Which of the following is not a backtracking algorithm?

Answer: Towers of Hanoi is not a backtracking algorithm.

• Knight tour: This is solved by exploring possible knight moves recursively and backtracking when a move leads to a dead end; it is a search with branching and undoing of choices.

• N-queen: Place queens one by one and backtrack whenever a placement causes a conflict; that trial-and-error with undoing is backtracking.

• M-coloring: Assign colors to vertices and backtrack on conflicts to try alternative colorings; this is also a classic backtracking approach.

• Towers of Hanoi: Solved using a fixed recursive procedure that follows a specific move pattern. It does not involve exploring multiple alternative choices and undoing them in the sense of backtracking, so it is categorized as a recursion problem rather than a backtracking search.

Key idea: Backtracking involves branching over alternative choices and undoing (backtracking) when a branch fails; recursion can be used without backtracking when the sequence of recursive calls is deterministic.