How to resolve the algorithm Solve a Holy Knight's tour step by step in the Python programming language

Published on 12 May 2024 09:40 PM
#Python

How to resolve the algorithm Solve a Holy Knight's tour step by step in the Python programming language

Table of Contents

Problem Statement

Chess coaches have been known to inflict a kind of torture on beginners by taking a chess board, placing pennies on some squares and requiring that a Knight's tour be constructed that avoids the squares with pennies. This kind of knight's tour puzzle is similar to   Hidato. The present task is to produce a solution to such problems. At least demonstrate your program by solving the following:

Note that the zeros represent the available squares, not the pennies. Extra credit is available for other interesting examples.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Solve a Holy Knight's tour step by step in the Python programming language

The provided Python code is designed to solve knight's tour puzzles, a common combinatorial problem where the objective is to find a path for a knight on a chessboard that visits every square exactly once.

At the core of the code is a recursive function solve which iterates through a set of possible moves for a knight, attempts to place the knight on each valid square, and recursively calls itself to solve the remaining puzzle. The solve function returns 1 if a solution is found, and 0 otherwise.

The main logic is in the find_solution function. It takes a puzzle string and its size as inputs. The puzzle string represents the initial board state, with '.' indicating empty squares, 'x' indicating obstacles, and 's' indicating the starting position of the knight. The function converts the puzzle string into a 2D array, placing appropriate values for empty squares, obstacles, and the knight's starting position.

The find_solution function then calls the solve function to attempt to find a solution to the puzzle. If a solution is found, it prints the solution board. Otherwise, it prints an error message indicating that no solution could be found.

The code also includes two example puzzles that are solved and printed as part of its execution.

Overall, the provided code effectively demonstrates a technique for solving knight's tour puzzles using a recursive approach and a set of predefined knight moves.

Source code in the python programming language

from sys import stdout
moves = [
    [-1, -2], [1, -2], [-1, 2], [1, 2],
    [-2, -1], [-2, 1], [2, -1], [2, 1]
]


def solve(pz, sz, sx, sy, idx, cnt):
    if idx > cnt:
        return 1

    for i in range(len(moves)):
        x = sx + moves[i][0]
        y = sy + moves[i][1]
        if sz > x > -1 and sz > y > -1 and pz[x][y] == 0:
            pz[x][y] = idx
            if 1 == solve(pz, sz, x, y, idx + 1, cnt):
                return 1
            pz[x][y] = 0

    return 0


def find_solution(pz, sz):
    p = [[-1 for j in range(sz)] for i in range(sz)]
    idx = x = y = cnt = 0
    for j in range(sz):
        for i in range(sz):
            if pz[idx] == "x":
                p[i][j] = 0
                cnt += 1
            elif pz[idx] == "s":
                p[i][j] = 1
                cnt += 1
                x = i
                y = j
            idx += 1

    if 1 == solve(p, sz, x, y, 2, cnt):
        for j in range(sz):
            for i in range(sz):
                if p[i][j] != -1:
                    stdout.write(" {:0{}d}".format(p[i][j], 2))
                else:
                    stdout.write("   ")
            print()
    else:
        print("Cannot solve this puzzle!")


# entry point
find_solution(".xxx.....x.xx....xxxxxxxxxx..x.xx.x..xxxsxxxxxx...xx.x.....xxx..", 8)
print()
find_solution(".....s.x..........x.x.........xxxxx.........xxx.......x..x.x..x..xxxxx...xxxxx..xx.....xx..xxxxx...xxxxx..x..x.x..x.......xxx.........xxxxx.........x.x..........x.x.....", 13)

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