Please give the complete method and prove its correctness

Problem 3. You are given two strings A and B of length n, each consisting of possibly repeated characters from an alphabet of size M. Two strings A and B are said to be anagrams of one another if it is possible to reorder the characters in A to obtain string B (without removing or adding any characters). For instance, the strings "ELEVEN PLUS TWO" and "TWELVE PLUS ONE" are anagrams of one another (think of empty-space also as a character in the alphabet). Your goal is to design an algorithm that decides if a given pair of strings are anagrams of one another. You may assume that all characters in the alphabet can represented by distinct integers in the set {1,2,,M}, and that you can convert any character to its integer representation in O(1) time (note that M can be much larger than n ). (a) Design an algorithm for this problem with worst-case runtime of O(n+M). (15 points) (b) Design a randomized algorithm for this problem with worst-case expected runtime of O(n). (10 points)