true since for an array of unit sizes the value of left will be equal to the value of right.
The following is the code implementation of the merge_sort function. The merge function is used to merge two subarrays of arr, arr[left..mid] and arr[mid+1..right]. For this, two arrays left_arr and right_arr are created to store items in the range left to mid and mid+1 to right respectively.
In the above merge function we are taking an array and left, mid, and right values as parameters. It will merge two subarrays of arr, the first subarray is arr[left..mid] and the second subarray is arr[mid+1..right]. Now we will create two arrays left_arr and right_arr and store items in the range left to mid and mid+1 to right respectively.
External sorting is a class of sorting algorithms that can handle massive amounts of data. External sorting is required when the data being sorted do not fit into the main memory of a computing device (usually RAM) and instead, they must reside in the slower external memory, usually a disk drive.
Each call to merge_sort triggers two recursive calls thus if we could deduce that a binary tree of recursive calls is formed although only one of those two recursive calls is performed at a time. The first recursive call ends before the second call starts. Thus, at any given time, only one branch of the tree is being explored. This branch is represented by the "call stack".
Merge sort is one of the most efficient sorting algorithms. It works on the principle of Divide and Conquer based on the idea of breaking down a list into several sub-lists until each sublist consists of a single element and merging those sublists in a manner that results into a sorted list.
Merge Sort is a recursive algorithm and time complexity can be expressed as following recurrence relation. T(n) = 2T(n/2) + O(n) The solution of the above recurrence is O(nLogn). The list of size N is divided into a max of Logn parts, and the merging of all sublists into a single list takes O(N) time, the worst-case run time of this algorithm is O(nLogn) Best Case Time Complexity: O(n*log n) Worst Case Time Complexity: O(n*log n) Average Time Complexity: O(n*log n) The time complexity of MergeSort is O(n*Log n) in all the 3 cases (worst, average and best) as the mergesort always divides the array into two halves and takes linear time to merge two halves. Further Readings:
Since they can often reduce the complexity of a problem, sorting algorithms are very important in computer science. These algorithms have direct applications in searching algorithms, database algorithms, divide and conquer methods, data structure algorithms, and many more.
The answers to these questions may determine which algorithm is going to work best for each situation. Some algorithms like merge sort may need a lot of space or memory to run, while insertion sort is not always the fastest, but doesn't require many resources to run.
Bucket sort is a comparison sort algorithm that operates on elements by dividing them into different buckets and then sorting these buckets individually. Each bucket is sorted individually using a separate sorting algorithm like insertion sort, or by applying the bucket sort algorithm recursively.
Bucket sort is mainly useful when the input is uniformly distributed over a range. For example, imagine you have a large array of floating point integers distributed uniformly between an upper and lower bound.
This property can be leveraged to access the maximum element in the heap in O(logn) time using the maxHeapify method. We perform this operation n times, each time moving the maximum element in the heap to the top of the heap and extracting it from the heap and into a sorted array. Thus, after n iterations we will have a sorted version of the input array.
The best, worst and average case time complexity of Heapsort is O(nlogn). Although heapsort has a better worse-case complexity than quicksort, a well-implemented quicksort runs faster in practice. This is a comparison-based algorithm so it can be used for non-numerical data sets insofar as some relation (heap property) can be defined over the elements.
QuickSort, MergeSort, and HeapSort are comparison-based sorting algorithms. CountSort is not. It has the complexity of O(n+k), where k is the maximum element of the input array. So, if k is O(n), CountSort becomes linear sorting, which is better than comparison based sorting algorithms that have O(nlogn) time complexity.
For each digit i where i varies from the least significant digit to the most significant digit of a number, sort input array using countsort algorithm according to ith digit. We used count sort because it is a stable sort.
Just like the way bubbles rise from the bottom of a glass, bubble sort is a simple algorithm that sorts a list, allowing either lower or higher values to bubble up to the top. The algorithm traverses a list and compares adjacent values, swapping them if they are not in the correct order.
With a worst-case complexity of O(n^2), bubble sort is very slow compared to other sorting algorithms like quicksort. The upside is that it is one of the easiest sorting algorithms to understand and code from scratch.
Quick sort is an efficient divide and conquer sorting algorithm. Average case time complexity of Quick Sort is O(nlog(n)) with worst case time complexity being O(n^2) depending on the selection of the pivot element, which divides the current array into two sub arrays.
On the other hand, if the algorithm, which selects of pivot element of the input arrays, consistently outputs 2 sub arrays with a large difference in terms of array sizes, quick sort algorithm can achieve the worst case time complexity of O(n^2).
Merge Sort is a Divide and Conquer algorithm. It divides input array in two halves, calls itself for the two halves and then merges the two sorted halves. The major portion of the algorithm is given two sorted arrays, and we have to merge them into a single sorted array. The whole process of sorting an array of N integers can be summarized into three steps-
There is something known as the Two Finger Algorithm that helps us merge two sorted arrays together. Using this subroutine and calling the merge sort function on the array halves recursively will give us the final sorted array we are looking for.
Putting it in plain English, we break down the subproblem into two parts at every step and we have some linear amount of work that we have to do for merging the two sorted halves together at each step. 2b1af7f3a8