Let G be an undirected graph, and s and t be arbitrary vertices of G. We are interested in the possible lengths of (non necessarily) simple paths from s to t.

a. Design an algorithm that determines whether there is a path from s to t with an odd number of edges. Do the same for an even number of edges. Argue that your algorithm is correct and analyze its running time.
b. Design an algorithm that determines whether there is a path from s to t whose length is divisible by 3. Argue that your algorithm is correct and analyze its running time. (Hint: It might be useful to also consider paths whose length is 1 or 2 modulo 3).

File account.java (see previous exercise) contains a definition for a simple bank account class with methods to withdraw, deposit, get the balance and account number, and return a string representation. note that the constructor for this class creates a random account number. save this class to your directory and study it to see how it works. then write the following additional code: 1. suppose the bank wants to keep track of how many accounts exist. a. declare a private static integer variable numaccounts to hold this value. like all instance and static variables, it will be initialized (to 0, since it’s an int) automatically. b. add code to the constructor to increment this variable every time an account is created. c. add a static method getnumaccounts that returns the total number of accounts. think about why this method should be static - its information is not related to any particular account. d. file testaccounts1.java contains a simple program that creates the specified number of bank accounts then uses the getnumaccounts method to find how many accounts were created. save it to your directory, then use it to test your modified account class.