Show, in the style of the trace given with the code, how the entropy-optimal sort first partitions the array B A B A B A B A C A D A B R A Use the form to answer the question as same on the picture. lt i gt 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 B A B A B A B A C A D A B R A.

Now let's examine a Dynamic Program algorithm to solve this problem. 3.3 Let's say we have an array of length X+1. How would we define array[x]? or What is array[x] defined for?

Very confused about this problem. Any help is appercaited

Given an array A = [10, 7, 4, 2, 1], and target = 7, return the index of the target if found, else return -1. 1. Can this problem be solved in O(logN)?  2. If so, write the implementation. Mention time and space complexity 3. If this problem cannot be solved using O(logN), what is the solution that you suggest - write the code and also mention time and space complexity.

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:…