Assume you have a 2D matrix. Values are sorted in ascending order from left to write and top to bottom, e.g., 1 7 16 21 34 4 9 20 25 41 6 16 31 33 44 11 19 49 50 61 I'm curious if my value x is in this matrix. I could take a brute force approach, considering all cells via the following code: def find in matrix(m, num_rows, num cols, x): for į in range(num_rows): for j in range(num cols): if m[i]i]==x: return True return False What would be the big O estimate of the run-time for this brute force approach? How could I take a divide-and-conquer approach? Briefly describe (in words) how you could use what is known about the structure of the 2D matrix to divide and conquer.

Assume you have a 2D matrix. Values are sorted in ascending order from left to write and top to bottom, e.g., 1 7 16 21 34 4 9 20 25 41 6 16 31 33 44 11 19 49 50 61 I'm curious if my value x is in this matrix. I could take a brute force approach, considering all cells via the following code: def find in matrix(m, num_rows, num cols, x): for į in range(num_rows): for j in range(num cols): if m[i]i]==x: return True return False What would be the big O estimate of the run-time for this brute force approach? How could I take a divide-and-conquer approach? Briefly describe (in words) how you could use what is known about the structure of the 2D matrix to divide and conquer.

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter15: Recursion

Section: Chapter Questions

Problem 18SA

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A matrix is an array of numbers of size m by n (i.e., m x n). When we multiply 2 matrices, we multiply the matching numbers, then sum them up. Multiplying a matrix of size m x n with another matrix of size n x q will result in a matrix of size m x q. An example is shown in Figure 1: [ ? ? ? ? ? ? ] x [ ? ? ? ? ] = [ ?? +?? ?? + ?? ?? + ?? ?? + ?? ?? + ?? ?? + ?? ] Matrix 3 x 2 Matrix 2 x 2 Matrix 3 x 2 Figure 1: Multiplication of Matrix 3 x 2 and 2 x 2 Write a C++ program that multiplies 2 matrices and return the sum of the transposed matrix. Your program shall include the following: a) Define two 2 dimensional arrays, M and N that each represents a matrix of size 3 x 2 and a matrix of size 2 x 2. Request the user to enter the values for the 2 arrays using advanced pointer notations (refer to your slides for the list of array pointer notations). b) Create a function named multMatrix() that passes as arguments, the values of array M and N, multiplies them and store the results in a new…
I am having trouble with a individual coding problem I am doing in python: Ar = int(input("How many rows does your matrix have? "))Ac = int(input("How many columns does your matrix have? ")) win = GraphWin('Matrix A', 300,300) win.setBackground('white') for p in range(Ac):y = 75 + 40*pfor q in range(Ac):x = 50 + 50*qinputText = Entry(Point(x,y), 3)inputText.setText('0')inputText.draw(win) ## The issue I having is that I want to be able to get the users inputs from their entries so that I can do matrix operations on them. However, anytime I try to append their entries at best I just get their last entry repeated (n)(m) times. I would be very thankful if you can show me how I can change my code so that I append all user entries correctly.
Let m be a matrix with n rows and n columns whose entries are either 1 or 0. recall that the element of m on row i and column j is denoted by mij . the diagonal entries of m are {mii} for 1 ≤ i ≤ n. We call M permutable if it is possible to swap some of the rows and some of columns so that all diagonal entries are 1. Design a polynomial time algorithm that decides whether a binary matrix M is permutable or not. Note that we can swap any two rows or two columns. Also, the order in which these swaps are done is not important.
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.
You will be given a square matrix of N rows and N columns (1 <= N <= 1000) containing positive and negative integers with absolute value not larger than 1000. You are required to compute the greatest sum achievable by walking a path, starting at any cell of the matrix and always moving downwards or rightwards. Additionally, you have to report the number of times that value is achievable. N will be in the first line of the input. N lines follow with N integers each. You should output a single line with two integers separated by a single blank space: first one is the greatest sum, second one is the number of times this value can be reached.
