The theory and practice of building of the Hanoi towers
Sergey ZhigalikОписание
The book contains the description of the solution path of generalized variant of the problem, which is known as The Tower of Hanoi puzzle. The general formula for problems of a certain type is derived on the base of such concepts as the optimal process and the “complete decomposition tree”. The book offers the types of problems for which the solutions and the optimality of these solutions are “obvious”.
The formulas for defining the number of steps to solve these problems are given. The conclusions, based on the considered problems of simple types, are defined the solution path to generalized problem with any number of discs and pegs.
It is given a method of all optimal decompositions obtaining, any of which can be used for the best solution of the particular problem. That makes it possible to get different solutions of the problem and the ability to determine all possible optimal solutions.
It is considered the Formula of Frame-Stewart. It is shown, why it is possible to find the optimal solution using this formula. Here is given a method how to find all possible coefficients to solve the particular problem using the given formula.
It is described a universal algorithm for the solution of the generalized the “Tower of Hanoi” problem.
