def F(self, i, j, m, x):
if (i == 0 or j == 0):
return 0
if (m > j or m > i):
return 0
if (abs(x) > m):
return 0
W_tmp = vector_min(self.W, j)[:i]
T_tmp = vector_min(self.T, j)[:i]
if (max_rook_num(W_tmp) < x):
return 0
if (-max_rook_num(L_vector(W_tmp, T_tmp, j)) > x):
return 0
if (is_single_type(W_tmp, T_tmp, j)):
return F_0(i, j, m, x, what_single_type(W_tmp, T_tmp, j))
if (W_tmp[-1] == j): ## corner is in W
width = width_to_remove(W_tmp)
maximum_rooks_in_right = min(width, j)
sum = 0
for r in range(min(maximum_rooks_in_right, m) + 1):
sum += self.values[i - width, j, m - r,
x - r] * single_type_rectangle(
width, j - (m - r), r)
return sum
if (T_tmp[-1] < j): ## corner is in L
height = j - T_tmp[-1]
maximum_rooks_in_top = min(i, height)
sum = 0
for r in range(min(maximum_rooks_in_top, m) + 1):
F_tmp = self.values[i, j - height, m - r, x + r]
top = single_type_rectangle(i - (m - r), height, r)
sum += F_tmp * top
return sum
# REMISY
if (is_double_type_with_tie(W_tmp, T_tmp, j)):
return F_1(i, j, m, x, W_tmp, T_tmp,
what_double_type(W_tmp, T_tmp, j))
if (T_tmp[-1] == j): ## corner is in T
width = width_to_remove(T_tmp)
height = T_tmp[-1] - W_tmp[-1]
maximum_rooks_in_top = min(i - width, height)
maximum_rooks_in_right = min(width, j - height)
maximum_rooks_in_corner = min(width, height)
sum = 0
for r_3 in range(min(maximum_rooks_in_top, m) + 1):
for r_2 in range(min(maximum_rooks_in_corner, m) + 1):
for r_1 in range(min(maximum_rooks_in_right, m) + 1):
if (r_1 + r_2 + r_3 <= m):
r_4 = m - r_1 - r_2 - r_3
F_tmp = self.values[i - width, j - height, r_4,
x - r_1 + r_3]
top = single_type_rectangle(
i - width - r_4, height, r_3)
corner = single_type_rectangle(
width, height - r_3, r_2)
right = single_type_rectangle(
width - r_2, j - height - r_4, r_1)
sum += F_tmp * top * corner * right
return sum
def rotate_clash_matrix(self):
tmp_W = self.fields_number - np.flip(self.T, 0) ## to jest nowe W
self.T = self.fields_number - np.flip(self.W, 0) ## to jest nowe T
self.W = tmp_W
self.knots = find_knots(self.W, self.T)
self.m_constraints = find_m_constraints(self.knots, self.fields_number).astype(int)
self.x_max = np.max(max_rook_num(self.W))
## i, j, m, x order
self.values = np.zeros((self.fields_number + 1, self.fields_number + 1, self.fields_number + 1, self.x_max + 1))
def reload(self, A, B):
self.A = A
self.B = B
self.fields_number = A.shape[0]
if(int(self.fields_number / 2) * 2 == self.fields_number):
print("Even number of fields!!!")
return
self.W, self.T = single_payoff_matrix_vectors(A, B)
self.knots = find_knots(self.W, self.T)
self.m_constraints = find_m_constraints(self.knots, self.fields_number).astype(int)
self.x_max = max_rook_num(self.W)
## i, j, m, x order
self.values = np.zeros((self.fields_number + 1, self.fields_number + 1, self.fields_number + 1, self.x_max + 1))
def F(i, j, m, x, W, T):
if (i == 0 or j == 0):
return 0
if (m > j or m > i):
return 0
if (abs(x) > m):
return 0
if (max_rook_num(W) < x):
return 0
if (-max_rook_num(L_vector(W, T, j)) > x):
return 0
if (is_single_type(W, T, j)):
return F_0(i, j, m, x, what_single_type(W, T, j))
if (W[-1] == j): ## corner is in W
# print("W CORNER")
width = width_to_remove(W)
maximum_rooks_in_right = min(width, j)
sum = 0
for r in range(min(maximum_rooks_in_right, m) + 1):
sum += F(i - width, j, m - r, x - r, W[:-width],
T[:-width]) * single_type_rectangle(
width, j - (m - r), r)
return sum
if (T[-1] < j): ## corner is in L
# print("L CORNER")
height = j - T[-1]
maximum_rooks_in_top = min(i, height)
sum = 0
for r in range(min(maximum_rooks_in_top, m) + 1):
F_tmp = F(i, j - height, m - r, x + r, vector_min(W, j - height),
vector_min(T, j - height))
top = single_type_rectangle(i - (m - r), height, r)
sum += F_tmp * top
## TODO czy nie powinniśmy zmniejszać W i T? done, bez zmian
return sum
# REMISY
if (is_double_type_with_tie(W, T, j)):
return F_1(i, j, m, x, W, T, what_double_type(W, T, j))
if (T[-1] == j): ## corner is in T
# print("WESZLIŚMY W REMISY")
width = width_to_remove(T)
height = T[-1] - W[-1]
maximum_rooks_in_top = min(i - width, height)
maximum_rooks_in_right = min(width, j - height)
maximum_rooks_in_corner = min(width, height)
sum = 0
for r_3 in range(min(maximum_rooks_in_top, m) + 1):
for r_2 in range(min(maximum_rooks_in_corner, m) + 1):
for r_1 in range(min(maximum_rooks_in_right, m) + 1):
if (r_1 + r_2 + r_3 <= m):
r_4 = m - r_1 - r_2 - r_3
F_tmp = F(i - width, j - height, r_4, x - r_1 + r_3,
vector_min(W[:-width], j - height),
vector_min(T[:-width], j - height))
top = single_type_rectangle(i - width - r_4, height,
r_3)
corner = single_type_rectangle(width, height - r_3,
r_2)
right = single_type_rectangle(width - r_2,
j - height - r_4, r_1)
sum += F_tmp * top * corner * right
## TODO czy nie powinniśmy zmniejszać W i T? done, bez zmian
return sum