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# What is the best case for merge sort?

## What is the best case for merge sort?

n*log(n)Merge sort / Best complexity

Table of Contents

## What is the best case run time for merge sort?

Ω(N log N)
Time and Space Complexity Comparison Table :

Sorting Algorithm Time Complexity
Best Case Worst Case
Merge Sort Ω(N log N) O(N log N)
Heap Sort Ω(N log N) O(N log N)
Quick Sort Ω(N log N) O(N2)

What is the average time complexity of merge sort?

O(n*Log n)
Time Complexity 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.

What are the average case and worst case complexities for merge sort algorithm are?

Complexity Analysis of Merge Sort

• Time complexity of Merge Sort is O(n*Log n) in all the 3 cases (worst, average and best) as merge sort always divides the array in two halves and takes linear time to merge two halves.
• It requires equal amount of additional space as the unsorted array.

### What is the average case complexity of quicksort?

O(n logn)
What is the average case run time complexity of Quick Sort? The average case run time of quick sort is O(n logn) . This case happens when we dont exactly get evenly balanced partitions. We might get at worst a 3-to-1 split on either side of pivot element.

### How do you optimize a merge sort?

Start by thinking of merge sort in this way. 0: Consider the input array A0 as a collection of ordered sequences of length 1. 1: Merge each consecutive pair of sequences from A0, constructing a new temporary array A1. 2: Merge each consecutive pair of sequences from A1, constructing a new temporary array A2.

What is average case efficiency?

Best Case Efficiency – is the minimum number of steps that an algorithm can take any collection of data values. Smaller Comparisons.In Big Oh Notation,O(1) is considered os best case efficiency. Average Case Efficiency – average comparisons between minimum no. of comparisons and maximum no.

What is the average-case complexity of selection sort?

O(n2)
Explanation: The best, average and worst case complexities of selection sort is O(n2).

#### What is the average case running time of an insertion sort algorithm?

O(N2)
3. What is the average case running time of an insertion sort algorithm? Explanation: The average case analysis of a tight bound algorithm is mathematically achieved to be O(N2).

#### What is the best case average case and worst case running time of merge sort?

O(n log n)
Merge Sort is an efficient, stable sorting algorithm with an average, best-case, and worst-case time complexity of O(n log n). Merge Sort has an additional space complexity of O(n) in its standard implementation.

What is the average and worst case time complexity of quicksort?

The worst case time complexity of a typical implementation of QuickSort is O(n2). The worst case occurs when the picked pivot is always an extreme (smallest or largest) element. This happens when input array is sorted or reverse sorted and either first or last element is picked as pivot.

What is the average case complexity of quicksort Mcq?

O(N log N)
Explanation: The best case and average case analysis of a quick sort algorithm are mathematically found to be O(N log N).

## What are the different cases of merge sort?

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. We will compare the results with other sorting algorithms at the end.

## What is the advantage of merge sort over other sort algorithms?

1 Slower comparative to the other sort algorithms for smaller tasks. 2 Merge sort algorithm requires additional memory space of 0 (n) for the temporary array . 3 It goes through the whole process even if the array is sorted.

How to analyze the time complexity of merge sort?

In order to analyze time complexity of merge sort first we must know about the time complexity of merging of two sorted array of length n,into another sorted array of length 2n, it comes out to be O (2 n), Now in merge sort we are dividing array in two equal parts untill we get array of one element, and again joining them in sorted order,

How do you find the recurrence of a merge sort?

Analysis. If the running time of merge sort for a list of length n is T ( n ), then the recurrence T ( n) = 2 T ( n /2) + n follows from the definition of the algorithm (apply the algorithm to two lists of half the size of the original list, and add the n steps taken to merge the resulting two lists).