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degree_freedom_queen.py
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degree_freedom_queen.py
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import numpy as np
def degree_freedom_queen(p_k1, p_k2, p_q1, s):
"""
This function returns a matrix of ones and zeros where 1 specify a location in which the Queen can move to. The king
will never choose an unsafe location.
:param p_k1: position of King 1
:param p_k2: position of King 2
:param p_q1: position of Queen
:param s: board
:return: dfQ1: Degrees of Freedom of the Queen, a_q1: Allowed actions for the Queen, dfQ1_: Squares the Queen is threatening
"""
size_board = s.shape[0]
dfQ1 = np.zeros([size_board, size_board], dtype=int)
dfQ1[p_q1[0], p_q1[1]] = 1
# King 2 reach
k2r = [[p_k2[0] - 1, p_k2[1]], # up
[p_k2[0] + 1, p_k2[1]], # down
[p_k2[0], p_k2[1] - 1], # left
[p_k2[0], p_k2[1] + 1], # right
[p_k2[0] - 1, p_k2[1] - 1], # up-left
[p_k2[0] - 1, p_k2[1] + 1], # up-right
[p_k2[0] + 1, p_k2[1] - 1], # down-left
[p_k2[0] + 1, p_k2[1] + 1]] # down-right
k2r = np.array(k2r)
# King 1 reach
k1r = [[p_k1[0] - 1, p_k1[1]], # up
[p_k1[0] + 1, p_k1[1]], # down
[p_k1[0], p_k1[1] - 1], # left
[p_k1[0], p_k1[1] + 1], # right
[p_k1[0] - 1, p_k1[1] - 1], # up-left
[p_k1[0] - 1, p_k1[1] + 1], # up-right
[p_k1[0] + 1, p_k1[1] - 1], # down-left
[p_k1[0] + 1, p_k1[1] + 1]] # down-right
k1r = np.array(k1r)
dfQ1_ = np.zeros([size_board, size_board], dtype=int) # King without King 2 reach
dfQ1_[p_q1[0], p_q1[1]] = 1
# Queen
blocked = np.zeros(8, dtype=int)
blocked2 = np.zeros(8, dtype=int)
a_q1 = np.zeros([8 * (size_board - 1), 1], dtype=int)
for j in range(size_board):
# allow_down
if p_q1[0] + j < size_board - 1:
if (p_q1[0] + j + 1 == p_k1[0] and p_q1[1] == p_k1[1]) or ((p_q1[0] + j + 1 == p_k2[0] and p_q1[1] == p_k2[1])):
blocked[0] = 1
if p_q1[0] + j + 1 == p_k1[0] and p_q1[1] == p_k1[1]:
blocked2[0] = 1
if blocked[0] == 0:
tmp = np.zeros([8], dtype=int)
for i in range(k2r.shape[0]):
if p_q1[0] + j + 1 != k2r[i, 0] or p_q1[1] != k2r[i, 1]:
tmp[i] = 1
if np.all(tmp):
dfQ1[p_q1[0] + j + 1, p_q1[1]] = 1
a_q1[j] = 1
else:
for i in range(len(tmp)):
if tmp[i] == 0:
for ii in range(k1r.shape[0]):
if p_q1[0] + j + 1 == k1r[ii, 0] and p_q1[1] == k1r[ii, 1]:
dfQ1[p_q1[0] + j + 1, p_q1[1]] = 1
a_q1[j] = 1
if blocked2[0] == 0:
dfQ1_[p_q1[0] + j + 1, p_q1[1]] = 1
# allow_up
if p_q1[0] - j > 0:
if (p_q1[0] - j - 1 == p_k1[0] and p_q1[1] == p_k1[1]) or ((p_q1[0] - j - 1 == p_k2[0] and p_q1[1] == p_k2[1])):
blocked[1] = 1
if p_q1[0] - j - 1 == p_k1[0] and p_q1[1] == p_k1[1]:
blocked2[1] = 1
if blocked[1] == 0:
tmp = np.zeros([8], dtype=int)
