![]() Similarly, the array will recursively divide into two halves till we get all sub-array containing of exactly 1 element. As we know |7/2|=3, so while the first division of array, the size of one part will be 3 and another part will be (7-3=4). So in the above picture we see that the size of the array is (n=7). Observe each step in the image below carefully and try to visualize the concept of this algorithm. ![]() ![]() Let’s understand it with an example of odd size array– Because in linked list it can be implemented without extra space as elements can be inserted in the middle in O(1) extra space and O(1) time. Merge Sort is a best-sorting technique for sorting Linked Lists.Merge Sort is a stable sort, which means the “equal” elements appear in the same order in the sorted array as they were in the unsorted array.Hence, it’s not at all recommended for sorting large size list. It requires an equal amount of additional space as the unsorted list.It is not an in-place sorting algorithm as it requires additional scratch space proportional to the size of the input array.Time complexity of Merge Sort is O(n*logn) in all 3 cases (worst, average and best) as in merge sort, array is recursively divided into two halves and take linear time to merge two halves.Using Masters Theorem, we get -> T(n)=O(n*logn). We can express time complexity of merge sort by this recurrence relation: T(n) = 2T(n/2) + O(n).Merge Sort is a type of recursive algorithm.Here are some key points of merge sort algorithm – This will be our sorted array at the end. Then, the sub-arrays are repeatedly merged, to produce new array until there is one array remaining. In merge sort the array is firstly divided into two halves, and then further sub-arrays are recursively divided into two halves till we get N sub-arrays, each containing 1 element. Then after entering the numbers, the compiler will print the number in the order according to merge sort algorithm.Merge Sort is a divide and conquers algorithm in which original data is divided into a smaller set of data to sort the array. Merge Sort Program in Cīelow is the program of merge sort in c where after executing the compiler will ask the user to enter the number of integers to sort. Disadvantages:Īdditional memory is required for the merging process. This can be derived as follows:( Here 2 is base) Advantages:īest and worst-case efficiency is O(nlog2n). Hence the time complexity of Merge Sort is O(n log2 n). In each iteration, n elements are merged. The total number of iterations in Merge sort is log2n. Step 3: Merge (a,0,4) i.e Merge a and a into a which is the sorted list Time Complexity of Merge Sort The same steps are carried out for the second half. Merge a and a into a i.e Īt this stage, the first half is sorted. Let us consider an example of sorting 5 elementsĪ=. In such a case, one sublist will have an additional element. However, the list may contain an odd number of elements. In the example shown, each sublist has an even number of elements. The sublists are then merged to create sorted lists until all elements are in a single list. The elements are successively divided into two sublists till we cannot divide any further i.e, we reach a sublist of size 1. Let us consider the example of sorting 20,40,50,15,30,35,10 and 5.Initially they are all in one list. Merge (a,mid,high) //Merge sorted sub lists MergeSort (a,mid+1,high) //sort second sub list MergeSort (a,low,mid) //Sort first sub list Mid=(low + high) / 2 //Divide a into two sublists Void MergeSort (int a, int low, int high)
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