Suppose you are writing an algorithm to merge k sorted arrays of size n into a single sorted array of size kn. You write an algorithm to do so that (1) makes a recursive call to merge the first k/2 arrays, (2) makes another recursive call to merge the remaining k/2 arrays, then (3) merges the results from the calls in (1) and (2). Suppose the cost of merging two sorted arrays of sizes a and b is a+b. Suppose you are sitting at the root of the recursion tree, where the last two arrays of size kn/2 will be merged. What will be the total cost of the algorithm at this level of the tree? Give your answer as an expression in terms of n and k (in simplest form). nk'log(nk) Question 7 Given the recursive algorithm above for merging k sorted arrays, what will be the total cost of the algorithm at the bottom of the recursion tree (the sum of the work performed at the leaves)? You can assume that k is a power of 2. Give your answer as a simplified expression in terms of n and k.

Consider a scenario in which you are presented with a data set of length K. Write a simple recursive algorithm to choose all possible pairs of elements in the set. Assess the computational complexity and explain your calculations.

Merge sort is an efficient sorting algorithm with a time complexity of O(n log n). This means that as the number of elements (chocolates or students) increases significantly, the efficiency of merge sort remains relatively stable compared to other sorting algorithms. Merge sort achieves this efficiency by recursively dividing the input array into smaller sub-arrays, sorting them individually, and then merging them back together. The efficiency of merge sort is primarily determined by its time complexity, which is , where n is the number of elements in the array. This time complexity indicates that the time taken by merge sort grows logarithmically with the size of the input array. Therefore, even as the number of chocolates or students increases significantly, merge sort maintains its relatively efficient performance. Regarding the distribution of a given set of x to y using iterative and recursive functions, the complexity analysis depends on the specific implementation of each…

Question Which of the following statements about mergesort are true? Unless otherwise specified, assume that mergesort refers to the pure recursive (top-down) version of mergesort (with no optimizations), using the merging subroutine described in lecture. Answer Mark all that apply. OThe number of compares to bottom-up mergesort an array depends only on the length of the array n (and not on the keys or order of the keys in the array). O Mergesort is a stable sorting algorithm. Suppose that n is a power of 2. For any array of n distinct keys, top-down mergesort and bottom-up mergesort compare exactly the same pairs of keys (but possibly in a different order). OMergesort uses only a logarithmic amount of space (other than the input array). OIt is possible to design a compare-based algorithm to merge any two sorted arrays, each of length n, with no more than 3/2 n compares.