MergeSort

See following for details. http://www.geeksforgeeks.org/stability-in-sorting-algorithms/

Selection sort makes O(n) swaps which is minimum among all sorting algorithms mentioned above.

The data can be sorted using external sorting which uses merging technique. This can be done as follows: 1. Divide the data into 10 groups each of size 100. 2. Sort each group and write them to disk. 3. Load 10 items from each group into main memory. 4. Output the smallest item from the main memory to disk. Load the next item from the group whose item was chosen. 5. Loop step #4 until all items are not outputted. The step 3-5 is called as merging technique.

The time complexity is given by: T(N) = T(N/3) + T(2N/3) + N Solving the above recurrence relation gives, T(N) = N(logN base 3/2)

The insertion sort will take (n) time when input array is already sorted.

The recurrence tree for merge sort will have height Log(n). And O(n^2) work will be done at each level of the recurrence tree (Each level involves n comparisons and a comparison takes O(n) time in worst case). So time complexity of this Merge Sort will be .

Worst case complexities for the above sorting algorithms are as follows: Merge Sort — nLogn Bubble Sort — n^2 Quick Sort — n^2 Selection Sort — n^2

See Merge Sort and this.

Time complexity of merge sort is Θ(nLogn)

c*64Log64 is 30
c*64*6 is 30
c is 5/64

For time 6 minutes

5/64*nLogn = 6*60

nLogn = 72*64 = 512 * 9

n = 512. 

Most practical implementations of Quick Sort use randomized version. The randomized version has expected time complexity of O(nLogn). The worst case is possible in randomized version also, but worst case doesn’t occur for a particular pattern (like sorted array) and randomized Quick Sort works well in practice. Quick Sort is also a cache friendly sorting algorithm as it has good locality of reference when used for arrays. Quick Sort is also tail recursive, therefore tail call optimizations is done.