well the divide and conquer approach for matrix multiplication is as-
the strassen algo and its complexity is as-
Question #4 (15 points) In class, we discussed a divide-and-conquer algorithm for matrix multiplication that involved...
4.5-2 Professor Caesar wishes to develop a matrix-multiplication algorithm that is asymptotically faster than Strassen’s algorithm. His algorithm will use the divide- and-conquer method, dividing each matrix into pieces of size n/4 x n/4, and the divide and combine steps together will take O(n) time. He needs to determine how many subproblems his algorithm has to create in order to beat Strassen’s algo- rithm. If his algorithm creates a subproblems, then the recurrence for the running time T(n) becomes T(n)...
I already solved part A and I just need help with part B 1. Matrix Multiplication The product of two n xn matrices X and Y is a third n x n matrix 2 = XY, with entries 2 - 21; = xixYk x k=1 There are n’ entries to compute, each one at a cost of O(n). The formula implies an algorithm with O(nº) running time. For a long time this was widely believed to be the best running...
Please help me with this divide and conquer question. Please show your work. NOTES: The multiplication we covered in class are grade-school and Karatsuba multiplication algorithm. 3. Give the best algorithm you can to convert an n digit number base 10 into binary. Here, we are counting operations on single digits as single steps, not arithmetic operations. You can use any of the multiplication algorithms we described in class.) 3. Give the best algorithm you can to convert an n...
Please give me a divide and conquer algorithm that has runtime better than O(n^2) along with justification. Also please do a runtime analysis on this algorithm. Please DONT copy and paste other's solution.THANKS 3. Give the best algorithm you can to convert an n digit number base 10 into binary. Here, we are counting operations on single digits as single steps, not arithmetic operations. You can use any of the multiplication algorithms we described in class.)
Question 4 [12 marks] Some applications of mathematics require the use of very large matrices (several thousand rows for example) and this in turn directs attention to efficient ways to manipulate them. This question focuses on the efficiency of matrix multiplication, counting the number of numerical arithmetic operations (addition, subtraction and multiplication) involved. We start with very simplest case of 2x2 matrices. (a) The standard way of multiplying 2x2 matrices uses 8 multiplications and 4 additions. List the 8 products...
Infix Expression Evaluator For this project, write a C program that will evaluate an infix expression. The algorithm REQUIRED for this program will use two stacks, an operator stack and a value stack. Both stacks MUST be implemented using a linked list. For this program, you are to write functions for the linked list stacks with the following names: int isEmpty (stack); void push (stack, data); data top (stack); void pop (stack); // return TRUE if the stack has no...
Infix Expression Evaluator For this project, write a C program that will evaluate an infix expression. The algorithm REQUIRED for this program will use two stacks, an operator stack and a value stack. Both stacks MUST be implemented using a linked list. For this program, you are to write functions for the linked list stacks with the following names: int isEmpty (stack); void push (stack, data); data top (stack); void pop (stack); // return TRUE if the stack has no...