The Classical Tower of Hanoi Problem and Its Generalizations Vol. 1 (Paperback)

This book deals with the theoretical and the computational aspects of the classical Tower of Hanoi Problem (THP) and its multi-peg generalization. Chapter 1 reviews the classical THP in its general form with n( 1) discs and 3 pegs, with the algorithms, both recursive and iterative. Chapter 2 considers the multi-peg generalization with n discs and p pegs, and gives some local-value relationships satisfied by M(n, p), kmin(n, p) and kmax(n, p), where M(n, p) is the presumed minimum number of moves, and kmin(n, p) and kmax(n, p) are the optimal partition numbers, and presents a recursive algorithm Chapter 3 gives the closed-form expressions for M(n,4), kmin(n,4) and kmax(n,4), and gives an iterative algorithm based on the divide-and-conquer approach. It is shown that, for n 6, the presumed minimum solution is the optimal solution. Chapter 4 extends the results of Chapter 3 to find the explicit forms of M(n, p), kmin(n, p) and kmax(n, p), and establishes the equivalence of four formulations of the multi-peg THP. The divide-and-conquer approach has also been extended.