3. Suppose that a divide and conquer algorithm for multiplication of n x n matrices is...

3. Suppose that a divide and conquer algorithm for multiplication of n x n matrices is found such that it requires 6 multiplications and 31 additions of n/2 x n/2 submatrices. Write the recurrence for the running time T(n) of this algorithm and find the order of T(n).

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Colby Messinger answered 2 years ago

Divide and Conquer (Strassen’s Matrix Multiplication) Given two square matrices A and B of size n...

Divide and Conquer (Strassen’s Matrix Multiplication) Given two square matrices A and B of size n x n each, find their multiplication matrix. Naive Method Following is a simple way to multiply two matrices. void multiply(int A[][N], int B[][N], int C[][N]) { for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { C[i][j] = 0; for (int k = 0; k < N; k++) { C[i][j] += A[i][k]*B[k][j]; }...

Let A be an integer array of length n. Design a divide and conquer algorithm (description...

Let A be an integer array of length n. Design a divide and conquer algorithm (description and pseudo code) to find the index of an element of the minimum value in the array. If there are several such elements, your algorithm must return the index of the rightmost element. For instance, if A = {0,2,4,5,2,0,3,10}, then the algorithm should return 5, which is the index of the second 0.

Polynomial Multiplication by Divide-&-Conquer A degree n-1 polynomial ? (?) =Σ(n-1)(i=0) ???i = ?0 + ?1?...

Polynomial Multiplication by Divide-&-Conquer A degree n-1 polynomial ? (?) =Σ(n-1)(i=0) ???i = ?0 + ?1? + ?2?2 ... + ??−1?n-1 can be represented by an array ?[0. . ? − 1] of its n coefficients. Suppose P(x) and Q(x) are two polynomials of degree n-1, each given by its coefficient array representation. Their product P(x)Q(x) is a polynomial of degree 2(n-1), and hence can be represented by its coefficient array of length 2n-1. The polynomial multiplication problem is to...

Design and analyze a divide-and-conquer algorithm for finding the maximum element in a list: L[0: n – 1].

The following submission rules apply:· For those questions requiring programs, the solutions must be implemented using JavaScript or Java.o Appropriate self-documenting comments in the source code are mandatory, consistent with good programming practices.o Solutions must be provided in plain text so that formatting is not lost.· All answers must be provided in this document.· Sources must be given accurate and complete citations sufficient for the instructor to find and confirm them.Design and analyze a divide-and-conquer algorithm for finding the maximum...

Divide and conquer problem. Suppose we are given two sorted arrays A[1 . . . n]...

Divide and conquer problem. Suppose we are given two sorted arrays A[1 . . . n] and B[1 . . . n] and an integer k. Describe an algorithm to find the kth smallest element in the union of A and B in O(log n) time. For example, if k = 1, your algorithm should return the smallest element of A ∪ B; if k = n, your algorithm should return the median of A ∪ B.) You can assume...

2. Using matrices, create an algorithm that takes a matrix of dimension N x N and...

2. Using matrices, create an algorithm that takes a matrix of dimension N x N and feed it in a spiral shape with the sequential number from 1 to N^2. Then do an algorithm in PSEint

The following divide-and-conquer algorithm is designed to return TRUE if and only if all elements of...

The following divide-and-conquer algorithm is designed to return TRUE if and only if all elements of the array have equal values. For simplicity, suppose the array size is n=2k for some integer k. Input S is the starting index, and n is the number of elements starting at S. The initial call is SAME(A, 0, n). Boolean SAME (int A[ ], int S, int n) { Boolean T1, T2, T3; if (n == 1) return TRUE; T1 = SAME (A,...

Q. Explain how a divide and conquer algorithm for detecting whether or not the number 5...

Q. Explain how a divide and conquer algorithm for detecting whether or not the number 5 exists in an array would work. Your explanation should include: - a description of your algorithm using psuedocode - a proof of correctness of your algorithm - an analysis of the runtime of the algorithm

Recall the Matrix Chain Multiplication Algorithm for determining the optimal parenthesization for a product of matrices....

Recall the Matrix Chain Multiplication Algorithm for determining the optimal parenthesization for a product of matrices. Provide a recursive implementation of the function void print_parenth(Matrix K[], int i, int j); that takes as input the matrix K of k values that are needed to construct the optimal parenthesization for Ai · · · Aj . Assume access to a print function that takes as input a string and prints its value. You may also assume a “+” operation for string...

1a. Write pseudocode for a divide-and-conquer algorithm for finding the po- sition of the largest element...

1a. Write pseudocode for a divide-and-conquer algorithm for finding the po- sition of the largest element in an array of n numbers. 5. Find the order of growth for solutions of the following recurrences. a . T(n)=4T(n/2)+n,T(1)=1 b. T(n)=4T(n/2)+n2,T(1)=1 c. T(n)=4T(n/2)+n3,T(1)=1

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3. Suppose that a divide and conquer algorithm for multiplication of n x n matrices is...

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