Where n can be subtituted to 2^k and the value of k is logN Now we can further divide the array into two halfs if size of the partition arrays are greater than 1. STEP-2 Now to merge baiscall traverse through all the elements. Int m =right -middle //size of rest of the elementsįor(int i=0 i&input, int left, int right) Int n =middle-left+1 // size of first array Void merge(vector &input, int left, int middle, int right) Merge the two halves sorted in step 2 and 3: Find the middle point to divide the input into two halves:Ĥ. intially left =0 and right = input.size()-1 ġ. PSEUDO CODE OF MERGE SORT MergeSort(vector input, left, right) In simple terms merge sort is an sorting algorithm in which it divides the input into equal parts until only two numbers are there for comparisons and then after comparing and odering each parts it merges them all together back to the input. Let us get started with Time & Space Complexity of Merge Sort. Comparison with other sorting algorithms.Average Case Time Complexity of Merge Sort.Worst Case Time Complexity of Merge Sort.Best case Time Complexity of Merge Sort.We will compare the results with other sorting algorithms at the end. The two subarrays are merged back together in order.In this article, we have explained the different cases like worst case, best case and average case Time Complexity (with Mathematical Analysis) and Space Complexity for Merge Sort.At this point, each subarray is in the correct order. The start, middle, and end index are used to create 2 subarrays, the first ranging from start to middle and second ranging from middle to end. The merge() function typically gets 4 parameters: the complete array and the starting, middle, and ending index of the subarray.At this point, the merge() function is called to begin merging the smaller subarrays into a larger sorted array. These recursive calls will run until there is only one item passed into each subarray. The second includes indexes from middle+1.lastIndex.The first includes indexes from 0.middle.Make 2 recursive calls to the mergeSort() function:.Find the index in the middle of the first and last index passed into the mergeSort() function.Initialize the main mergeSort() function passing in the array, the first index, and the last index.The algorithm executes in the following steps: While right_index < len ( right_array ): array = right_array right_index += 1 current_index += 1 if _name_ = '_main_' : array = merge_sort ( array ) print ( array ) Walkthrough While left_index < len ( left_array ): array = left_array left_index += 1 current_index += 1 # copy remaining elements of right_array if any While left_index < len ( left_array ) and right_index < len ( right_array ): if left_array < right_array : array = left_array left_index += 1 else : array = right_array right_index += 1 current_index += 1 # copy remaining elements of left_array if any Left_index = 0 right_index = 0 current_index = 0 # compare each index of the subarrays adding the lowest value to the current_index Merge_sort ( right_array ) # Sorting the second half Merge_sort ( left_array ) # Sorting the first half ![]() Right_array = array # fill in right array Class MergeSort ĭef merge_sort ( array ): if len ( array ) > 1 : middle = len ( array ) // 2 # divide array length in half and use the "//" operator to *floor* the result
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