for i in range(k2r.shape[0]):
if p_q1[0] - j - 1 != k2r[i, 0] or p_q1[1] != k2r[i, 1]:
tmp[i] = 1
if np.all(tmp):
dfQ1[p_q1[0] - j - 1, p_q1[1]] = 1
a_q1[j + (size_board - 1)] = 1
else:
for i in range(len(tmp)):
if tmp[i] == 0:
for ii in range(k1r.shape[0]):
if p_q1[0] - j - 1 == k1r[ii, 0] and p_q1[1] == k1r[ii, 1]:
dfQ1[p_q1[0] - j - 1, p_q1[1]] = 1
a_q1[j + (size_board - 1)] = 1
if blocked2[1] == 0:
dfQ1_[p_q1[0] - j - 1, p_q1[1]] = 1
# allow_right
if p_q1[1] + j < size_board - 1:
if (p_q1[0] == p_k1[0] and p_q1[1] + j + 1 == p_k1[1]) or ((p_q1[0] == p_k2[0] and p_q1[1] + j + 1 == p_k2[1])):
blocked[2] = 1
if p_q1[0] == p_k1[0] and p_q1[1] + j + 1 == p_k1[1]:
blocked2[2] = 1
if blocked[2] == 0:
tmp = np.zeros([8], dtype=int)
for i in range(k2r.shape[0]):
if p_q1[0] != k2r[i, 0] or p_q1[1] + j + 1 != k2r[i, 1]:
tmp[i] = 1
if np.all(tmp):
dfQ1[p_q1[0], p_q1[1] + j + 1] = 1
a_q1[j + 2 * (size_board - 1)] = 1
else:
for i in range(len(tmp)):
if tmp[i] == 0:
for ii in range(k1r.shape[0]):
if p_q1[0] == k1r[ii, 0] and p_q1[1] + j + 1 == k1r[ii, 1]:
dfQ1[p_q1[0], p_q1[1] + j + 1] = 1
a_q1[j + 2 * (size_board - 1)] = 1
if blocked2[2] == 0:
dfQ1_[p_q1[0], p_q1[1] + j + 1] = 1
# allow_left
if p_q1[1] - j > 0:
if (p_q1[0] == p_k1[0] and p_q1[1] - j - 1 == p_k1[1]) or ((p_q1[0] == p_k2[0] and p_q1[1] - j - 1 == p_k2[1])):
blocked[3] = 1
if p_q1[0] == p_k1[0] and p_q1[1] - j - 1 == p_k1[1]:
blocked2[3] = 1
if blocked[3] == 0:
tmp = np.zeros([8], dtype=int)
for i in range(k2r.shape[0]):
if p_q1[0] != k2r[i, 0] or p_q1[1] - j - 1 != k2r[i, 1]:
tmp[i] = 1
if np.all(tmp):
dfQ1[p_q1[0], p_q1[1] - j - 1] = 1
a_q1[j + 3 * (size_board - 1)] = 1
else:
for i in range(len(tmp)):
if tmp[i] == 0:
for ii in range(k1r.shape[0]):
if p_q1[0] == k1r[ii, 0] and p_q1[1] - j - 1 == k1r[ii, 1]:
dfQ1[p_q1[0], p_q1[1] - j - 1] = 1
a_q1[j + 3 * (size_board - 1)] = 1
if blocked2[3] == 0:
dfQ1_[p_q1[0], p_q1[1] - j - 1] = 1
# allow_down_right
if p_q1[0] + j < size_board - 1 and p_q1[1] + j < size_board - 1:
if (p_q1[0] + j + 1 == p_k1[0] and p_q1[1] + j + 1 == p_k1[1]) or ((p_q1[0] + j + 1 == p_k2[0] and p_q1[1] + j + 1 == p_k2[1])):
blocked[4] = 1
if p_q1[0] + j + 1 == p_k1[0] and p_q1[1] + j + 1 == p_k1[1]:
blocked2[4] = 1
if blocked[4] == 0:
tmp = np.zeros([8], dtype=int)
for i in range(k2r.shape[0]):
if p_q1[0] + j + 1 != k2r[i, 0] or p_q1[1] + j + 1 != k2r[i, 1]:
tmp[i] = 1
if np.all(tmp):
dfQ1[p_q1[0] + j + 1, p_q1[1] + j + 1] = 1
a_q1[j + 4 * (size_board - 1)] = 1
else:
for i in range(len(tmp)):
if tmp[i] == 0:
for ii in range(k1r.shape[0]):
if p_q1[0] + j + 1 == k1r[ii, 0] and p_q1[1] + j + 1 == k1r[ii, 1]:
dfQ1[p_q1[0] + j + 1, p_q1[1] + j + 1] = 1
a_q1[j + 4 * (size_board - 1)] = 1
