Get the time complexity function from the pseudocode for the addition of the 2 matrices below, and prove whether the big-oh is O(n^2) so that it satisfies the rule f(n) <= c g(n) for(i = 0 ; i < rows; i++){ for(j = 0; j < columns; j++) matrix2[i][j] = matrix1[i][j] + matrix2[i][j]; } for(i = 0 ; i < rows; i++){ for(j = 0; j < columns; j++){ printf("%d ", matrix2[i][j]); } printf("\n"); }

please answer this question using java

I need the algorithm, proof of correctness and runtime analysis for the problem. No code necessary ONLY algorithm. And runtime should be O(n^2).

N is not computing what is wrong with code?

Problem 2. Suppose we have an array A[1 : n] which consists of numbers {1,...,n} written in some arbitrary order (this means that A is a permutation of the set {1,...,n}). Our goal in this problem is to design a very fast randomized algorithm that can find an index i in this array such that A[i] mod 8 € {1,2}, i.e., the reminder of dividing A[i] by 8 is either 1 or 2. For simplicity, in the following, we assume that n itself is a multiple of 8 and is at least 8 (so a correct answer always exist). For instance, if n = 8 and the array is A = [8,7, 2,5, 4, 6,3, 1], we want to output either of indices 3 or 8. (a) Suppose we sample an index i from {1,...,n} uniformly at random. What is the probability that i is a correct answer, i.e., A[i] mod 8 E {1,2}? (b) Suppose we sample m indices from {1,...,n} uniformly at random and with repetition. What is the probability that none of these indices is a correct answer? Now, consider the following simple algorithm for this problem: Find-Index-1(A[1:…