Given two sorted arrays, each of length n, we can merge them into a sorted array in O(n) time. True False If we solve T(n) = 9T(n/3) + O(n), then we have T(n) = E(n log n). True False The running time of the Strassen's algorithm for multiplying two n-by-n matrices is E(n³). True False

Suppose that each row of an n × n array A consists of 1's and 0's such that in any row of A all the 1's come before any O's in that row. Assuming that A is already in memory, describe an algorithm running in O(n) time for finding the row that contains the most 1's. Write the algorithm following the style of your course-notes.

We are given a code symmetry, that takes an n x n matrix as its argument. It returns true if the matrix is symmetric and false if it is not. The run time of the code is calculated by counting how many times the /= comparison is executed.  procedure symmetry(M)      for x:=1 to (n-1)            for y:=(i+1) to n               if mxy /= myx then return false               else return true (a) Calculate the best case run time for symmetry (will be a number). (b) Calculate the worst case run time for symmetry (will be a polynomial in n, it will be helpful to draw matrices of different sizes and compare the number of comparisons to find a pattern).  (c) Determine the worst case run time in big O notation (d) Using the following definition of big O notation, prove the answer to (c) Definition: Let f and g be functions from the set of integers or the set of real numbers to the set of real numbers. We say that f(x) is O(g(x)) if there are constants C and k such that whenever x > k. [This is…

We can sort n integers between 0 and 2n in O(n) time. True False Given a sorted array of n integers, we can find the median of them in O(1) time. True False If ƒ = 0(g), then g = 0(f). False True