Graph theory Shortest circuit 01--shortest circuit matrix (FLOYD) algorithm

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% Shortest path matrix algorithm, Floyd algorithm

% targeted: Program budget, can find out the shortest possible between the short (minimum cost, etc.)
%========================================================

function D=zuiduanjulijuzhen (quanzhijuzhen)

N=length (Quanzhijuzhen);
D=quanzhijuzhen;
M=1;
While M<=n
For I=1:n
For J=1:n
If D (i,j) >d (i,m) +d (M,J)
D (i,j) =d (i,m) +d (M,J);
End
End
End
m=m+1;
End
D

%========================================================
% Evaluation: Matrix Shortest Path algorithm, you can find all point to point minimum distance, but with its shortcomings,
% is not given a specific path, the program D is the shortest distance matrix

%========================================================

Example: the shortest distance between each point in the request.

Solution: (1) Write Weights matrix

Quanzhijuzhen =[0 2 8 1 inf inf INF

2 0 6 INF 1 inf INF
8 6 0 7 5 1 2 INF
1 INF 7 0 INF INF 9 inf
INF 1 5 INF 0 3 INF 8
INF INF 1 INF 3 0 4 6
INF INF 2 9 INF 4 0 3
INF inf INF 8 6 3 0]

(2) Bring in the procedure

>> D=zuiduanjulijuzhen (Quanzhijuzhen)

Description: Line 1th represents the distance between point 1 and other points, and the I=2-8 line represents the distance between the I point and other points.

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Graph theory Shortest circuit 01--shortest circuit matrix (FLOYD) algorithm