(Knight’s Tour) This chapter described the backtracking algorithm and how to use recursion...

(Knight’s Tour) This chapter described the backtracking algorithm and how to use recursion to implement it. Another well-known chessboard problem that can be solved using the backtracking algorithm is a knight’s tour. Given an initial board position, determine a sequence of moves by a knight that visits every square of the chessboard exactly once. For example, for a 5 × 5 and 6 × 6 square board, the sequence of moves are shown in Figure:

FIGURE 6-18

Knight’s tour

A knight moves by jumping two positions either vertically or horizontally and one position in the perpendicular direction. Write a recursive backtracking program that takes as input an initial board position and determines a sequence of moves by a knight that visits each square of the board exactly once.