Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 4.2, Problem 3E
Program Plan Intro
To modify Strassen’s
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How would you modify Strassen's algorithm to multiply n n matrices in which n is not an exact power of 2? Explain how your algorithm works for the case where n = 30.
Determind the complexity of the following implementations of the algorithms for adding, multiplying, and transposing n x n matrices
Explain how to implement Warshall’s algorithm without using extra memory for storing elements of the algorithm’s intermediate matrices. You need to show that we can simply overwrite elements of R(k-1) with elements of R(k) without any other changes in the algorithm.
Chapter 4 Solutions
Introduction to Algorithms
Ch. 4.1 - Prob. 1ECh. 4.1 - Prob. 2ECh. 4.1 - Prob. 3ECh. 4.1 - Prob. 4ECh. 4.1 - Prob. 5ECh. 4.2 - Prob. 1ECh. 4.2 - Prob. 2ECh. 4.2 - Prob. 3ECh. 4.2 - Prob. 4ECh. 4.2 - Prob. 5E
Ch. 4.2 - Prob. 6ECh. 4.2 - Prob. 7ECh. 4.3 - Prob. 1ECh. 4.3 - Prob. 2ECh. 4.3 - Prob. 3ECh. 4.3 - Prob. 4ECh. 4.3 - Prob. 5ECh. 4.3 - Prob. 6ECh. 4.3 - Prob. 7ECh. 4.3 - Prob. 8ECh. 4.3 - Prob. 9ECh. 4.4 - Prob. 1ECh. 4.4 - Prob. 2ECh. 4.4 - Prob. 3ECh. 4.4 - Prob. 4ECh. 4.4 - Prob. 5ECh. 4.4 - Prob. 6ECh. 4.4 - Prob. 7ECh. 4.4 - Prob. 8ECh. 4.4 - Prob. 9ECh. 4.5 - Prob. 1ECh. 4.5 - Prob. 2ECh. 4.5 - Prob. 3ECh. 4.5 - Prob. 4ECh. 4.5 - Prob. 5ECh. 4.6 - Prob. 1ECh. 4.6 - Prob. 2ECh. 4.6 - Prob. 3ECh. 4 - Prob. 1PCh. 4 - Prob. 2PCh. 4 - Prob. 3PCh. 4 - Prob. 4PCh. 4 - Prob. 5PCh. 4 - Prob. 6P
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- How to multiply two matrices (n*m and m*t) using two dimensional arrays ?arrow_forwardGet the time complexity function from the pseudocode for the addition of the 2 matrices below, and prove whether the big-oh is O(n^2) so that it satisfies the rule f(n) <= c g(n); / add two matricesfor(i = 0 ; i < rows; i++){for(j = 0; j < columns; j++)matrix2[i][j] = matrix1[i][j] + matrix2[i][j];}// display the resultfor(i = 0 ; i < rows; i++){for(j = 0; j < columns; j++){printf("%d ", matrix2[i][j]);}printf("\n");}arrow_forwardShow how to find all the factors of the following numbers in an efficient manner. Explain why you can stop checking for factors when you do. A. 63 B. 75 C. 126arrow_forward
- Suppose that a Professor were to develop a method of multiplying two 12 x 12 matrices using 150 scalar multiplications and a constant number of scalar additions and subtractions: Write down the recurrence equation that describes the resulting divide and conquer algorithm for multiplying two n x n matrices. Write down the asymptotic solution of your equation from above.arrow_forwardIf d(n) is odd, show that n is square.arrow_forwardsuppose a computer solves a 100x100 matrix using Gauss elimination with partial pivoting in 1 second, how long will it take to solve a 300x300 matrix using Gauss elimination with partial pivoting on the same computer? and if you have a limit of 100 seconds to solve a matrix of size (N x N) using Gauss elimination with partial pivoting, what is the largest N can you do? show all the steps of the solutionarrow_forward
- Suppose that a Professor were to develop a method of multiplying two 12 x 12 matrices using 150 scalar multiplications and a constant number of scalar additions and subtractions: What is the recurrence equation that describes the resulting divide and conquer algorithm for multiplying two n x n matrices? And what is the asymptotic solution of the equation (use big O notation)?arrow_forwardGet the time complexity function from the pseudocode for adding 2 matrices below // add two matricesfor(i = 0 ; i < rows; i++){for(j = 0; j < columns; j++)matrix2[i][j] = matrix1[i][j] + matrix2[i][j];}// display the resultfor(i = 0 ; i < rows; i++){for(j = 0; j < columns; j++){printf("%d ", matrix2[i][j]);}printf("\n");}arrow_forwardExplain how to implement Warshall's method without needing extra RAM to store the intermediate matrices of the algorithm. You must demonstrate that we can simply replace elements of R(k-1) with elements of R(k) without making any other changes to the method.arrow_forward
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