Problem 2. We can generalize the maximum contiguous sum problem" to a torus. Assume that we use 0 indexing on an mxn array of numbers (which can be negative). Each entry A[i, j] has four neighbors: Ai, (i+1) mod n], A[i, (j-1) mod n], A[(i+1) mod m,j], and A[(i-1) mod m,j]. Find the largest sum in a contiguous rectangle, which includes the interior. So a m' x n' subarray has m'n' numbers. (a) Write down an English description of the "brute force algorithm for the torus version. One or two sentences should suffice. (b) Write down the "brute force algorithm in pseudocode. (c) How many times is the inner loop executed? Write it using summations. (d) Simplify your summation. Justify. Problem 2. We can generalize the maximum contiguous sum problem" to a torus. Assume that we use 0 indexing on an mxn array of numbers (which can be negative). Each entry A[i, j] has four neighbors: Ai, (i+1) mod n], A[i, (j-1) mod n], A[(i+1) mod m,j], and A[(i-1) mod m,j]. Find the largest sum in a contiguous rectangle, which includes the interior. So a m' x n' subarray has m'n' numbers. (a) Write down an English description of the "brute force algorithm for the torus version. One or two sentences should suffice. (b) Write down the "brute force algorithm in pseudocode. (c) How many times is the inner loop executed? Write it using summations. (d) Simplify your summation. Justify