if blocked2[4] == 0:
dfQ1_[p_q1[0] + j + 1, p_q1[1] + j + 1] = 1
# allow_down_left
if p_q1[0] + j < size_board - 1 and p_q1[1] - j > 0:
if (p_q1[0] + j + 1 == p_k1[0] and p_q1[1] - j - 1 == p_k1[1]) or ((p_q1[0] + j + 1 == p_k2[0] and p_q1[1] - j - 1 == p_k2[1])):
blocked[5] = 1
if p_q1[0] + j + 1 == p_k1[0] and p_q1[1] - j - 1 == p_k1[1]:
blocked2[5] = 1
if blocked[5] == 0:
tmp = np.zeros([8], dtype=int)
for i in range(k2r.shape[0]):
if p_q1[0] + j + 1 != k2r[i, 0] or p_q1[1] - j - 1 != k2r[i, 1]:
tmp[i] = 1
if np.all(tmp):
dfQ1[p_q1[0] + j + 1, p_q1[1] - j - 1] = 1
a_q1[j + 5 * (size_board - 1)] = 1
else:
for i in range(len(tmp)):
if tmp[i] == 0:
for ii in range(k1r.shape[0]):
if p_q1[0] + j + 1 == k1r[ii, 0] and p_q1[1] - j - 1 == k1r[ii, 1]:
dfQ1[p_q1[0] + j + 1, p_q1[1] - j - 1] = 1
a_q1[j + 5 * (size_board - 1)] = 1
if blocked2[5] == 0:
dfQ1_[p_q1[0] + j + 1, p_q1[1] - j - 1] = 1
# allow_up_right
if p_q1[0] - j > 0 and p_q1[1] + j < size_board - 1:
if (p_q1[0] - j - 1 == p_k1[0] and p_q1[1] + j + 1 == p_k1[1]) or ((p_q1[0] - j - 1 == p_k2[0] and p_q1[1] + j + 1 == p_k2[1])):
blocked[6] = 1
if p_q1[0] - j - 1 == p_k1[0] and p_q1[1] + j + 1 == p_k1[1]:
blocked2[6] = 1
if blocked[6] == 0:
tmp = np.zeros([8], dtype=int)
for i in range(k2r.shape[0]):
if p_q1[0] - j - 1 != k2r[i, 0] or p_q1[1] + j + 1 != k2r[i, 1]:
tmp[i] = 1
if np.all(tmp):
dfQ1[p_q1[0] - j - 1, p_q1[1] + j + 1] = 1
a_q1[j + 6 * (size_board - 1)] = 1
else:
for i in range(len(tmp)):
if tmp[i] == 0:
for ii in range(k1r.shape[0]):
if p_q1[0] - j - 1 == k1r[ii, 0] and p_q1[1] + j + 1 == k1r[ii, 1]:
dfQ1[p_q1[0] - j - 1, p_q1[1] + j + 1] = 1
a_q1[j + 6 * (size_board - 1)] = 1
if blocked2[6] == 0:
dfQ1_[p_q1[0] - j - 1, p_q1[1] + j + 1] = 1
# allow_up_left
if p_q1[0] - j > 0 and p_q1[1] - j > 0:
if (p_q1[0] - j - 1 == p_k1[0] and p_q1[1] - j - 1 == p_k1[1]) or ((p_q1[0] - j - 1 == p_k2[0] and p_q1[1] - j - 1 == p_k2[1])):
blocked[7] = 1
if p_q1[0] - j - 1 == p_k1[0] and p_q1[1] - j - 1 == p_k1[1]:
blocked2[7] = 1
if blocked[7] == 0:
tmp = np.zeros([8], dtype=int)
for i in range(k2r.shape[0]):
if p_q1[0] - j - 1 != k2r[i, 0] or p_q1[1] - j - 1 != k2r[i, 1]:
tmp[i] = 1
if np.all(tmp):
dfQ1[p_q1[0] - j - 1, p_q1[1] - j - 1] = 1
a_q1[j + 7 * (size_board - 1)] = 1
else:
for i in range(len(tmp)):
if tmp[i] == 0:
for ii in range(k1r.shape[0]):
if p_q1[0] - j - 1 == k1r[ii, 0] and p_q1[1] - j - 1 == k1r[ii, 1]:
dfQ1[p_q1[0] - j - 1, p_q1[1] - j - 1] = 1
a_q1[j + 7 * (size_board - 1)] = 1
if blocked2[7] == 0:
dfQ1_[p_q1[0] - j - 1, p_q1[1] - j - 1] = 1
dfQ1[p_q1[0], p_q1[1]] = 0
dfQ1[p_k1[0], p_k1[1]] = 0
if p_k2[0] != np.inf:
dfQ1[p_k2[0], p_k2[1]] = 0
return dfQ1, a_q1, dfQ1_