Explain the concept of binary search, and compare it with linear search. Discuss the advantages and limitations of each algorithm and provide examples where each algorithm would be most suitable. Also, analyze the time complexity of both algorithms in terms of the number of elements being searched.

Describe the time complexity of the binary search algorithm in terms of the number of comparisons used (and ignoring the time required to compute m = [(i + j)/2] in each iteration of the loop in the algorithm).

Question 6: Professor Holmes has come up with a new sorting algorithm. He calls it Trinary Sort and "claims" that it is asymptotically faster than Merge Sort, despite the fact both the algorithms operate using similar logic. But, unlike Merge Sort, Trinary Sort splits the input array into (roughly) 3 equal parts at each step of the recursion as long as the array is splittable (i.e., has at least 3 elements). Trinary Sort's merge subroutine, similar in principle to the one used by Merge Sort, takes 3 sorted subarrays and merges them to produce a single sorted array. Given all of this, answer the following questions. (a) In Merge Sort, the merge subroutine makes n-1 comparisons to merge 2 arrays of size n/2, which takes (n) time. How many comparisons will the merge subroutine of Trinary Sort make to merge 3 arrays of size n/3? What would be the (...) bound on the running time for this subroutine? (b) What is the (...) bound on the running time of the Trinary Sort algorithm? Come up with…

The sequential search algorithm and the binary search algorithm both have their own individual set of advantages, but what are some general rules that may be followed to determine when either approach should be used?