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Common sorting algorithms include bubble sort, quick sort, dictionary sort, merge sort, and heap sort. For example, the sorting algorithm is used to sort the exam scores of a school or data reports of a company in descending order.
MERGEX SORT TIME COMPLEXITY SERIES
Function to merge the sorted sub-arrays into a bigger array.The sorting algorithm is used to sort a series of data in a specific sequence. Print( "Sorted array using merge sort: " + str(array)) MergeSort (aux_array, array, 0, len(array) - 1) # Allocate space for the auxiliary vector Merge (aux_array, array, low, mid, high) # Merge the left and the right half of the array keeping it sorted. MergeSort (aux_array, array, mid + 1, high) # Recursively splits the right half of the array MergeSort (aux_array, array, low, mid) # Recursively splits the left half of the array def MergeSort (aux_array : List, array : List, low : int, high : int): # MergeSort function splits each sub-array till only a single element is available in the sub-array # and then proceeds with the merge of the sub-arrays into a bigger auxiliary array. # There are still some unpicked numbers in the right part for i in range(right_index, high + 1):Īux_index += 1 # Copy numbers from the sorted auxiliary array into the original array for i in range(low, high + 1): # There are still some unpicked numbers in the left part for i in range(left_index, mid + 1): # Merge elements from array and array # ^ ^ # | | # left_index right_index # Pick the smaller number between the left part and the right part while (left_index <= mid and right_index <= high): def Merge (aux_array : List, array : List, low : int, mid : int, high : int): Program for sorting an array using Merge Sortįrom typing import List # For annotations # Function to merge the sorted sub-arrays into a bigger array. Space complexity : O ( n ), as an auxiliary array is needed for merging the sub-arrays.
![mergex sort time complexity mergex sort time complexity](https://www.happycoders.eu/wp-content/uploads/2020/07/mergesort_time_complexity_divide-224x114.png)
Thus the complexity of merge sort is O ( n log ( n ) ) Since merging happens at each level during the way out, the time complexity is O ( n ) * (number of levels) i.e log ( n ). The time complexity of merging two sorted sub-arrays each of length n is 2n. Copy the ( sorted ) numbers from the auxiliary array back to the original array.
![mergex sort time complexity mergex sort time complexity](https://www.happycoders.eu/wp-content/uploads/2020/07/mergesort_time_complexity_divide-944x481.png)
![mergex sort time complexity mergex sort time complexity](https://i.stack.imgur.com/rPhxO.png)
If there are still numbers left in the right sub-array, then add them to the auxiliary array.ĥ. If there are still numbers left in the left sub-array, then add them to the auxiliary array.Ĥ. Pick the smaller number at the front of either of the two sub-arrays and place this number in the auxiliary array.ģ. While the left sub-array i.e array and the right sub-array i.e are not empty. The merging operation happens during the way out of the recursion stack and requires an additional array for merging.ġ. Merge the sub-arrays into a bigger sorted sub-array using additional space. Recursively split the right half : MergeSort ( array, mid + 1, high )Ģ. Recursively split the left half : MergeSort ( array, low, mid )Ĥ. The splitting operation makes use of recursion and continues as recursion progresses.ģ. Split the array all the way down until each sub-array contains a single element. During the merge operation, the sub-arrays are merged in sorted order into an auxiliary array.ġ. Merge Sort begins by splitting the array into two halves (sub-arrays) and continues doing so recursively till a sub-array is reduced to a single element, after which merging begins. Merge Sort is an array sorting algorithm based on the divide and conquer strategy.