How to resolve the algorithm Knight's tour step by step in the Julia programming language
How to resolve the algorithm Knight's tour step by step in the Julia 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 Julia programming language
This code solves the Hidato puzzle defined in the variable chessboard
.
A Hidato puzzle is a puzzle where you have to fill a grid with numbers from 1 to the size of the grid, such that each number is adjacent to the previous and next number in the sequence.
The code first defines the knightmoves
array, which contains all the possible moves a knight can make in a chess game.
Then it calls the hidatoconfigure
function, which takes the chessboard
string as input and returns a tuple containing the board
array, the maxmoves
integer variable, the fixed
array, and the starts
tuple containing the starting row and column.
The board
array is a 2D array of integers representing the puzzle grid, where 0 represents an empty cell.
The maxmoves
integer variable is the maximum number of moves allowed to solve the puzzle.
The fixed
array is a 2D array of booleans indicating which cells are fixed and cannot be changed.
The starts
tuple contains the starting row and column of the puzzle.
The code then calls the printboard
function to print the initial state of the board, and then calls the hidatosolve
function to solve the puzzle.
The hidatosolve
function takes the board
, maxmoves
, knightmoves
, fixed
, sr
, sc
, and m
arguments, where sr
and sc
are the starting row and column, and m
is the current move number.
The hidatosolve
function uses a recursive backtracking algorithm to solve the puzzle.
It first checks if the current move number is greater than the maximum number of moves allowed, and if so, it returns false.
It then checks if the current cell is fixed, and if so, it checks if the current move number is equal to the value in the fixed cell.
If the current move number is not equal to the value in the fixed cell, the function returns false.
If the current cell is not fixed, the function loops through all the possible moves from the current cell, and for each move, it checks if the move is valid (i.e. the cell is empty and not fixed), and if so, it recursively calls the hidatosolve
function to solve the puzzle starting from the new cell.
If any of the recursive calls return true, the function returns true, indicating that the puzzle has been solved.
If none of the recursive calls return true, the function returns false, indicating that the puzzle could not be solved.
The code then calls the printboard
function to print the solved puzzle.
Source code in the julia programming language
using .Hidato # Note that the . here means to look locally for the module rather than in the libraries
const chessboard = """
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 """
const knightmoves = [[-2, -1], [-2, 1], [-1, -2], [-1, 2], [1, -2], [1, 2], [2, -1], [2, 1]]
board, maxmoves, fixed, starts = hidatoconfigure(chessboard)
printboard(board, " 0", " ")
hidatosolve(board, maxmoves, knightmoves, fixed, starts[1][1], starts[1][2], 1)
printboard(board)
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