(a) Hamiltonian-Cycle problem is the problem that takes a graph as input and asks whether there is a simple cycle in 6 that visits each vertex of 6 exactly once and then return to its starting vertex. Such a cycle is called a Hamiltonian cycle of G. Describe a nondeterministic polynomial time algorithm for this problem. (b) The 3-Partition problem is defined as follows. Given a finite set A of 3m elements, a bound B Z* (a positive integer) and a size s(a) Z* for each element a A such that s(a) satisfies the following inequalities: B/4