Many useful calculations in probability and physics require us to perform certain weighted sums related to pairs of integers (i,j). Consider the following sum: EM- =) E'=zi+]ci Assume that the coefficients Cij (for all i, j, i=1,2,...n, j=1,2,...n) are given to you as inputs as the entries of a matrix C. a. (25 points) Write a pseudo-code that computes the above sum given the n*n coefficient matrix C with entries Cij, b. ( 12 points) Find the number of operations (only arithmetic and logical) that your algorithm performs in the worst case. C. (8 points) Assume now that the coefficients Cij are not given to you but have to be calculated for each i.j using an algorithm that requires O(log n) steps. Give a big-O estimate for computing the sum under this assumption (you don't have to write the pseudo-code but explain all details). Many useful calculations in probability and physics require us to perform certain weighted sums related to pairs of integers (i,j). Consider the following sum: EM- =) E'=zi+]ci Assume that the coefficients Cij (for all i, j, i=1,2,...n, j=1,2,...n) are given to you as inputs as the entries of a matrix C. a. (25 points) Write a pseudo-code that computes the above sum given the n*n coefficient matrix C with entries Cij, b. ( 12 points) Find the number of operations (only arithmetic and logical) that your algorithm performs in the worst case. C. (8 points) Assume now that the coefficients Cij are not given to you but have to be calculated for each i.j using an algorithm that requires O(log n) steps. Give a big-O estimate for computing the sum under this assumption (you don't have to write the pseudo-code but explain all details)