假设我有以下列表：
data= ['a','b','c','d','e','f','g','h','i']
如何在每组中创建所有可能的3个列表组而不重复？示例输出将是：
[[['a','b','c'],['d','e','f'],['g','h','i']],[['a','b','e'],['c','d','g'],['f','h','i']]...] etc
编辑：代码中不应重复。例如，如果代码输出[['a','b','c'],['d','e','f'],['g','h','i']]
那么它不应该输出变体
[['a','b','c'],['g','h','i'],['d','e','f']]或[['c','b','a'],['d','e','f'],['g','h','i']]
答案 0 :(得分：2)
攻击此问题的一种方法是将其视为Exact Cover问题。正如维基百科所提到的，解决此类问题的标准方法是使用Knuth的算法X.在使用Knuth的“Dancing Links”算法实现的其他语言中。我们可以在Python中做到这一点，但由于我们没有指针，因此它有点乏味。但Ali Assaf已经展示了如何使用Python的dict和set对象来执行算法X.
下面的代码执行所需的分区，不重复，保持data字符串中使用的字母的顺序。
"""
Partition a list into equal parts
Uses Knuth's Algorithm X for the exact cover problem.
The Algorithm X code, using dicts instead of doubly-linked
circular lists was written by Ali Assaf.
See http://www.cs.mcgill.ca/~aassaf9/python/algorithm_x.html
and http://www.cs.mcgill.ca/~aassaf9/python/sudoku.txt
"""
from itertools import product, combinations
#Algorithm X functions
def solve(X, Y, solution):
if X:
c = min(X, key=lambda c: len(X[c]))
for r in list(X[c]):
solution.append(r)
cols = select(X, Y, r)
yield from solve(X, Y, solution)
deselect(X, Y, r, cols)
solution.pop()
else:
yield list(solution)
def select(X, Y, r):
cols = []
for j in Y[r]:
for i in X[j]:
for k in Y[i]:
if k != j:
X[k].remove(i)
cols.append(X.pop(j))
return cols
def deselect(X, Y, r, cols):
for j in reversed(Y[r]):
X[j] = cols.pop()
for i in X[j]:
for k in Y[i]:
if k != j:
X[k].add(i)
#Invert subset collection
def exact_cover(X, Y):
newX = {j: set() for j in X}
for i, row in Y.items():
for j in row:
newX[j].add(i)
return newX
#----------------------------------------------------------------------
data = 'abcdefghi'
Y = {''.join(t): t for t in combinations(data, 3)}
X = exact_cover(data, Y)
for i, solution in enumerate(solve(X, Y, []), 1):
print(i, solution)
<强>输出
1 ['aei', 'bgh', 'cdf']
2 ['aei', 'bch', 'dfg']
3 ['aei', 'bcf', 'dgh']
4 ['aei', 'bfh', 'cdg']
5 ['aei', 'bcg', 'dfh']
6 ['aei', 'bdg', 'cfh']
7 ['aei', 'bfg', 'cdh']
8 ['aei', 'bdf', 'cgh']
9 ['aei', 'bdh', 'cfg']
10 ['aei', 'bcd', 'fgh']
11 ['abf', 'cgh', 'dei']
12 ['abf', 'ceh', 'dgi']
13 ['abf', 'dgh', 'cei']
14 ['abf', 'cdh', 'egi']
15 ['abf', 'chi', 'deg']
16 ['abf', 'egh', 'cdi']
17 ['abf', 'ghi', 'cde']
18 ['abf', 'deh', 'cgi']
19 ['abf', 'ehi', 'cdg']
20 ['abf', 'dhi', 'ceg']
21 ['ace', 'bgh', 'dfi']
22 ['ace', 'dgi', 'bfh']
23 ['ace', 'dgh', 'bfi']
24 ['ace', 'dfg', 'bhi']
25 ['ace', 'fgh', 'bdi']
26 ['ace', 'fgi', 'bdh']
27 ['ace', 'ghi', 'bdf']
28 ['ace', 'bdg', 'fhi']
