Consider the chain of matrices below. M = M1 x M2 x M3 x M4 [15 x 5] [5 x 25] [25 x 30] [30 x 45] (a) Show the complete table used by the dynamic programming algorithm for the matrix chain problem.
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Consider the chain of matrices below. M = M1 x M2 x M3 x M4
[15 x 5] [5 x 25] [25 x 30] [30 x 45]
(a) Show the complete table used by the dynamic
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- Consider the following snapshot of a system: Allocation Max Available A B C D A B C D A B C D P0 0 0 1 2 0 0 1 2 1 5 2 0 P1 1 0 0 0 1 7 5 0 P2 1 3 5 4 2 3 5 6 P3 0 6 3 2 0 6 5 2 P4 0 0 1 4 0 6 5 6 Answer the following questions using the banker’s algorithm: a). What is the content of the matrix Need? b). Is the system in a safe state? c). If a request from process P1 arrives for (0,4,2,0), can the request be granted immediately?Write down the tensor expression for the following matrix operations. Where A,B are 3 × 3, C is 3 × 4, and D is 4 × 7 matrices. And for a matrix M, its i-th row j-th column component will be denoted as M_ij . (a) det(A · B^T ).(b) Tr[A · B].(c) B · C · D, and explicitly spell out all the index summation.(d)δ_ii =?(e) ϵ_ijkϵ_ijk =?A is be a 4×3 matrix and B is a 3×2 matrix. Which of the following gives a 2×4 matrix as a result? Select one alternative: a. BT AT b. BT A c. B A d. A + BT
- write a C++ program to Given a matrix of dimension m*n where each cell in the matrix can have values 0, 1 or 2 whichhas the following meaning:0: Empty cell1: Cells have fresh oranges2: Cells have rotten orangesSo we have to determine what is the minimum time required so that all the oranges becomerotten. A rotten orange at index [i,j] can rot other fresh orange at indexes [i-1,j], [i+1,j], [i,j-1],[i,j+1] (up, down, left and right). If it is impossible to rot every orange then simply return -1.Examples:Input: arr[][C] = { {2, 1, 0, 2, 1},{1, 0, 1, 2, 1},{1, 0, 0, 2, 1}};Output:All oranges can become rotten in 2 time frames.Input: arr[][C] = { {2, 1, 0, 2, 1},Tahir Iqbal Department of Computer Sciences. BULC{0, 0, 1, 2, 1},{1, 0, 0, 2, 1}};Output:All oranges cannot be rotten.Below is algorithm.1) Create an empty Q.2) Find all rotten oranges and enqueue them to Q. Also enqueuea delimiter to indicate beginning of next time frame.3) While Q is not empty do following3.a) While delimiter in…Matrix multiplication plays an important role in a number of applications. Two matrices can only be multiplied if the number of columns of the fi rst matrix is equal to the number of rows in the second.Let’s assume we have an m × n matrix A and we want to multiply it by an n × p matrix B. We can express their product as an m × p matrix denoted by AB (or A ⋅ B). If we assign C = AB, and ci,j denotes the entry in C at position (i, j), then for each element i and j with 1 ≤ i ≤ m and 1 ≤ j ≤ p. Now we want to see if we can parallelize the computation of C. Assume that matrices are laid out in memory sequentially as follows: a1,1, a2,1, a3,1, a4,1, ..., etc.Assume that we are going to compute C on both a single core shared memory machine and a 4-core shared-memory machine. Compute the speedup we would expect to obtain on the 4-core machine, ignoring any memory issues.Repeat above Exercise, assuming that updates to C incur a cache miss due to false sharing when consecutive elements are in a…Consider the matrices are given the sequence {4, 10, 3, 12, 20, and 7} values of dimension array p in matrix chain multiplication, then optimal value of MCM matrix M [2, 4] when indices are starting from 1 not 0 A- M [2, 4] = 1320 B- M [2, 4] = 2760 C- M [2, 4] = 1080 D- M [2, 4] = 1344
- We define a magic square to be an matrix of distinct positive integers from to where the sum of any row, column, or diagonal of length is always equal to the same number: the magic constant. You will be given a matrix of integers in the inclusive range . We can convert any digit to any other digit in the range at cost of . Given , convert it into a magic square at minimal cost. Print this cost on a new line. Note: The resulting magic square must contain distinct integers in the inclusive range . Example $s = [[5, 3, 4], [1, 5, 8], [6, 4, 2]] The matrix looks like this: 534158642 We can convert it to the following magic square: 834159672 This took three replacements at a cost of . Function Description Complete the formingMagicSquare function in the editor below. formingMagicSquare has the following parameter(s): int s[3][3]: a array of integers Returns int: the minimal total cost of converting the input square to a magic square Input Format Each of the lines…Problem 1) Change the diagonal elements of a 3X3 matrix to 1. Diagonal elements of the example matrix shown here are 10, 8, 2 10 -4 0 7 8 3 0 0 2 Read the given values from input (cin) using for loops and then write your code to solve the diagonal.If a matrix A has size 5x6 and a matrix B has a size 6x4, then what will be the size of a matrix A*B?
- I do not understand this expression. so is c[i][j] += a[i][h] * b[h][j] mean c[i][j] = a[i][h] * b[h][j] + c[i][j]?? ; We do not know about the + matrix c right?Given a matrix of dimension m*n where each cell in the matrix can have values 0, 1 or 2 which has the following meaning: 0: Empty cell 1: Cells have fresh oranges 2: Cells have rotten oranges So we have to determine what is the minimum time required so that all the oranges become rotten. A rotten orange at index [i,j] can rot other fresh orange at indexes [i-1,j], [i+1,j], [i,j-1], [i,j+1] (up, down, left and right). If it is impossible to rot every orange then simply return -1. Examples: Input: arr[][C] = { {2, 1, 0, 2, 1}, {1, 0, 1, 2, 1}, {1, 0, 0, 2, 1}}; Output: All oranges cannot be rotten. Below is algorithm. 1) Create an empty Q. 2) Find all rotten oranges and enqueue them to Q. Also enqueue a delimiter to indicate beginning of next time frame. 3) While Q is not empty do following 3.a) While delimiter in Q is not reached (i) Dequeue an orange from queue, rot all adjacent oranges. While rotting the adjacents, make sure that time frame is incremented only once. And time frame is…Given an n x n matrix where each of the rows and columns is sorted in ascending order, return the kth smallest element in the matrix. Note that it is the kth smallest element in the sorted order, not the kth distinct element. You must find a solution with a memory complexity better than O(n2). Example 1: Input: matrix = [[1,5,9],[10,11,13],[12,13,15]], k = 8 Output: 13 Explanation: The elements in the matrix are [1,5,9,10,11,12,13,13,15], and the 8th smallest number is 13 Example 2: Input: matrix = [[-5]], k = 1 Output: -5