Completeness in search - artificial intelligence:

It's also importance trying to calculate the number of solutions to a problem, and the density of those solutions amongst the non solutions. In a search problem, there can be any number of solutions, and the problem specification can involve, finding some, finding just one or finding all the solutions. For example, imagine a military application searches for routes that an opponent might take. The question: "Can the opponent get from A to B" requires searching only one solution, whereas the question: "How many ways can the opponent get from A to B" will require the agent to find all the solutions.

When an agent is asked to search just one solution, we can frequently program it to prune its search space quite heavily, for example, govern out particular operators at particular times to be more efficient. However, this can also prune some of the solutions, so if our agent is asked to search all of them, the pruning has to be controlled so that we know that  pruned  areas  of  the  search  space  e  contain  no  solutions or  contain solutions which are repeated in another (non-pruned) part of the space.

If our search method is guaranteed to search all the solutions eventually, then we say that it is complete. Repeatedly, it is clear that all the solutions are in the search space, but in other cases, we have to prove this fact mathematically to be confident that our space is complete. A  complete  search problem is that - where the solution is

Surely it can take much time to find the solution, sometimes so long that the strategy is effectively useless. Some of the people use the word exhaustive when they describe complete searches, because the strategy exhausts  whole possibilities in the search space.