This paper describes what is termed as backtracking using maze problem and what is termed as branch & bound using Hamiltonian cycle. A backtracking algorithm is a recursive method of building up feasible solutions to a combinatorial optimization problem one step at a time. A backtracking algorithm is an exhaustive search, that is, all feasible solutions are considered and it will thus always find the optimal solution. It is a generalized of the ordinary maze problem to find a path from start

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... m finish. One or more sequences of choices may lead to a solution. Many of the maze problem can be solved with backtracking. Branch and bound (BB, B&B, or BnB) is an algorithm design paradigm for discrete and combinatorial optimization problems, as well as mathematical optimization. A branch-and-bound algorithm consists of a systematic enumeration. The algorithm explores branches of this tree, which represent subsets of the solution set. Using a Hamiltonian cycle a path which passes once and exactly once through every vertex of G (G can be digraph).