“A” array has a members and “B” array has b members which are sorted. I need an algorithm to find the k-th member in a new array which is a mix of “A” and “B”. The runtime must be O(log(a+b))

You are given an array J[1 : n] which includes the scores of n players in a game. You are additionally given an array P[1 : m] with the score of m new players. Design and analyze an algorithm that given both arrays J and P, can find the rank of each player P inside the array J, i.e., for each P[i], determines what would be the rank of P[i] in the array consisting of all elements of J plus P[i]. Your algorithm should run in O((n + m) ·log n) time.

Problem 2: Suppose you are given an integer array A of length n and some integer z. Write an algorithm that searches the array for two integers x and y such that x + y = z. The algorithm should return the pair (x, y) if it finds that and some reserved token "NONE" if two such integers do not exist. Your algorithm must run in O(n) time and O(n) space.

Problem2: A square matrix can be represented by a two-dimensionalarray with N rows and N columns. You may assume a maximum size of 50 rows and 50 columns. 1. Write an algorithm MakeEmpty(n), which sets the first n rows and n columns to zero. 2. Write an algorithm Add(M1, M2, M3), which adds two matrices M1 and M2 together to produce matrix M3. 3. Write an algorithm Subtract(M1, M2, M3), which subtracts matrix M2 from matrix M1 to produce matrix M3. 4. Write an algorithm Copy(M1, M2), which copies matrix M1 into matrix M2.