<algorithm> A scheme for solving a series of sub-problems each of which may have multiple possible solutions and where the solution chosen for one sub-problem may affect the possible solutions of later sub-problems.
To solve the overall problem, we find a solution to the first sub-problem and then attempt to recursively solve the other sub-problems based on this first solution.
If we cannot, or we want all possible solutions, we backtrack and try the next possible solution to the first sub-problem and so on. Backtracking terminates when there are no more solutions to the first sub-problem.
This is the algorithm used by logic programming
languages such as Prolog
to find all possible ways of proving a goal
An optimisation known as "intelligent backtracking
" keeps track of the dependencies between sub-problems and only re-solves those which depend on an earlier solution which has changed.
Backtracking is one algorithm
which can be used to implement nondeterminism
It is effectively a depth-first search
of a problem space.