-
Notifications
You must be signed in to change notification settings - Fork 0
/
forb_subfunctions.sage
executable file
·233 lines (175 loc) · 6.95 KB
/
forb_subfunctions.sage
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
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
load("../pattern-avoidance/sub_functions.sage")
'''
TODO: Go through and clean up
Is everything in here in use?
'''
# Helper function for find_badpatts and para_find_badpatts
def rec(C,forb,lst):
#pruning lst
newlst = []
for L in lst:
if L.issubset(forb):
return []
if not C.intersection(L):
newlst.append(L)
if newlst:
lst0 = newlst[0]
i = 0
while lst0[i] in forb:
i = i+1
return rec( C.union(Set([lst0[i]])), forb, newlst ) + rec( C, forb.union(Set([lst0[i]])), newlst )
else:
return [C]
def rec_w_reduce(C,forb,lst,perm):
global badpatts
global check_interval
#pruning lst
newlst = []
for L in lst:
if L.issubset(forb): # If a member of lst is inside forb then it is impossible to satisfy that member
return []
if not C.intersection(L): # Here we find the members of lst that have not yet been satisfied
newlst.append(L)
if newlst:
lst0 = newlst[0] # Now we aim for satisfying the first member of lst, lst0
i = 0 # Here we find the first box in lst0 that we are allowed to fill in (i.e., put in C)
while lst0[i] in forb:
i = i+1
'''
This was added in September 2012.
We now check if the addition of the box lst0[i] makes this entire branch in the
recursion redundant.
'''
D = C.union(Set([lst0[i]]))
for j in check_interval:
if j == len(perm):
break
for cl_patt in badpatts[j]:
if mesh_has_mesh_many_shadings((perm,D),cl_patt,badpatts[j][cl_patt]):
return rec_w_reduce( C, forb.union(Set([lst0[i]])), newlst, perm )
return rec_w_reduce( D, forb, newlst, perm ) + rec_w_reduce( C, forb.union(Set([lst0[i]])), newlst, perm )
else:
return [C]
def rec_w_reduce_pattern_pos( C, forb, lst, perm, pattern_positions, check_interval ):
global badpatts
#pruning lst
newlst = []
for L in lst:
if L.issubset(forb): # If a member of lst is inside forb then it is impossible to satisfy that member
return []
if not C.intersection(L): # Here we find the members of lst that have not yet been satisfied
newlst.append(L)
if newlst:
lst0 = newlst[0] # Now we aim for satisfying the first member of lst, lst0
i = 0 # Here we find the first box in lst0 that we are allowed to fill in (i.e., put in C)
while lst0[i] in forb:
i = i+1
'''
This was added in September 2012.
We now check if the addition of the box lst0[i] makes this entire branch in the
recursion redundant.
'''
D = C.union(Set([lst0[i]]))
for j in check_interval:
if j == len(perm):
break
for cl_patt in badpatts[j]:
if mesh_has_mesh_with_positions(perm, D, pattern_positions[cl_patt], badpatts[j][cl_patt]):
return rec_w_reduce_pattern_pos( C, forb.union(Set([lst0[i]])), newlst, perm, pattern_positions, check_interval )
return rec_w_reduce_pattern_pos( D, forb, newlst, perm, pattern_positions, check_interval ) + rec_w_reduce_pattern_pos( C, forb.union(Set([lst0[i]])), newlst, perm, pattern_positions, check_interval )
else:
return [C]
#
# This function checks if mesh_patt occurs in mesh_perm
#
def mesh_has_mesh_with_positions(perm, S, pattern_pos, Rs):
# If there are no occurrences we return False
if not pattern_pos:
return False
# Otherwise the length of the pattern we are looking at is given
# by the length of the first occurrence of it in perm
else:
k = len(pattern_pos[0])
n = len(perm)
Gperm = G(perm)
Scomp = Set(map(lambda x: tuple(x),CartesianProduct([0..n],[0..n]))).difference(S)
for H in pattern_pos:
X = dict( (x+1,y+1) for (x,y) in enumerate(H) )
Y = dict( G(sorted(perm[j] for j in H)) )
X[0], X[k+1] = 0, n+1
Y[0], Y[k+1] = 0, n+1
for R in Rs:
shady = ( X[i] < x < X[i+1] and Y[j] < y < Y[j+1]\
for (i,j) in R\
for (x,y) in Gperm\
)
shaky = ( X[i] <= x < X[i+1] and Y[j] <= y < Y[j+1]\
for (i,j) in R\
for (x,y) in Scomp\
)
if not any(shady):
if not any(shaky):
return True
return False
def mesh_has_mesh(mesh_perm,mesh_patt):
pat = mesh_patt[0]
R = mesh_patt[1]
perm = mesh_perm[0]
S = mesh_perm[1]
k = len(pat)
n = len(perm)
if k > n:
return False
pat = G(pat)
perm = G(perm)
Scomp = Set(map(lambda x: tuple(x),CartesianProduct([0..n],[0..n]))).difference(S)
for H in Subwords(perm, k):
X = dict(G(sorted(i for (i,_) in H)))
Y = dict(G(sorted(j for (_,j) in H)))
if H == [ (X[i], Y[j]) for (i,j) in pat ]:
X[0], X[k+1] = 0, n+1
Y[0], Y[k+1] = 0, n+1
shady = ( X[i] < x < X[i+1] and Y[j] < y < Y[j+1]\
for (i,j) in R\
for (x,y) in perm\
)
shaky = ( X[i] <= x < X[i+1] and Y[j] <= y < Y[j+1]\
for (i,j) in R\
for (x,y) in Scomp\
)
if not any(shady):
if not any(shaky):
return True
return False
'''
Specialized version of the function above
'''
def mesh_has_mesh_many_shadings(mesh_perm,patt,Rs):
perm = mesh_perm[0]
S = mesh_perm[1]
k = len(patt)
n = len(perm)
if k > n:
return False
patt = G(patt)
perm = G(perm)
Scomp = Set(map(lambda x: tuple(x),CartesianProduct([0..n],[0..n]))).difference(S)
for H in Subwords(perm, k):
X = dict(G(sorted(i for (i,_) in H)))
Y = dict(G(sorted(j for (_,j) in H)))
if H == [ (X[i], Y[j]) for (i,j) in patt ]:
X[0], X[k+1] = 0, n+1
Y[0], Y[k+1] = 0, n+1
for R in Rs:
shady = ( X[i] < x < X[i+1] and Y[j] < y < Y[j+1]\
for (i,j) in R\
for (x,y) in perm\
)
shaky = ( X[i] <= x < X[i+1] and Y[j] <= y < Y[j+1]\
for (i,j) in R\
for (x,y) in Scomp\
)
if not any(shady):
if not any(shaky):
return True
return False