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CS70_Exam_2__Fall_2006

# CS70_Exam_2__Fall_2006 - CS570 Analysis of Algorithms Fall...

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CS570 Analysis of Algorithms Fall 2006 Exam 2 Name: _____________________ Student ID: _________________ Maximum Received Problem 1 10 Problem 2 20 Problem 3 10 Problem 4 20 Problem 5 20 Problem 6 20 Note: The exam is closed book closed notes.

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1) 10 pts By using Strassen's algorithm, we can computes the product of two n x n matrices in O(n^2.81) time. This was achieved because we found a way to multiply the n/2 x n/2 matrices with only 7 multiplications rather than 8. Suppose we came up with a Strassen-like algorithm as follows. Assume that instead of splitting each matrix into four n/2 x n/2 matrices, we split each matrix into sixteen n/4 x n/4 matrices, and that the result is computed with only m multiplications instead of the normal 64. How small should m be for this new algorithm to be asymptotically faster than the original Strassen algorithm?
2) 20 pts a- Given an array of integers A[1…n], give a divide-and-conquer algorithm to find the minimum ratio of A[i]/A[i+1] for 0<i<n. Your answer should clearly say how to divide the problem into subproblems and how to merge the results.

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