The Backtracking Method

One of the best known general techniques for developing of the algorithms is the Backtracking method. It seeks to eliminate the generation of all possibilities in order to get the result. The Backtracking method can be applied to those problems for which the solution can be represented as a vector whose elements take values in some finite sets and who meet certain internal conditions. In the Backtracking method, the vector elements are expressed one at a time, assigning a value to a component will be done only after values have been assigned to all its previous components, and no incompatibilities exist between these values. Classical problems solved by this method are: queens’ problem, Cartesian product generation, the generation of combinations, the 0-1 knapsack problem. The book is structured into 7 chapters and provides the solutions to a number of 19 classical problems by using versions of the backtracking algorithm. Most of the paragraphs are followed by a section with solved exercises and problems.