# The shortest distance and path between any two points of the most short-circuit 02-1--in graph theory

Source: Internet
Author: User

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Find the shortest distance between any two points and their paths. (Universal shortest circuit)
Input: Weight matrix, start point, end point
Output: Shortest distance matrix, specifying commencement point path (elapsed vertex number)
Lay the groundwork for the shortest path to any other point
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function [P D]=liangdianzuiduanlu (W,qidian,zhongdian)
W
N=length (W);
D=w;
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=d (Qidian,zhongdian);
P1=zeros (1,n);
k=1;
P1 (k) =zhongdian;
V=ones (1,n) *inf;
Kk=zhongdian;
While Kk~=qidian;
For I=1:n
V (1,i) =d (QIDIAN,KK)-W (I,KK);
If V (1,i) ==d (qidian,i)
P1 (k+1) =i;
Kk=i;
k=k+1;
End
End
End
k=1;
Wrow=find (p1~=0);
For J=length (wrow):(-1): 1
P (k) =p1 (Wrow (j));
k=k+1;

End

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Comment: The disadvantage is that the cohesion function is not good, the next "improvement of any two points between the shortest distance and road

This shortcoming will be solved by the "path".
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Example: Finding the shortest distance and path of midpoint 1 to 8

Solution: (1) Write Weight matrix

quanzhijuzhen=[ 0     2     8     1   INF   INF &N Bsp INF   INF
&NBSP;2     0     6   INF     1   INF   INF & nbsp INF
8     6     0     7     5     1     2   INF
1   INF     7     0   INF   INF     9 &N Bsp INF
inf     1     5   INF     0     3   INF   &NBSP ; 8
inf   INF     1   INF     3     0     4     6
inf   INF     2     9   INF     4     0     3
inf   INF   INF   INF     8     6     3     0]

(2) Bring in the procedure

[P D]=liangdianzuiduanlu (quanzhijuzhen,1,8)

P =

1 2 5 8

D =

11

Note: The path is 1->2->5->8 and the shortest distance is 11.

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The shortest distance and path between any two points of the most short-circuit 02-1--in graph theory

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