29 ['ace', 'bfg', 'dhi']
30 ['ace', 'bgi', 'dfh']
31 ['ach', 'dfi', 'beg']
32 ['ach', 'dfg', 'bei']
33 ['ach', 'bfi', 'deg']
34 ['ach', 'def', 'bgi']
35 ['ach', 'fgi', 'bde']
36 ['ach', 'efg', 'bdi']
37 ['ach', 'efi', 'bdg']
38 ['ach', 'bfg', 'dei']
39 ['ach', 'bdf', 'egi']
40 ['ach', 'bef', 'dgi']
41 ['afh', 'bei', 'cdg']
42 ['afh', 'dgi', 'bce']
43 ['afh', 'egi', 'bcd']
44 ['afh', 'cei', 'bdg']
45 ['afh', 'cgi', 'bde']
46 ['afh', 'dei', 'bcg']
47 ['afh', 'bdi', 'ceg']
48 ['afh', 'bgi', 'cde']
49 ['afh', 'bci', 'deg']
50 ['afh', 'cdi', 'beg']
51 ['aci', 'deg', 'bfh']
52 ['aci', 'bgh', 'def']
53 ['aci', 'beg', 'dfh']
54 ['aci', 'dgh', 'bef']
55 ['aci', 'dfg', 'beh']
56 ['aci', 'fgh', 'bde']
57 ['aci', 'bdg', 'efh']
58 ['aci', 'efg', 'bdh']
59 ['aci', 'bfg', 'deh']
60 ['aci', 'egh', 'bdf']
61 ['abh', 'dfi', 'ceg']
62 ['abh', 'cef', 'dgi']
63 ['abh', 'cfi', 'deg']
64 ['abh', 'dfg', 'cei']
65 ['abh', 'def', 'cgi']
66 ['abh', 'fgi', 'cde']
67 ['abh', 'efg', 'cdi']
68 ['abh', 'efi', 'cdg']
69 ['abh', 'cfg', 'dei']
70 ['abh', 'cdf', 'egi']
71 ['ahi', 'cdg', 'bef']
72 ['ahi', 'deg', 'bcf']
73 ['ahi', 'ceg', 'bdf']
74 ['ahi', 'beg', 'cdf']
75 ['ahi', 'dfg', 'bce']
76 ['ahi', 'bcg', 'def']
77 ['ahi', 'bdg', 'cef']
78 ['ahi', 'efg', 'bcd']
79 ['ahi', 'bfg', 'cde']
80 ['ahi', 'cfg', 'bde']
81 ['adi', 'cef', 'bgh']
82 ['adi', 'ceg', 'bfh']
83 ['adi', 'bce', 'fgh']
84 ['adi', 'beg', 'cfh']
85 ['adi', 'ceh', 'bfg']
86 ['adi', 'efh', 'bcg']
87 ['adi', 'beh', 'cfg']
88 ['adi', 'efg', 'bch']
89 ['adi', 'bef', 'cgh']
90 ['adi', 'egh', 'bcf']
91 ['acg', 'dfi', 'beh']
92 ['acg', 'bfh', 'dei']
93 ['acg', 'fhi', 'bde']
94 ['acg', 'bfi', 'deh']
95 ['acg', 'efh', 'bdi']
96 ['acg', 'def', 'bhi']
97 ['acg', 'efi', 'bdh']
98 ['acg', 'bdf', 'ehi']
99 ['acg', 'bef', 'dhi']
100 ['acg', 'dfh', 'bei']
101 ['acd', 'bei', 'fgh']
102 ['acd', 'egi', 'bfh']
103 ['acd', 'fhi', 'beg']
104 ['acd', 'bfi', 'egh']
105 ['acd', 'fgi', 'beh']
106 ['acd', 'ghi', 'bef']
107 ['acd', 'efi', 'bgh']
108 ['acd', 'ehi', 'bfg']
109 ['acd', 'bhi', 'efg']
110 ['acd', 'bgi', 'efh']
111 ['aeg', 'cfh', 'bdi']
112 ['aeg', 'bch', 'dfi']
113 ['aeg', 'chi', 'bdf']
114 ['aeg', 'cdh', 'bfi']
115 ['aeg', 'bfh', 'cdi']
116 ['aeg', 'fhi', 'bcd']
117 ['aeg', 'bhi', 'cdf']
118 ['aeg', 'bdh', 'cfi']
119 ['aeg', 'dfh', 'bci']
120 ['aeg', 'dhi', 'bcf']
121 ['abc', 'dfi', 'egh']
122 ['abc', 'dfg', 'ehi']
123 ['abc', 'fgh', 'dei']
124 ['abc', 'fhi', 'deg']
125 ['abc', 'efh', 'dgi']
126 ['abc', 'def', 'ghi']
127 ['abc', 'fgi', 'deh']
128 ['abc', 'efg', 'dhi']
