Backtracking

Abstract

Backtracking or nondeterministic programming is an ingenious technique useful for solving a very common and important type of search problem. Such problems can be regarded as logical or combinatorial “mazes” which a program must explore in order to find a desired solution point. In favorable cases, one will be able to do this by devising an algorithm which proceeds in relatively direct fashion from an initial position to a solution, along a path involving little or no trial and error. However, some problems are too complex for such algorithms to be available, and it is for these problems that the method of backtracking is most useful. Characteristically, programs for solving these problems encounter situations in which a decision must be made as to which of several alternatives is to be explored next, but in which no clear grounds can be found for making one rather than another decision. A correct decision will lead on to a solution of the problem being explored, but an incorrect decision will wind up in a dead end, and the program will have to revert to the point at which it took its first wrong turning and try an alternative originally ignored. Finding paths through mazes and solving geometric and spatial puzzles like “instant insanity” are obvious examples of this kind of problem.