Task: Knight's tour


C++: #include <iostream>
#include <iomanip>
#include <array>
#include <string>
#include <tuple>
#include <algorithm>
using namespace std;

template<int N = 8>
class Board 
{
public:
    array<pair<int, int>, 8> moves;
    array<array<int, N>, N> data;

    Board() 
    {
        moves[0] = make_pair(2, 1);
        moves[1] = make_pair(1, 2);
        moves[2] = make_pair(-1, 2);
        moves[3] = make_pair(-2, 1);
        moves[4] = make_pair(-2, -1);
        moves[5] = make_pair(-1, -2);
        moves[6] = make_pair(1, -2);
        moves[7] = make_pair(2, -1);
    }

    array<int, 8> sortMoves(int x, int y) const 
    {
        array<tuple<int, int>, 8> counts;
        for(int i = 0; i < 8; ++i) 
        {
            int dx = get<0>(moves[i]);
            int dy = get<1>(moves[i]);

            int c = 0;
            for(int j = 0; j < 8; ++j) 
            {
                int x2 = x + dx + get<0>(moves[j]);
                int y2 = y + dy + get<1>(moves[j]);

                if (x2 < 0 || x2 >= N || y2 < 0 || y2 >= N)
                    continue;
                if(data[y2][x2] != 0)
                    continue;

                c++;
            }

            counts[i] = make_tuple(c, i);
        }

        
        random_shuffle(counts.begin(), counts.end());

        
        sort(counts.begin(), counts.end());

        array<int, 8> out;
        for(int i = 0; i < 8; ++i)
            out[i] = get<1>(counts[i]);
        return out;
    }

    void solve(string start) 
    {
        for(int v = 0; v < N; ++v)
            for(int u = 0; u < N; ++u)
                data[v][u] = 0;

        int x0 = start[0] - 'a';
        int y0 = N - (start[1] - '0');
        data[y0][x0] = 1;

        array<tuple<int, int, int, array<int, 8>>, N*N> order;
        order[0] = make_tuple(x0, y0, 0, sortMoves(x0, y0));

        int n = 0;
        while(n < N*N-1) 
        {
            int x = get<0>(order[n]);
            int y = get<1>(order[n]);

            bool ok = false;
            for(int i = get<2>(order[n]); i < 8; ++i) 
            {
                int dx = moves[get<3>(order[n])[i]].first;
                int dy = moves[get<3>(order[n])[i]].second;

                if(x+dx < 0 || x+dx >= N || y+dy < 0 || y+dy >= N)
                    continue;
                if(data[y + dy][x + dx] != 0) 
                    continue;

                get<2>(order[n]) = i + 1;
                ++n;
                data[y+dy][x+dx] = n + 1;
                order[n] = make_tuple(x+dx, y+dy, 0, sortMoves(x+dx, y+dy));
                ok = true;
                break;
            }

            if(!ok) 
            {
                data[y][x] = 0;
                --n;
            }
        }
    }

    template<int N>
    friend ostream& operator<<(ostream &out, const Board<N> &b);
};

template<int N>
ostream& operator<<(ostream &out, const Board<N> &b) 
{
    for (int v = 0; v < N; ++v) 
    {
        for (int u = 0; u < N; ++u) 
        {
            if (u != 0) out << ",";
            out << setw(3) << b.data[v][u];
        }
        out << endl;
    }
    return out;
}

int main() 
{
    Board<5> b1;
    b1.solve("c3");
    cout << b1 << endl;

    Board<8> b2;
    b2.solve("b5");
    cout << b2 << endl;

    Board<31> b3; 
    b3.solve("a1");
    cout << b3 << endl;
    return 0;
}






Python: import copy

boardsize=6
_kmoves = ((2,1), (1,2), (-1,2), (-2,1), (-2,-1), (-1,-2), (1,-2), (2,-1)) 


def chess2index(chess, boardsize=boardsize):
    'Convert Algebraic chess notation to internal index format'
    chess = chess.strip().lower()
    x = ord(chess[0]) - ord('a')
    y = boardsize - int(chess[1:])
    return (x, y)
    
def boardstring(board, boardsize=boardsize):
    r = range(boardsize)
    lines = ''
    for y in r:
        lines += '\n' + ','.join('%2i' % board[(x,y)] if board[(x,y)] else '  '
                                 for x in r)
    return lines
    
def knightmoves(board, P, boardsize=boardsize):
    Px, Py = P
    kmoves = set((Px+x, Py+y) for x,y in _kmoves)
    kmoves = set( (x,y)
                  for x,y in kmoves
                  if 0 <= x < boardsize
                     and 0 <= y < boardsize
                     and not board[(x,y)] )
    return kmoves

def accessibility(board, P, boardsize=boardsize):
    access = []
    brd = copy.deepcopy(board)
    for pos in knightmoves(board, P, boardsize=boardsize):
        brd[pos] = -1
        access.append( (len(knightmoves(brd, pos, boardsize=boardsize)), pos) )
        brd[pos] = 0
    return access
    
def knights_tour(start, boardsize=boardsize, _debug=False):
    board = {(x,y):0 for x in range(boardsize) for y in range(boardsize)}
    move = 1
    P = chess2index(start, boardsize)
    board[P] = move
    move += 1
    if _debug:
        print(boardstring(board, boardsize=boardsize))
    while move <= len(board):
        P = min(accessibility(board, P, boardsize))[1]
        board[P] = move
        move += 1
        if _debug:
            print(boardstring(board, boardsize=boardsize))
            input('\n%2i next: ' % move)
    return board

if __name__ == '__main__':
    while 1:
        boardsize = int(input('\nboardsize: '))
        if boardsize < 5:
            continue
        start = input('Start position: ')
        board = knights_tour(start, boardsize)
        print(boardstring(board, boardsize=boardsize))