How to find all possible routes with a given node matrix?
2 Ansichten (letzte 30 Tage)
Ältere Kommentare anzeigen
Jung Sunghun
am 25 Apr. 2018
Kommentiert: Jung Sunghun
am 20 Okt. 2018
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 Kommentare
Walter Roberson
am 15 Okt. 2018
You effectively have an undirected graph. There are an infinite number of routes unless you add constraints.
Akzeptierte Antwort
Bruno Luong
am 15 Okt. 2018
Bearbeitet: Bruno Luong
am 15 Okt. 2018
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 Kommentare
Bruno Luong
am 15 Okt. 2018
Nope find all paths has exponential complexity. AFAIK this is intrinsic to the problem you want to solve rather than the algorithm.
Weitere Antworten (1)
Walter Roberson
am 15 Okt. 2018
2 Kommentare
Walter Roberson
am 19 Okt. 2018
See also https://www.geeksforgeeks.org/find-paths-given-source-destination/ which gives code in C, Java, and Python.
Siehe auch
Kategorien
Mehr zu Variables finden Sie in Help Center und File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!