How to find all possible routes with a given node matrix?

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Jung Sunghun
Jung Sunghun 2018-4-25
评论： Jung Sunghun 2018-10-20
Hello,
I am trying to write a function to find all possible routes from the Start node, 6, to the Goal node, 21, with the given node matrix, A, as shown in the below.
A =
1 6
1 23
2 3
2 4
2 5
3 2
4 2
4 7
5 2
5 11
6 1
6 26
7 4
7 8
8 7
8 9
8 24
9 8
9 23
10 11
10 13
10 15
10 16
11 5
11 10
12 13
12 14
13 10
13 12
13 24
14 12
14 19
15 10
15 17
16 10
16 17
16 18
17 15
17 16
17 25
18 16
18 19
18 22
19 14
19 18
19 20
20 19
21 22
21 27
22 18
22 21
22 25
23 1
23 9
24 8
24 13
25 17
25 22
26 6
27 21
I would like to build a function which results the following outputs.
[6,1,23,9,8,7,4,2,5,11,10,15,17,25,22,21]
[6,1,23,9,8,7,4,2,5,11,10,15,17,16,18,22,21]
[6,1,23,9,8,7,4,2,5,11,10,16,17,25,22,21]
[6,1,23,9,8,7,4,2,5,11,10,16,18,22,21]
[6,1,23,9,8,24,13,10,15,17,25,22,21]
[6,1,23,9,8,24,13,10,16,17,25,22,21]
[6,1,23,9,8,24,13,10,16,18,22,21]
[6,1,23,9,8,24,13,12,14,19,18,16,10,15,17,25,22,21]
[6,1,23,9,8,24,13,12,14,19,18,16,17,25,22,21]
[6,1,23,9,8,24,13,12,14,19,18,22,21]
Thank you very much for your invaluable time to help on this problem.
Best regards,
Sunghun Jung
  3 个评论
显示 1更早的评论
Walter Roberson
Walter Roberson 2018-10-15
You effectively have an undirected graph. There are an infinite number of routes unless you add constraints.
Jung Sunghun
Jung Sunghun 2018-10-15
Dear Sir,
The constraint is that the node could only be used once in the path.

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采纳的回答

Bruno Luong
Bruno Luong 2018-10-15
编辑：Bruno Luong 2018-10-15
I found actually 13 paths, more than the 10 you have listed:
[6 1 23 9 8 7 4 2 5 11 10 13 12 14 19 18 16 17 25 22 21]
[6 1 23 9 8 7 4 2 5 11 10 13 12 14 19 18 22 21]
[6 1 23 9 8 7 4 2 5 11 10 15 17 16 18 22 21]
[6 1 23 9 8 7 4 2 5 11 10 15 17 25 22 21]
[6 1 23 9 8 7 4 2 5 11 10 16 17 25 22 21]
[6 1 23 9 8 7 4 2 5 11 10 16 18 22 21]
[6 1 23 9 8 24 13 10 15 17 16 18 22 21]
[6 1 23 9 8 24 13 10 15 17 25 22 21]
[6 1 23 9 8 24 13 10 16 17 25 22 21]
[6 1 23 9 8 24 13 10 16 18 22 21]
[6 1 23 9 8 24 13 12 14 19 18 16 10 15 17 25 22 21]
[6 1 23 9 8 24 13 12 14 19 18 16 17 25 22 21]
[6 1 23 9 8 24 13 12 14 19 18 22 21]
Test code:
A =[ 1 6
1 23
2 3
2 4
2 5
3 2
4 2
4 7
5 2
5 11
6 1
6 26
7 4
7 8
8 7
8 9
8 24
9 8
9 23
10 11
10 13
10 15
10 16
11 5
11 10
12 13
12 14
13 10
13 12
13 24
14 12
14 19
15 10
15 17
16 10
16 17
16 18
17 15
17 16
17 25
18 16
18 19
18 22
19 14
19 18
19 20
20 19
21 22
21 27
22 18
22 21
22 25
23 1
23 9
24 8
24 13
25 17
25 22
26 6
27 21];
p = gallpaths(A,6,21);
for k=1:length(p)
fprintf('%s\n', mat2str(p{k}));
end
Using this function GALLPATHS I made
function p = gallpaths(A,start,last)
% find all direct paths from start to last
% A is (n x 2) each row is an edges
A = sortrows(A);
b = true(size(A,1),1);
p = gapengine(A,b,start,last);
end
function p = gapengine(A,b,start,last)
% recursive engine
if start==last
p = {last};
else
bs = A(:,1) == start;
next = A(bs & b,2);
p = {};
b(bs) = false;
for k=1:length(next)
i = next(k);
pk = gapengine(A,b,i,last);
pk = cellfun(@(p) [start, p], pk, 'unif', 0);
p = [p, pk];
end
end
end
  3 个评论
显示 1更早的评论
Bruno Luong
Bruno Luong 2018-10-15
Nope find all paths has exponential complexity. AFAIK this is intrinsic to the problem you want to solve rather than the algorithm.
Jung Sunghun
Jung Sunghun 2018-10-15
I got it. Thank you very much for your invaluable time. Have a great day!

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更多回答（1 个）

Walter Roberson
Walter Roberson 2018-10-15

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