How to resolve the algorithm Knight's tour step by step in the C# programming language
How to resolve the algorithm Knight's tour step by step in the C# programming language
Table of Contents
Problem Statement
Problem: you have a standard 8x8 chessboard, empty but for a single knight on some square. Your task is to emit a series of legal knight moves that result in the knight visiting every square on the chessboard exactly once. Note that it is not a requirement that the tour be "closed"; that is, the knight need not end within a single move of its start position. Input and output may be textual or graphical, according to the conventions of the programming environment. If textual, squares should be indicated in algebraic notation. The output should indicate the order in which the knight visits the squares, starting with the initial position. The form of the output may be a diagram of the board with the squares numbered according to visitation sequence, or a textual list of algebraic coordinates in order, or even an actual animation of the knight moving around the chessboard. Input: starting square Output: move sequence
Let's start with the solution:
Step by Step solution about How to resolve the algorithm Knight's tour step by step in the C# programming language
The code you provided is a solution to the Knight's Tour problem in C#. The Knight's Tour problem is a classical problem in computer science, in which a knight must move around a chessboard in such a way that it visits each square exactly once.
The code you provided uses a backtracking algorithm to solve the problem. The algorithm starts by placing the knight in the top-left corner of the board. It then tries all possible moves for the knight, and if the move is valid, it adds the move to a list and moves the knight to the new square. If the move is not valid, the algorithm tries the next move for the knight.
The algorithm continues in this way until the knight has visited all squares on the board. If the algorithm reaches a point where there are no more valid moves for the knight, it backtracks to the previous square and tries the next move for the knight.
The code you provided uses a struct called ListMoves
to store the list of moves for the knight. The struct has two fields, x
and y
, which store the coordinates of the square that the knight is currently on.
The code also uses a two-dimensional array called board
to store the state of the board. The array has eight rows and eight columns, and each element of the array stores the number of times that the knight has visited the corresponding square.
The code you provided uses a function called Move_Possible
to determine if a move is valid. The function takes three arguments: the board, the current coordinates of the knight, and the proposed move. The function returns true
if the move is valid and false
otherwise.
A move is valid if the knight has not visited the square before and the square is within the bounds of the board.
The code you provided uses a function called Main
to run the algorithm. The function first creates a new board and initializes it to all zeros. It then places the knight in the top-left corner of the board and adds the move to a list.
The function then enters a loop that continues until the knight has visited all squares on the board. In each iteration of the loop, the function tries all possible moves for the knight. If the move is valid, the function adds the move to the list and moves the knight to the new square. If the move is not valid, the function tries the next move for the knight.
If the function reaches a point where there are no more valid moves for the knight, it backtracks to the previous square and tries the next move for the knight.
When the knight has visited all squares on the board, the function prints out the list of moves.
The code you provided is a correct solution to the Knight's Tour problem. It uses a backtracking algorithm to find a solution, and it prints out the list of moves that the knight takes.
Source code in the csharp programming language
using System;
using System.Collections.Generic;
namespace prog
{
class MainClass
{
const int N = 8;
readonly static int[,] moves = { {+1,-2},{+2,-1},{+2,+1},{+1,+2},
{-1,+2},{-2,+1},{-2,-1},{-1,-2} };
struct ListMoves
{
public int x, y;
public ListMoves( int _x, int _y ) { x = _x; y = _y; }
}
public static void Main (string[] args)
{
int[,] board = new int[N,N];
board.Initialize();
int x = 0, // starting position
y = 0;
List<ListMoves> list = new List<ListMoves>(N*N);
list.Add( new ListMoves(x,y) );
do
{
if ( Move_Possible( board, x, y ) )
{
int move = board[x,y];
board[x,y]++;
x += moves[move,0];
y += moves[move,1];
list.Add( new ListMoves(x,y) );
}
else
{
if ( board[x,y] >= 8 )
{
board[x,y] = 0;
list.RemoveAt(list.Count-1);
if ( list.Count == 0 )
{
Console.WriteLine( "No solution found." );
return;
}
x = list[list.Count-1].x;
y = list[list.Count-1].y;
}
board[x,y]++;
}
}
while( list.Count < N*N );
int last_x = list[0].x,
last_y = list[0].y;
string letters = "ABCDEFGH";
for( int i=1; i<list.Count; i++ )
{
Console.WriteLine( string.Format("{0,2}: ", i) + letters[last_x] + (last_y+1) + " - " + letters[list[i].x] + (list[i].y+1) );
last_x = list[i].x;
last_y = list[i].y;
}
}
static bool Move_Possible( int[,] board, int cur_x, int cur_y )
{
if ( board[cur_x,cur_y] >= 8 )
return false;
int new_x = cur_x + moves[board[cur_x,cur_y],0],
new_y = cur_y + moves[board[cur_x,cur_y],1];
if ( new_x >= 0 && new_x < N && new_y >= 0 && new_y < N && board[new_x,new_y] == 0 )
return true;
return false;
}
}
}
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