What is the best case time complexity for merge sort?
O(n*log n)The list of size N is divided into a max of Logn parts, and the merging of all sublists into a single list takes O(N) time, the worst-case run time of this algorithm is O(nLogn) Best Case Time Complexity: O(n*log n) Worst Case Time Complexity: O(n*log n) Average Time Complexity: O(n*log n) The time complexity of ...
What is the best case time complexity of merge sort Mcq?
What will be the best case time complexity of merge sort? Explanation: The time complexity of merge sort is not affected in any case as its algorithm has to implement the same number of steps. So its time complexity remains to be O(n log n) even in the best case.
What is the complexity of merge sort algorithm?
Merge sort is based on the divide and conquer approach. Therefore, the time complexity of Merge Sort is θ(nlogn).
What is worst case time complexity of merge sort?
Merge Sort is an efficient, stable sorting algorithm with an average, best-case, and worst-case time complexity of O(n log n).
How do I find the best case for merge sort?
For the best case, one can assume that the array is already sorted so in that case the number of comparisons would be minimum. In Merge Sort, the comparisons take place in the merge step....Therefore in Best Case,Input is already sorted.Best Case Time Complexity: O(N logN)Number of Comparisons: 0.5 N logN.
What is the best case of merge sort and insertion sort?
Insertion Sort is preferred for fewer elements. It becomes fast when data is already sorted or nearly sorted because it skips the sorted values. Efficiency: Considering average time complexity of both algorithm we can say that Merge Sort is efficient in terms of time and Insertion Sort is efficient in terms of space.
Why is merge sort the best?
What Are the Advantages of the Merge Sort? Merge sort can efficiently sort a list in O(n*log(n)) time. Merge sort can be used with linked lists without taking up any more space. A merge sort algorithm is used to count the number of inversions in the list.
Why space complexity is merge sort?
The Space Complexity of Merge Sort is O(log N) where N is the number of nodes in the linked list. This is because Merge sort algorithm is recursive, it requires O(log N) stack space for linked list cases.
Why space complexity of merge sort is n?
At first look, it makes sense that merge sort has space complexity of O(n) because to sort the unsorted array I'm splitting and creating subarrays but the sum of sizes of all the subarray will be n.
What is best and worst case complexity?
Usually the resource being considered is running time, i.e. time complexity, but could also be memory or some other resource. Best case is the function which performs the minimum number of steps on input data of n elements. Worst case is the function which performs the maximum number of steps on input data of size n.
What is the best and worst case time complexity?
The time complexity of Linear Search in the best case is O(1). In the worst case, the time complexity is O(n).
Is Big O always worst case?
Big-O, commonly written as O, is an Asymptotic Notation for the worst case, or ceiling of growth for a given function. It provides us with an asymptotic upper bound for the growth rate of the runtime of an algorithm.
What is the best case complexity of quick sort 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 is space complexity of merge sort Mcq?
b) O(n) c) O(log n) d) O(n log n) Explanation: Space complexity of in place version of merge sort is O(log n) which is used for storing call stack formed due to recursion.
What is the time complexity in worst case Mcq?
Explanation: The worst case complexity of linear search is O(n).
What is best and worst case complexity?
Usually the resource being considered is running time, i.e. time complexity, but could also be memory or some other resource. Best case is the function which performs the minimum number of steps on input data of n elements. Worst case is the function which performs the maximum number of steps on input data of size n.
What is merge sort?
Like QuickSort, Merge Sort is a Divide and Conquer algorithm. It divides the input array into two halves, calls itself for the two halves, and then merges the two sorted halves. The merge () function is used for merging two halves. The merge (arr, l, m, r) is a key process that assumes that arr [l..m] and arr [m+1..r] are sorted and merges the two sorted sub-arrays into one. See the following C implementation for details.
What is the memory space required for a merge sort algorithm?
Merge sort algorithm requires an additional memory space of 0 (n) for the temporary array.
How to merge an array into two halves?
MergeSort (arr [], l, r) If r > l 1. Find the middle point to divide the array into two halves: middle m = l+ (r-l)/2 2. Call mergeSort for first half: Call mergeSort (arr, l, m) 3. Call mergeSort for second half: Call mergeSort (arr, m+1, r) 4. Merge the two halves sorted in step 2 and 3: Call merge (arr, l, m, r)
Which is better: a partially sorted array or a fully sorted array?
With this modification, a fully sorted array will sort much faster, with a linear complexity, making it the best case, and a partially sorted array will behave better as well.
How to improve linear cost?
You can improve this algorithm at a linear cost by adding an initial comparison between the last element of the left slice and the first element of the right slice in the merge phase. If the comparison yields <= then you can skip the merge phase for this pair of slices.
Is mergesort a top down or bottom up function?
The cost of mergesort implemented classically either as a top-down recurs ive function or a bottom-up iterative with a small local array of pointers is the same: O (N.log (N)). The number of comparisons will vary depending on the actual contents of the array, but by at most a factor of 2.
How does mergesort work?
As we know, Mergesort is a divide and conquer algorithm that splits the array to halves recursively until it reaches an array of the size of 1, and after that it merges sorted subarrays until the original array is fully sorted. Typical implementation of merge sort works in O (n Log n) time in all three cases (best, average and worst).
What is the recursive relation for a sorted array?
This will lead us to the recursive relation T (n) = 2*T (n/2) + 1 which can be resolved by the master’s theorem, so T (n) = n.
What is the time complexity of a radix sort?
For the radix sort that uses counting sort as an intermediate stable sort, the time complexity is O (d (n+k)).
What is the worst case of an array?
Worst case occurs when the array is already sorted either in ascending or descending order.
How does Radix sort work?
Radix sort is a sorting technique that sorts the elements by first grouping the individual digits of the same place value. Then, sort the elements according to their increasing/decreasing order.
What is the complexity of radix?
Radix sort complexity is O (kn) for n keys which are integers of word size k. For all there cases time i.e best , worst and average time complexity is O (kn).
What is the combine step in math?
In the combine step,we are combining the elements of the smaller subarrays. Adding all of them,the number of elements is n. So we have to merge n
What is the running time of an algorithm?
The running time of an algorithm depends on two things: (i) the particular input it's given, and (ii) the random choices made while running. There are multiple possible "time complexities", depending on whether we take the average or worst-case of each.
Can Big O run faster than heapsort?
Yes. Big-O really only becomes interesting and useful for large input sizes. For example: a Bubble Sort (O (n^2)) can often run faster than a heapsort or introsort (O n log n) when the input size is small.
