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# The knight's tour problem in c++

Posted on 2002-11-25

hi

i need some help in the knight's tour problem..if anyone did this problem befor in c++ and have a possible solution for me i will be more than thankful

Problem Description

One of the more interesting puzzlers for chess buffs is the Knight's Tour problem, originally proposed by the mathematician Euler. The question is this: Can the chess piece called the knight move around an empty chessboard and touch each of the 64 squares once and only once?

The knight makes L-shaped moves (over two in one direction and then over one in a perpendicular direction. Thus, from a square in the middle of an empty chessboard, the knight can make eight different moves (numbered 0 through 7) as shown in the following figure:

0 1 2 3 4 5 6 7

0

1 2 1

2 3 0

3 k

4 4 7

5 5 6

6

7

Trial Solution

Develop a program that will move the knight around a chessboard. The board is represented by an 8-by-8 double-subscripted array board. Each of the squares is initialized to zero. We describe each of the eight possible moves in terms of both their horizontal and vertical components. For example, a move of type 0 as shown above consists of moving two squares horizontally to the right and one square vertically upward. Move 2 consists of moving one square horizontally to the left and two squares vertically upward. Horizontal moves to the left and vertical moves upward are indicated with negative numbers. The eight moves may be described by two single-subscripted arrays, horizontal and vertical, as follows:

horizontal[0] = 2

horizontal[1] = 1

horizontal[2] = -1

horizontal[3] = -2

horizontal[4] = -2

horizontal[5] = -1

horizontal[6] = 1

horizontal[7] = 2vertical[0] = -1

vertical[1] = -2

vertical[2] = -2

vertical[3] = -1

vertical[4] = 1

vertical[5] = 2

vertical[6] = 2

vertical[7] = 1Let the variables currentRow and currentColumn indicate the row and column of the knight's current position. To make a move of type moveNumber, where moveNumber is between 0 and 7, your program uses the statements

currentRow += vertical[moveNumber];

currentColumn += horizontal[moveNumber];Keep a counter that varies from 1 to 64. Record the latest count in each square the knight moves to. Remember to test each potential move to see if the knight has already visited that square. And, of course, test every potential move to make sure that the knight does not land off the chessboard. now write a program to move the knight around the chessboard. Run the program. How many moves did the knight make?