use the Process object of the multiprocessing module to make Python implement row-partitioning for parallel matrix multiplication. Each of the three processes receives its row and matrix B from the master process and multiplies them to create the row of the output matrix C. The input matrices A and B are tiny 33 matrices. A worker then sends its related row of matrixC to the master. For this algorithm, we must take the following into account: The data of the parent process is entirely present in the process when it is launched using the Process module, but any changes it makes are not reflected in the parent process. In order to have the product matrix C shared between the processes, we need to use the Manager object of the multiprocessing module and define C as an array to be shared from this object. Each worker process performs  multiplication and stores the result in its row entry of matrix C.

1. Asymptotics. Given an array A of n integers, you'd like to output a two-dimensional n x n array B in which B[i, j] = max {A[i], A[i + 1],..., A[j]} for each i < j. For i j the value of B[i, j] can be left as is. for i = 1,2, η for j = i + 1, n " Compute the maximum of the entries A[i], A[i + 1], , A[j]. Store the maximum value in B[i, j]. (a) Find a function of such that the running time of the algorithm is O(f(n)), and clearly explain why. (b) For the same function f argue that the running time of the algorithm is also (f(n)). (This establishes an asymptotically tight bound (f(n)).) (c) Design and analyze a faster algorithm for this problem. You should give an algorithm with running O(g(n)), where lim→∞ g(n)/f(n) = 0.

Find a sorted matrix: The input is a real number x and a matrix A[1..n, 1..m] of nm real numbers, with each row A[i, 1..m] and column A[1..n, j] sorted. The objective is to locate the largest array entry A[i, j] that is less than or equal to x, or to report that all components of A are greater than x. Create and test an iterative method that analyses as few matrix elements as feasible. Be cautious if you assume a simple binary search would fix the problem. Find a sorted matrix: The input is a real number x and a matrix A[1..n, 1..m] of nm real numbers, with each row A[i, 1..m] and column A[1..n, j] sorted. The objective is to locate the largest array entry A[i, j] that is less than or equal to x, or to report that all components of A are greater than x. Create and test an iterative method that analyses as few matrix elements as feasible. Be cautious if you assume a simple binary search would fix the problem.

Search a sorted matrix: The input consists of a real number x and a matrix A[1..n, 1..m] of nm real values, where A[i, 1..m] and A[1..n, j] are the rows and columns, respectively, of the matrix. The objective is to either state that all of the members of A are greater than x or to locate the largest array entry A[i, j] that is less than or equal to x. Create and evaluate an iterative approach for this issue that looks at the least amount of matrix entries feasible. If you think the issue can be resolved with a straightforward binary search, think twice.