Python: How do I move around a numpy array chessboard, as a knight?

Question

I have the following code for a numpy array:

import numpy as np

a = np.array([[0,1,2,3,4,5,6,7],
[8,9,10,11,12,13,14,15],
[16,17,18,19,20,21,22,23],
[24,25,26,27,28,29,30,31],
[32,33,34,35,36,37,38,39],
[40,41,42,43,44,45,46,47],
[48,49,50,51,52,53,54,55],
[56,57,58,59,60,61,62,63]])

Given a starting point, I need to move around this board as a knight would on a chess board (2 spaces vertically, 1 horizontally, or vice versa).

I can use np.argwhere to get coordinates of the starting point:

np.argwhere(a==13) returns [[1 5]].

What can I do to move around from there? I'd like to test all possible moves, and return all coordinates.

Answer 1

There would be eight such possible combinations. We could those as offsets in a 8 x 2 array and do broadcasted addition with the starting XY. Additionally, we need to fitter out the ones going beyond the chessboard limits.

Thus, an implementation given the start X,Y as a tuple would be -

def knight_move(start_xy):
    offset1 = np.array([[-2,-1],[-2,1],[2,-1],[2,1]])    
    idx = np.row_stack((offset1, offset1[:,::-1])) + start_xy    
    return idx[~((idx < 0) | (idx > 7)).any(1)]

Sample run -

In [66]: a   # Chessboard as array
Out[66]: 
array([[ 0,  1,  2,  3,  4,  5,  6,  7],
       [ 8,  9, 10, 11, 12, 13, 14, 15],
       [16, 17, 18, 19, 20, 21, 22, 23],
       [24, 25, 26, 27, 28, 29, 30, 31],
       [32, 33, 34, 35, 36, 37, 38, 39],
       [40, 41, 42, 43, 44, 45, 46, 47],
       [48, 49, 50, 51, 52, 53, 54, 55],
       [56, 57, 58, 59, 60, 61, 62, 63]])

In [67]: newXYs = knight_move((1,5)) # 13

In [68]: newXYs
Out[68]: 
array([[3, 4],
       [3, 6],
       [0, 3],
       [2, 3],
       [0, 7],
       [2, 7]])

In [69]: a[newXYs[:,0], newXYs[:,1]]
Out[69]: array([28, 30,  3, 19,  7, 23])

Answer 2

The position of the knight can be represented by [xy] with 0 <= x,y < 8 . The possible 8 directions of movement can be represented by the vectors [+/-1 +/-2], [+/-2 +/-1] . But a move is only valid if the resulting field is valid (see the above limits on x,y ). This method works without using an array.

A more efficient way, using a 1-dimensional array, is the following: a border of width 2 is added around the 8x8 chessboard. This enlarged 12x12 board is encoded in a 1-dimensional array where the cell value signals the corresponding field`s validity:

board = [-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
         -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
         -1,-1, 0, 0, 0, 0, 0, 0, 0, 0,-1,-1,
         -1,-1, 0, 0, 0, 0, 0, 0, 0, 0,-1,-1,
         -1,-1, 0, 0, 0, 0, 0, 0, 0, 0,-1,-1,
         -1,-1, 0, 0, 0, 0, 0, 0, 0, 0,-1,-1,
         -1,-1, 0, 0, 0, 0, 0, 0, 0, 0,-1,-1,
         -1,-1, 0, 0, 0, 0, 0, 0, 0, 0,-1,-1,
         -1,-1, 0, 0, 0, 0, 0, 0, 0, 0,-1,-1,
         -1,-1, 0, 0, 0, 0, 0, 0, 0, 0,-1,-1,
         -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
         -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1]

The position of the knight is represented by one index (eg 26 for the upper left corner) and the possible movements of the knights by the index offsets +/-1 + 12*(+/-2) and +/-2 + 12*(+/-1) , so alltogether 25, -23, 23, -25, 14, -10, 10, -14 . The validity of a move is again checked by the validity of the resulting index which reduces to board[index+move] == 0 .