Task: Solve a Holy Knight's tour


C++: #include <vector>
#include <sstream>
#include <iostream>
#include <iterator>
#include <stdlib.h>
#include <string.h>

using namespace std;

struct node
{
    int val;
    unsigned char neighbors;
};

class nSolver
{
public:
    nSolver()
    {
	dx[0] = -1; dy[0] = -2; dx[1] = -1; dy[1] =  2;
	dx[2] =  1; dy[2] = -2; dx[3] =  1; dy[3] =  2;
	dx[4] = -2; dy[4] = -1; dx[5] = -2; dy[5] =  1; 
	dx[6] =  2; dy[6] = -1; dx[7] =  2; dy[7] =  1;
    }

    void solve( vector<string>& puzz, int max_wid )
    {
	if( puzz.size() < 1 ) return;
	wid = max_wid; hei = static_cast<int>( puzz.size() ) / wid;
	int len = wid * hei, c = 0; max = len;
	arr = new node[len]; memset( arr, 0, len * sizeof( node ) );

	for( vector<string>::iterator i = puzz.begin(); i != puzz.end(); i++ )
	{
	    if( ( *i ) == "*" ) { max--; arr[c++].val = -1; continue; }
	    arr[c].val = atoi( ( *i ).c_str() );
	    c++;
	}

	solveIt(); c = 0;
	for( vector<string>::iterator i = puzz.begin(); i != puzz.end(); i++ )
	{
	    if( ( *i ) == "." )
	    {
		ostringstream o; o << arr[c].val;
		( *i ) = o.str();
	    }
	    c++;
	}
	delete [] arr;
    }

private:
    bool search( int x, int y, int w )
    {
	if( w > max ) return true;

	node* n = &arr[x + y * wid];
	n->neighbors = getNeighbors( x, y );

	for( int d = 0; d < 8; d++ )
	{
	    if( n->neighbors & ( 1 << d ) )
	    {
		int a = x + dx[d], b = y + dy[d];
		if( arr[a + b * wid].val == 0 )
		{
		    arr[a + b * wid].val = w;
		    if( search( a, b, w + 1 ) ) return true;
		    arr[a + b * wid].val = 0;
		}
	    }
	}
	return false;
    }

    unsigned char getNeighbors( int x, int y )
    {
	unsigned char c = 0; int a, b;
	for( int xx = 0; xx < 8; xx++ )
	{
	    a = x + dx[xx], b = y + dy[xx];
	    if( a < 0 || b < 0 || a >= wid || b >= hei ) continue;
	    if( arr[a + b * wid].val > -1 ) c |= ( 1 << xx );
	}
	return c;
    }

    void solveIt()
    {
	int x, y, z; findStart( x, y, z );
	if( z == 99999 ) { cout << "\nCan't find start point!\n"; return; }
	search( x, y, z + 1 );
    }

    void findStart( int& x, int& y, int& z )
    {
	z = 99999;
	for( int b = 0; b < hei; b++ )
	    for( int a = 0; a < wid; a++ )
		if( arr[a + wid * b].val > 0 && arr[a + wid * b].val < z ) 
		{ 
		    x = a; y = b;
		    z = arr[a + wid * b].val;
		}

    }

    int wid, hei, max, dx[8], dy[8];
    node* arr;
};

int main( int argc, char* argv[] )
{
    int wid; string p;
    
    p = "* * * * * 1 * . * * * * * * * * * * . * . * * * * * * * * * . . . . . * * * * * * * * * . . . * * * * * * * . * * . * . * * . * * . . . . . * * * . . . . . * * . . * * * * * . . * * . . . . . * * * . . . . . * * . * * . * . * * . * * * * * * * . . . * * * * * * * * * . . . . . * * * * * * * * * . * . * * * * * * * * * * . * . * * * * * "; wid = 13;
    istringstream iss( p ); vector<string> puzz;
    copy( istream_iterator<string>( iss ), istream_iterator<string>(), back_inserter<vector<string> >( puzz ) );
    nSolver s; s.solve( puzz, wid );
    int c = 0;
    for( vector<string>::iterator i = puzz.begin(); i != puzz.end(); i++ )
    {
	if( ( *i ) != "*" && ( *i ) != "." )
	{
	    if( atoi( ( *i ).c_str() ) < 10 ) cout << "0";
	    cout << ( *i ) << " ";
        }
	else cout << "   ";
	if( ++c >= wid ) { cout << endl; c = 0; }
    }
    cout << endl << endl;
    return system( "pause" );
}


