Is an optimal algorithm a complete algorithm?

Question

I do understand that a complete algorithm is one where if there is a solution, the algorithm can find it and that optimal algorithm is one where it manages to find the least cost solution.

But is an optimal algorithm, a complete algorithm? Can please briefly explain?

Thanks.

Answer 1

Here are some properties of search algorithms and the solutions they find:

1. Termination: The computation is insured to terminate, no matter how large the search space is.

2. Completeness: An algorithm is considered to be complete if it ends with a solution when one exists. Yes, by definition. Finding the optimal solution entails proving optimality. This can be done by finding all solutions or by proving that no solution can have a better cost than the one found already. In both cases, at least one solution has to be found.

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