129 ['abc', 'efi', 'dgh']
130 ['abc', 'dfh', 'egi']
131 ['abg', 'dfi', 'ceh']
132 ['abg', 'cfi', 'deh']
133 ['abg', 'chi', 'def']
134 ['abg', 'cei', 'dfh']
135 ['abg', 'fhi', 'cde']
136 ['abg', 'dei', 'cfh']
137 ['abg', 'efi', 'cdh']
138 ['abg', 'ehi', 'cdf']
139 ['abg', 'cdi', 'efh']
140 ['abg', 'dhi', 'cef']
141 ['adf', 'bei', 'cgh']
142 ['adf', 'ceg', 'bhi']
143 ['adf', 'bce', 'ghi']
144 ['adf', 'ceh', 'bgi']
145 ['adf', 'beg', 'chi']
146 ['adf', 'egi', 'bch']
147 ['adf', 'cei', 'bgh']
148 ['adf', 'beh', 'cgi']
149 ['adf', 'ehi', 'bcg']
150 ['adf', 'egh', 'bci']
151 ['agi', 'cfh', 'bde']
152 ['agi', 'cef', 'bdh']
153 ['agi', 'bch', 'def']
154 ['agi', 'bce', 'dfh']
155 ['agi', 'ceh', 'bdf']
156 ['agi', 'cde', 'bfh']
157 ['agi', 'bcf', 'deh']
158 ['agi', 'cdh', 'bef']
159 ['agi', 'bcd', 'efh']
160 ['agi', 'cdf', 'beh']
161 ['abi', 'cfh', 'deg']
162 ['abi', 'cgh', 'def']
163 ['abi', 'ceh', 'dfg']
164 ['abi', 'dgh', 'cef']
165 ['abi', 'cdh', 'efg']
166 ['abi', 'fgh', 'cde']
167 ['abi', 'efh', 'cdg']
168 ['abi', 'egh', 'cdf']
169 ['abi', 'deh', 'cfg']
170 ['abi', 'dfh', 'ceg']
171 ['aeh', 'cdg', 'bfi']
172 ['aeh', 'dgi', 'bcf']
173 ['aeh', 'dfg', 'bci']
174 ['aeh', 'cgi', 'bdf']
175 ['aeh', 'fgi', 'bcd']
176 ['aeh', 'bcg', 'dfi']
177 ['aeh', 'bdg', 'cfi']
178 ['aeh', 'bfg', 'cdi']
179 ['aeh', 'bgi', 'cdf']
180 ['aeh', 'cfg', 'bdi']
181 ['ade', 'cfi', 'bgh']
182 ['ade', 'chi', 'bfg']
183 ['ade', 'fhi', 'bcg']
184 ['ade', 'bfi', 'cgh']
185 ['ade', 'cgi', 'bfh']
186 ['ade', 'fgi', 'bch']
187 ['ade', 'ghi', 'bcf']
188 ['ade', 'bhi', 'cfg']
189 ['ade', 'bgi', 'cfh']
190 ['ade', 'bci', 'fgh']
191 ['afi', 'bgh', 'cde']
192 ['afi', 'cgh', 'bde']
193 ['afi', 'bch', 'deg']
194 ['afi', 'ceh', 'bdg']
195 ['afi', 'dgh', 'bce']
196 ['afi', 'cdh', 'beg']
197 ['afi', 'beh', 'cdg']
198 ['afi', 'deh', 'bcg']
199 ['afi', 'bdh', 'ceg']
200 ['afi', 'egh', 'bcd']
201 ['adh', 'cef', 'bgi']
202 ['adh', 'ceg', 'bfi']
203 ['adh', 'bce', 'fgi']
204 ['adh', 'cfi', 'beg']
205 ['adh', 'bcf', 'egi']
206 ['adh', 'cei', 'bfg']
207 ['adh', 'cgi', 'bef']
208 ['adh', 'bcg', 'efi']
209 ['adh', 'bci', 'efg']
210 ['adh', 'cfg', 'bei']
211 ['abd', 'cfi', 'egh']
212 ['abd', 'chi', 'efg']
213 ['abd', 'egi', 'cfh']
214 ['abd', 'cei', 'fgh']
215 ['abd', 'fhi', 'ceg']
216 ['abd', 'cgi', 'efh']
217 ['abd', 'fgi', 'ceh']
218 ['abd', 'ghi', 'cef']
219 ['abd', 'efi', 'cgh']
220 ['abd', 'ehi', 'cfg']
221 ['acf', 'deg', 'bhi']
222 ['acf', 'bgh', 'dei']
223 ['acf', 'dgi', 'beh']
224 ['acf', 'beg', 'dhi']
225 ['acf', 'dgh', 'bei']
