How many comparisons does merge sort take to sort n values?

Number of total comparison in merge sort = n*log2(n) – (n – 1). So, your constant is 1.

Why merge sort is NLOG N?

Time complexity of Merge Sort is ɵ(nLogn) in all 3 cases (worst, average and best) as merge sort always divides the array in two halves and take linear time to merge two halves. It divides input array in two halves, calls itself for the two halves and then merges the two sorted halves.

How many comparisons would be required to merge?

Explanation: To merge two lists of size m and n, we need to do m+n-1 comparisons in worst case. Since we need to merge 2 at a time, the optimal strategy would be to take smallest size lists first.

Why binary search has O log n )) but merge sort has O N * log n )) complexity?

Mergesort is a divide and conquer algorithm and is O(log n) because the input is repeatedly halved.

Does merge sort have comparisons?

In computer science, merge sort (also commonly spelled as mergesort) is an efficient, general-purpose, and comparison-based sorting algorithm. Most implementations produce a stable sort, which means that the order of equal elements is the same in the input and output.

Does merge sort repeat comparisons?

This process is repeated until the end of either input list is reached. Merging two lists with a combined length of N items will take at most N – 1 comparison operations. Fewer comparisons are necessary when one of the lists is shorter than the other, or when the end of one list is reached before the end of the other.

What is the average case complexity of merge sort?

O
In sorting n objects, merge sort has an average and worst-case performance of O(n log n).

Why is merge sort better than bubble sort?

(1) Merge-sort needs an auxiliary array (extra space) to sort and cause more memory access (2) If the data is already sorted then Bubble-sort will not move any elements. However, Merge-sort is O(n log n) and Bubble Sort is O(n*n) , therefore for any reasonable size data Merge-sort will outperform Bubble sort.

How many comparisons are there in selection sort?

If you think about it, you will see that regardless of the actual items to be sorted, or the original order of those items, 36 comparisons will always be required to sort eight items using the selection sort method.

Why is the worst case of merge sort nearly O(NLG N)?

This is because whether it be worst case or average case the merge sort just divide the array in two halves at each stage which gives it lg (n) component and the other N component comes from its comparisons that are made at each stage. So combining it becomes nearly O (nlg n).

Why does merge sort not work in place?

During merging, it makes a copy of the entire array being sorted, with one half in lowHalf and the other half in highHalf. Because it copies more than a constant number of elements at some time, we say that merge sort does not work in place.

What is the time complexity of merge sort?

Time Complexity: Sorting arrays on different machines. Merge Sort is a recursive algorithm and time complexity can be expressed as following recurrence relation. T (n) = 2T (n/2) + θ (n) The above recurrence can be solved either using the Recurrence Tree method or the Master method.

How many comparisons do I need to sort a set?

There are N/4 pairs of sets from #1 that are sorted with at most 3 comparisons each, for 3 ⋅ N / 4 comparisons. (With good code, on average half of those will require only 2 comparisons, but I will ignore those, and similar effects on larger partitions, to evaluate the worst case.)