The heuristic path algorithm is a best-first search in which f(n) = (2-w) g(n) + w h(n).Select the correct statement(s) - For w = 1, f(n) represents the A* algorithm. For w = 2, f(n) is complete. For w > 2, f(n) is optimal. For w = 0, f(n) represents UCS.

The statement "For w = 1, f(n) represents the A* algorithm" is correct. The A* algorithm is a special case of the heuristic path algorithm where w = 1, meaning that the cost function f(n) is equally influenced by the actual cost from the start node to the current node, g(n), and the estimated cost from the current node to the goal, h(n).

The statement "For w = 2, f(n) is complete" is not necessarily correct. The completeness of a search algorithm is determined by whether it is guaranteed to find a solution if one exists, not by the specific weighting of the cost function.

The statement "For w > 2, f(n) is optimal" is also not necessarily correct. The optimality of a search algorithm is determined by whether it is guaranteed to find the best solution, not by the specific weighting of the cost function. In fact, increasing w beyond 1 in the A* algorithm can lead to less optimal solutions because it places more emphasis on the heuristic, which is an estimate and may not accurately reflect the true cost.

The statement "For w = 0, f(n) represents UCS" is correct. UCS, or Uniform Cost Search, is a special case of the heuristic path algorithm where w = 0, meaning that the cost function f(n) is entirely determined by the actual cost from the start node to the current node, g(n), and does not take into account any heuristic information.