you will be given a square matrix of N rows and N columns (1 <= N <= 1000) containing positive and negative integers with absolute value not larger than 1000. You are required to compute the greatest sum achievable by walking a path, starting at any cell of the matrix and always moving downwards or rightwards. Additionally, you have to report the number of times that value is achievable. N will be in the first line of the input. N lines follow with N integers each. You should output a single line with two integers separated by a single blank space: first one is the greatest sum, second one is the number of times this value can be reached. Case 1: For the input provided as follows: 53 1 -2 1 1-6 -1 4 -1 -41 1 1 1 12 2 2 2 21 1 1 1 1 Output of the program will be: 15 1 Case 2: For the input provided as follows: 31 1 12 2 23 3 3 Output of the program will be: 12 1
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…
Search a sorted matrix: The input consistsof a real number x and a matrix A[1..n, 1..m] of nm real numbers such that each rowA[i, 1..m] is sorted and each column A[1..n, j] is sorted. The goal is to find the maximum array entry A[i, j] that is less than or equal to x, or report that all elements of Aare larger than x. Design and analyze an iterative algorithm for this problem that examines as few matrix entries as possible. Becareful if you believe that a simple binarysearch solves the problem. make a lower bound, and recursive algorithm.
Search a sorted matrix: The input consistsof a real number x and a matrix A[1..n, 1..m] of nm real numbers such that each rowA[i, 1..m] is sorted and each column A[1..n, j] is sorted. The goal is to find the maximum array entry A[i, j] that is less than or equal to x, or report that all elements of Aare larger than x. Design and analyze an iterative algorithm for this problem that examines as few matrix entries as possible. Becareful if you believe that a simple binarysearch solves the problem.
When dealing with large dense symmetric matrix it is recommended that to either store upper right or lower left entries only to avoid redundancy and thereby saving a lot of space (particularly when the matrix elements are of double type or any other user-defined datatype). Let us assume that we have decided to store only the upper right entries of a matrix inside a 1D array in the row-major arrangement. 1. Design an algorithm for accepting a symmetric matrix from the user and printing the same matrix. 2. Design an algorithm for multiplying a given symmetric matrix stored in a 1D array with a compatible vector.
Consider the following algorithm, which takes as input asequence of n integers a_1, a_2,… , a_n and produces as output a matrix M = {m_(ij)} where m_(ij) is the minimum termin the sequence of integers a_i, a_(i+1),… , a_j for j ≥ i andm_(ij) = 0 otherwise.initialize M so that m_(ij) = a_i if j ≥ i and m_(ij) = 0otherwisefor i := 1 to nfor j := i + 1 to nfor k := i + 1 to jm_(ij) := min(m_(ij), a_k)return M= {m_(ij)} {m_(ij) is the minimum term ofa_i, a_(i+1),… , a_j}a) Show that this algorithm uses O(n^3) comparisons tocompute the matrix M. b) Show that this algorithm uses Ω(n^3) comparisons tocompute the matrix M. Using this fact and part (a),conclude that the algorithms uses Θ(n^3) comparisons.[Hint: Only consider the cases where i ≤ n∕4 andj ≥ 3n∕4 in the two outer loops in the algorithm.]
For example, Input: {10, 12, 17, 14, 8, 3, 22} Output: {5, 4, 2, 3, 6, 7, 1} Given an array of different integers, replace each element by its corresponding descending order in the array. The maximum array element has the order 1; the second maximum element has order 2, and so on... a) Design a brute-force algorithm to solve this problem (4 marks), and analyse the complexity of your solution b) Design a more efficient algorithm to do the same task with less complexity , and analyse the complexity of your solution. c) Develop a python code to implement your efficient algorithm. depend on the correctness of the code, indentation, comments, test-case] d) Prepare a brief report (250 words) comparing the two algorithms