## What is the running time of merge sort?

Merge Sort is a stable sort which means that the same element in an array maintain their original positions with respect to each other. Overall time complexity of Merge sort is O(nLogn). It is more efficient as it is in worst case also the runtime is O(nlogn) The space complexity of Merge sort is O(n).

Is the running time of merge sort depends on the value of keys in input file?

Natural Merge Sort will only take O(n) time for an ordered input and in general be faster for a random input than for a reverse-ordered input. In the latter two cases, runtime will be O(n * log n).

### What is the running time of heapsort for input that is already sorted?

Solution: The running time of HEAPSORT on an array A of length n that is already sorted in increasing order is Г(nlgn) because even though it is already sorted, it will be transformed back into a heap and sorted. max element is removed and the HEAPIFY is called it will cover the full height of the tree. Exercise 2-5.

What is the best case running time for the merge sort algorithm?

O
Sorting algorithms

Algorithm Data structure Time complexity:Best
Quick sort Array O(n log(n))
Merge sort Array O(n log(n))
Heap sort Array O(n log(n))
Smooth sort Array O(n)

## What is the running time of merge sort when all elements of array A have the same value?

With a standard “vanilla” implementation of mergesort, the time required to sort an array will always be Θ(n log n) because the merges required at each step each take linear time. However, with the appropriate optimizations, it’s possible to get this to run in time O(n).

Why is merge sort fast?

Indeed, it is because merge sort is implemented recursively that makes it faster than the other algorithms we’ve looked at thus far. In part 2 of this series, we’ll look at the runtime complexity of merge sort, how this recursion actually makes it more efficient, and how merge sort stacks up against other algorithms.

### Which is better merge sort quick sort?

Merge sort is more efficient and works faster than quick sort in case of larger array size or datasets. Quick sort is more efficient and works faster than merge sort in case of smaller array size or datasets.

What is the running time of merge sort when all the elements of array A have the same value?

## What is the running time of HeapSort?

Heapsort has a worst- and average-case running time of O ( n log ⁡ n ) O(n \log n) O(nlogn) like mergesort, but heapsort uses O ( 1 ) O(1) O(1) auxiliary space (since it is an in-place sort) while mergesort takes up O ( n ) O(n) O(n) auxiliary space, so if memory concerns are an issue, heapsort might be a good, fast …

Why merge sort is better than HeapSort?

HeapSort: It is the slowest of the sorting algorithms but unlike merge and quick sort it does not require massive recursion or multiple arrays to work. Merge Sort: The merge sort is slightly faster than the heap sort for larger sets, but it requires twice the memory of the heap sort because of the second array.

### What’s best worst running time for 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 best case for merge sort?

n*log(n)
Merge sort/Best complexity

## Why does merge sort not work in place?

Because it copies more than a constant number of elements at some time, we say that merge sort does not work in place. By contrast, both selection sort and insertion sort do work in place, since they never make a copy of more than a constant number of array elements at any one time.

What is the total time for mergesort to merge?

The total time for mergeSort is the sum of the merging times for all the levels. If there are levels in the tree, then the total merging time is . So what is?

### How is merge sort based on divide and conquer?

M erge sort is based on the divide-and-conquer paradigm. Its worst-case running time has a lower order of growth than insertion sort. Since we are dealing with subproblems, we state each subproblem as sorting a subarray A [ p.. r ]. Initially, p = 1 and r = n, but these values change as we recurse through subproblems.

Is the merge sort algorithm an in-place sorting algorithm?

It is not an in-place sorting algorithm as it requires additional scratch space proportional to the size of the input array. It requires an equal amount of additional space as the unsorted list.