Under what conditions will an algorithm that recursively summons itself no longer do so?

Is it ever possible for an algorithm to fail?

Using the recursion three method find the upper and lower bounds for the following recur- rence (if they are the same, find the tight bound). T(n) = T(n/2) + 2T(n/3) + n.

Is it possible to write a tail-recursive version of the classic quicksort algorithm? Why or why not?

Explain the halting condition for the recursive binary search and why all recursive algorithms need one.

Consider the Sort-and-Count algorithm explained in section 5.3 of our text: "Counting Inversions"Suppose that the initial list is: 92 71 36 91 27 48 14 34 81 26 24 65 78 51 37 22 Sort-and-Count makes two recursive calls. The first recursive call inputs the first half of the initial list: 92 71 36 91 27 48 14 34 and returns the sorted version of the first half, as well as the number of inversions found in the first half (22). The second recursive call inputs the second half of the initial list: 81 26 24 65 78 51 37 22 and returns the sorted version of the second half, as well as the number of inversions found in the second half (19). Sort-and-Count then calls Merge-and-Count. To Merge-and-Count, Sort-and-Count passes the sorted versions of the two halves of the original list: 14 27 34 36 48 71 91 92, and 22 24 26 37 51 65 78 81 Merge-and-Count begins merging the two half-lists together, while counting...

Give a recursive algorithm for finding the sum of the first n positive integers

Explain the halting condition for the recursive binary search and why all recursive algorithms need one.

What is the difference between a recursive and an iterative algorithm?

Give an account of the stopping condition for the recursive binary search, and elaborate on why such a condition is required of all recursive algorithms.

Design and implement an algorithm using recursion and backtracking to sort an array of integers into ascending order. Consider the given array as input and produce a sorted array as output. Each time you take an integer from the input array, place it at the end of the output array. If the result is unsorted, backtrack.

Devise a recursive algorithm for finding n! mod m where n and m are positive integers.

Define and justify why stopping conditions are required for all recursive algorithms, such as the recursive binary search, in your own words.