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
|
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
multiset.py -- non-recursive n multichoose k and
non-recursive multiset permutations
for python lists
author: Erik Garrison <erik.garrison@bc.edu>
last revised: 2010-07-15
Copyright (c) 2010 by Erik Garrison
Permission is hereby granted, free of charge, to any person
obtaining a copy of this software and associated documentation
files (the "Software"), to deal in the Software without
restriction, including without limitation the rights to use,
copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the
Software is furnished to do so, subject to the following
conditions:
The above copyright notice and this permission notice shall be
included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
OTHER DEALINGS IN THE SOFTWARE.
"""
def multichoose(k, objects):
"""n multichoose k multisets from the list of objects. n is the size of
the objects."""
j,j_1,q = k,k,k # init here for scoping
r = len(objects) - 1
a = [0 for i in range(k)] # initial multiset indexes
while True:
yield [objects[a[i]] for i in range(0,k)] # emit result
j = k - 1
while j >= 0 and a[j] == r: j -= 1
if j < 0: break # check for end condition
j_1 = j
while j_1 <= k - 1:
a[j_1] = a[j_1] + 1 # increment
q = j_1
while q < k - 1:
a[q+1] = a[q] # shift left
q += 1
q += 1
j_1 = q
"""
Permutations of a multiset:
Algorithm 1
Visits the permutations of multiset E. The permutations are stored
in a singly-linked list pointed to by head pointer h. Each node in the linked
list has a value field v and a next field n. The init(E) call creates a
singly-linked list storing the elements of E in non-increasing order with h, i,
and j pointing to its first, second-last, and last nodes, respectively. The
null pointer is given by φ. Note: If E is empty, then init(E) should exit.
Also, if E contains only one element, then init(E) does not need to provide a
value for i.
[h, i, j] ← init(E)
visit(h)
while j.n ≠ φ orj.v <h.v do
if j.n ≠ φ and i.v ≥ j.n.v then
s←j
else
s←i
end if
t←s.n
s.n ← t.n
t.n ← h
if t.v < h.v then
i←t
end if
j←i.n
h←t
visit(h)
end while
... from "Loopless Generation of Multiset Permutations using a Constant Number
of Variables by Prefix Shifts." Aaron Williams, 2009
"""
class ListElement:
def __init__(self, value, next):
self.value = value
self.next = next
def nth(self, n):
o = self
i = 0
while i < n and o.__next__ is not None:
o = o.__next__
i += 1
return o
def __init(multiset):
multiset.sort() # ensures proper non-increasing order
h = ListElement(multiset[0], None)
for item in multiset[1:]:
h = ListElement(item, h)
return h, h.nth(len(multiset) - 2), h.nth(len(multiset) - 1)
def __visit(h):
"""Converts our bespoke linked list to a python list."""
o = h
l = []
while o is not None:
l.append(o.value)
o = o.__next__
return l
def permutations(multiset):
"""Generator providing all multiset permutations of a multiset."""
h, i, j = __init(multiset)
yield __visit(h)
while j.__next__ is not None or j.value < h.value:
if j.__next__ is not None and i.value >= j.next.value:
s = j
else:
s = i
t = s.__next__
s.next = t.__next__
t.next = h
if t.value < h.value:
i = t
j = i.__next__
h = t
yield __visit(h)
|