226 ['acf', 'egi', 'bdh']
227 ['acf', 'ghi', 'bde']
228 ['acf', 'bdg', 'ehi']
229 ['acf', 'bgi', 'deh']
230 ['acf', 'egh', 'bdi']
231 ['abe', 'dfi', 'cgh']
232 ['abe', 'dgi', 'cfh']
233 ['abe', 'cfi', 'dgh']
234 ['abe', 'chi', 'dfg']
235 ['abe', 'fhi', 'cdg']
236 ['abe', 'cgi', 'dfh']
237 ['abe', 'fgi', 'cdh']
238 ['abe', 'ghi', 'cdf']
239 ['abe', 'cdi', 'fgh']
240 ['abe', 'dhi', 'cfg']
241 ['adg', 'cfh', 'bei']
242 ['adg', 'cef', 'bhi']
243 ['adg', 'cfi', 'beh']
244 ['adg', 'bcf', 'ehi']
245 ['adg', 'bfh', 'cei']
246 ['adg', 'fhi', 'bce']
247 ['adg', 'bfi', 'ceh']
248 ['adg', 'efh', 'bci']
249 ['adg', 'efi', 'bch']
250 ['adg', 'bef', 'chi']
251 ['agh', 'bei', 'cdf']
252 ['agh', 'dfi', 'bce']
253 ['agh', 'cfi', 'bde']
254 ['agh', 'cei', 'bdf']
255 ['agh', 'bfi', 'cde']
256 ['agh', 'dei', 'bcf']
257 ['agh', 'efi', 'bcd']
258 ['agh', 'bdi', 'cef']
259 ['agh', 'bci', 'def']
260 ['agh', 'cdi', 'bef']
261 ['afg', 'bei', 'cdh']
262 ['afg', 'bce', 'dhi']
263 ['afg', 'ceh', 'bdi']
264 ['afg', 'cde', 'bhi']
265 ['afg', 'cei', 'bdh']
266 ['afg', 'bde', 'chi']
267 ['afg', 'beh', 'cdi']
268 ['afg', 'deh', 'bci']
269 ['afg', 'dei', 'bch']
270 ['afg', 'ehi', 'bcd']
271 ['aef', 'cdg', 'bhi']
272 ['aef', 'dgi', 'bch']
273 ['aef', 'dgh', 'bci']
274 ['aef', 'cdh', 'bgi']
275 ['aef', 'bdg', 'chi']
276 ['aef', 'bdh', 'cgi']
277 ['aef', 'bdi', 'cgh']
278 ['aef', 'cdi', 'bgh']
279 ['aef', 'dhi', 'bcg']
280 ['aef', 'bcd', 'ghi']
请注意，算法X不一定是找到给定问题的解决方案的最有效方法。在许多情况下，更具体的解决方案将具有更好的性能。
答案 1 :(得分：0)
一个显而易见的事情是做三个嵌套的choose-3循环。 （好吧，两个，因为最后一个将选择3个中的3个......）
如果您的输入是动态长度，我会使用"id_1"或递归，但我认为对于3x3情况，显式循环可能更简单：
List<TreeItem<String>> product =
map.entrySet().stream().map(
t -> {
TreeItem<String>father = new TreeItem<>(t.getKey().getName());
List<TreeItem<String>> children = t.getValue()
.stream()
.map(u -> u.getName())
.map(TreeItem::new)
.collect (Collectors.toList());
father.getChildren().addAll(children);
return father;
}
).collect (Collectors.toList());
答案 2 :(得分：0)
import itertools
data= ['a','b','c','d','e','f','g','h','i']
d=itertools.permutations(data,9)
for i in d:print(i[:3],i[3:6],i[6:])
答案 3 :(得分：0)
输入数据
data= ['a','b','c','d','e','f','g','h','i']
创建所有元素排列并将它们分成3个小组
permutation_list = permutations(data, 3)
创建所有分组元素的列表
out = []
for i in permutation_list:
out.append(i)
再次将列表拆分为3个小组
def split(out_list, count):
return [out_list[i::count] for i in range(count)]
result = split(out, int(len(out)/3))
输出：
[[('a', 'b', 'c'), ('d', 'a', 'b'), ('g', 'a', 'b')], [('a', 'b', 'd'), ('d', 'a', 'c'), ('g', 'a', 'c')],.....