Time complexity of a hybrid merge and selection sort algorithm

I’m trying to analyse the time and space complexity of the following algorithm, which is essentially a hybrid of a merge and selection sort. The algorithm is defined as follows:

def hybrid_merge_selection(L, k = 0):     N = len(L)     if N == 1:         return L     elif N <= k:         return selection_sort(L)     else:         left_sublist = hybrid_merge_selection(L[:N // 2])         right_sublist = hybrid_merge_selection(L[N // 2:])         return merge(left_sublist, right_sublist)  

My thinking is that the worst case scenario occurs when $ k$ is extremely large, which means that the insertion sort algorithm is always applied resulting in a time complexity of $ O(n^{2})$ , where $ n$ is the length of the list and the best case scenario occurs when $ N$ when $ k == 0$ , so the merge sort algorithm is only applied resulting in a time complexity of $ O(n\log_{2}n)$ . However, could somebody give me a more detailed and mathematical explanation of the time complexity, for all scenarios, namely worst, best, average.

Selection Sort vs Merge Sort

I recently wrote a written test for the recruitment of Scientists/Engineers in ISRO(Indian Space Research Organization) few days back and the following question appeared in the test.
Of the following algorithms, which has execution time that is least dependent on initial ordering of the input?

  1. Insertion Sort
  2. Quick Sort
  3. Merge Sort
  4. Selection Sort

Well if array is sorted, when we are doing 2 way merge always the left subarray will get exhausted and we have to simply fill in the right sub array. So, number of comparisons will be equal to length of left subarray everytime. In selection sort, if array is already sorted, number of comparisons will be the same as that of the worst case, however the index of minimum element will change only after 1 full pass.

In worst case, number of comparisons in 2 way merge will be (length of left subarray+length of right subarray-1). In selection sort, worst case minimum element’s index will keep on changing after every comparison.

Only 1 option can be correct. So, what’s the best answer?

Does input type=”file” selection support url ( upload from web ) ? -html

I wonder can I use the option of input type=”file” in html to upload from url ( web/ftp etc. ) ? Is there option to it? To more explain, I want to select zip file with url and uoload it to website.Which operating systems support it? How can do it on linux,mac and windows 10? I talking about the option on the link:

<input type="file">: How to Use This HTML Value

Genetic algorithm pressure using only selection

Suppose you have a population of N individuals with fitness 1, 2, . . . , N (i.e., all individuals have a unique fitness value). Suppose you repeatedly apply tournament selection without replacement with tournament size s = 2 to this population, without doing crossover, mutation, and replacement. In other words, you run a genetic algorithm with selection alone.

After a certain number of generations you will end up with a population consisting of N copies of the same individual. Can you give an estimate of the number of generations needed to achieve that?

Intuition behind min cut in a flow network? Whether it’s baseball elimination or project selection

I was wondering if someone can give me a general definition of a min-cut besides it being the max flow of a network.

For example, in the baseball elimination problem, if we wanted to find out if team z is eliminated, the min cut represents the team(s) that will beat team z out of the 1st place if the edges aren’t full saturated. If the edges are fully saturated, then min-cut is everything except t, and team z still has a chance.

For the project selection, the min cut contains the projects you should do to maximize your return.

How do people figure out that min-cut can be applied to these problems? What is it about min-cut that gives it such power?

Thank you!

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Weighted Activity Selection Problem with allowing shifting starting time

I have some activities with weights, and I would like to select non overlapping activities by maximizing the total weight. This is known problem and solution exists.

In my case, I am allowed to shift the start time of activities in some extend while duration remains same. This will give me some flexibility and I might increase my utilization.

Example scenario is something like the following:

(start, end, profit) a1: 10 12 120 a2: 10 13 100 a3: 14 18 150 a4: 14 20 100 

Without shifting flexibility, I would choose (a1, a3) and thats it. On the other hand I might shift the intervals by 5 units (In real case even 1000x greater than original task duration) to the left/right. In that case I might come up this schedule and all tasks can be selected.

a1: 8 10 120 (shifted -2 to left) a2: 10 13 100 a3: 14 18 150 a4: 18 23 100 (shifted +4 to right) 

Are there any feasible solution to this problem?