write a recurrence relation describing the running time of algorithm modified merge sort(A, p,r) include base case.

Consider sorting an unsorted array A, are merge sort and quick sort stable? Circle your answer below Insertion Sort Stable Unstable Merge Sort Stable Unstable Quick Sort Stable Unstable Counting Sort Stable Unstable Radix Sort Stable Unstable

Please, answer and provide an explenation.

Using Java, 1. Implement external sort: for sort phase use normal sort, for merge phase use two way merge to merge n sorted files (merge2way(n)), for array sort use heapsort. Also write merge(f1, f2, f3) to merge two sorted files f1 and f2 into f3.. Write mergenway(n) method and print execution time of both merges for initial input file over 10MB data. A sample input is as follow:Note:Fist input is max array size for sort 10 84 82 52 80 96 85 75 75 82 87 92 89 57 94 93 92 63 99 87 72 73 56 74 50 84 62 72 55 86 75 74 100 83 60 53 68 89 67 66 65 72 94 73 54 98 96 85 75 75 82 87 92 89

Design of algorithms - divide-and-conquer: (a) Design a divide-and-conquer algorithm DC_PROD that receives as input an array A with n>0 integers and returns the product of the elements in A. You may assume n is a power of 2. In your algorithm identify the relevant parts of a divide-and-conquer strategy: (i) divide, (ii) conquer, and (iii) combine. (b) Establish the recurrence relation for the running time, T(n), of DC_PROD. (c) Apply the Master Theorem to give a tight bound for T(n).

determine if each following statement is True or False

Use a merge sort to sort 3,6,9,4,2,10, 8, 1,7,5 into increasing order. Show all steps used by the algorithm

Show all steps that recursive merge sort algorithm would perform to sort the list of values [6,9,3,1,8,0,5,7,2] and mark their order of execution.

The pseudo-code to create the matrix:Procedure AdjacencyMatrix(N): //N represents the number of nodesMatrix[N][N]for i from 1 to N for j from 1 to N Take input -> Matrix[i][j] endforendforWe can also populate the Matrix using this common way: Procedure AdjacencyMatrix(N, E): // N -> number of nodesMatrix[N][E] // E -> number of edgesfor i from 1 to E input -> n1, n2, cost Matrix[n1][n2] = cost Matrix[n2][n1] = costendfor make a Java code implemented using above pseudo-code?

All parts of Q11 please.