C#: using System.Collections;
using System.Collections.Generic;
using static System.Console;
using static System.Math;
using static System.Linq.Enumerable;

public class Solver
{
    private static readonly (int dx, int dy)[]
        
        knightMoves = {(1,-2),(2,-1),(2,1),(1,2),(-1,2),(-2,1),(-2,-1),(-1,-2)};

    private (int dx, int dy)[] moves;
        
    public static void Main()
    {
        var knightSolver = new Solver(knightMoves);
        Print(knightSolver.Solve(true,
            ".000....",
            ".0.00...",
            ".0000000",
            "000..0.0",
            "0.0..000",
            "1000000.",
            "..00.0..",
            "...000.."));

        Print(knightSolver.Solve(true,
            ".....0.0.....",
            ".....0.0.....",
            "....00000....",
            ".....000.....",
            "..0..0.0..0..",
            "00000...00000",
            "..00.....00..",
            "00000...00000",
            "..0..0.0..0..",
            ".....000.....",
            "....00000....",
            ".....0.0.....",
            ".....0.0....." 
        ));
    }

    public Solver(params (int dx, int dy)[] moves) => this.moves = moves;

    public int[,] Solve(bool circular, params string[] puzzle)
    {
        var (board, given, count) = Parse(puzzle);
        return Solve(board, given, count, circular);
    }

    public int[,] Solve(bool circular, int[,] puzzle)
    {
        var (board, given, count) = Parse(puzzle);
        return Solve(board, given, count, circular);
    }

    private int[,] Solve(int[,] board, BitArray given, int count, bool circular)
    {
        var (height, width) = (board.GetLength(0), board.GetLength(1));
        bool solved = false;
        for (int x = 0; x < height && !solved; x++) {
            solved = Range(0, width).Any(y => Solve(board, given, circular, (height, width), (x, y), count, (x, y), 1));
            if (solved) return board;
        }
        return null;
    }

    private bool Solve(int[,] board, BitArray given, bool circular,
        (int h, int w) size, (int x, int y) start, int last, (int x, int y) current, int n)
    {
        var (x, y) = current;
        if (x < 0 || x >= size.h || y < 0 || y >= size.w) return false;
        if (board[x, y] < 0) return false;
        if (given[n - 1]) {
            if (board[x, y] != n) return false;
        } else if (board[x, y] > 0) return false;
        board[x, y] = n;
        if (n == last) {
            if (!circular || AreNeighbors(start, current)) return true;
        }
        for (int i = 0; i < moves.Length; i++) {
            var move = moves[i];
            if (Solve(board, given, circular, size, start, last, (x + move.dx, y + move.dy), n + 1)) return true;
        }
        if (!given[n - 1]) board[x, y] = 0;
        return false;

        bool AreNeighbors((int x, int y) p1, (int x, int y) p2) => moves.Any(m => (p2.x + m.dx, p2.y + m.dy).Equals(p1));
    }

    private static (int[,] board, BitArray given, int count) Parse(string[] input)
    {
        (int height, int width) = (input.Length, input[0].Length);
        int[,] board = new int[height, width];
        int count = 0;
        for (int x = 0; x < height; x++) {
            string line = input[x];
            for (int y = 0; y < width; y++) {
                board[x, y] = y < line.Length && char.IsDigit(line[y]) ? line[y] - '0' : -1;
                if (board[x, y] >= 0) count++;
            }
        }
        BitArray given = Scan(board, count, height, width);
        return (board, given, count);
    }

    private static (int[,] board, BitArray given, int count) Parse(int[,] input)
    {
        (int height, int width) = (input.GetLength(0), input.GetLength(1));
        int[,] board = new int[height, width];
        int count = 0;
        for (int x = 0; x < height; x++)
            for (int y = 0; y < width; y++)
                if ((board[x, y] = input[x, y]) >= 0) count++;
        BitArray given = Scan(board, count, height, width);
        return (board, given, count);
    }

    private static BitArray Scan(int[,] board, int count, int height, int width)
    {
        var given = new BitArray(count + 1);
        for (int x = 0; x < height; x++)
            for (int y = 0; y < width; y++)
                if (board[x, y] > 0) given[board[x, y] - 1] = true;
        return given;
    }

    private static void Print(int[,] board)
    {
        if (board == null) {
            WriteLine("No solution");
        } else {
            int w = board.Cast<int>().Where(i => i > 0).Max(i => (int?)Ceiling(Log10(i+1))) ?? 1;
            string e = new string('-', w);
            foreach (int x in Range(0, board.GetLength(0)))
                WriteLine(string.Join(" ", Range(0, board.GetLength(1))
                    .Select(y => board[x, y] < 0 ? e : board[x, y].ToString().PadLeft(w, ' '))));
        }
        WriteLine();
    }

}