1、目标:无指向or有指向的最短路径。
2、Matlab实现:
weight= [0 2 8 1 Inf Inf Inf Inf Inf Inf Inf; 2 0 6 Inf 1 Inf Inf Inf Inf Inf Inf; 8 6 0 7 5 1 2 Inf Inf Inf Inf; 1 Inf 7 0 Inf Inf 9 Inf Inf Inf Inf; Inf 1 5 Inf 0 3 Inf 2 9 Inf Inf; Inf Inf 1 Inf 3 0 4 Inf 6 Inf Inf; Inf Inf 2 9 Inf 4 0 Inf 3 1 Inf; Inf Inf Inf Inf 2 Inf Inf 0 7 Inf 9; Inf Inf Inf Inf 9 6 3 7 0 1 2; Inf Inf Inf Inf Inf Inf 1 Inf 1 0 4; Inf Inf Inf Inf Inf Inf Inf 9 2 4 0;]; [dis, path]=dijkstra(weight,1, 11) dijkstra.m function [min,path]=dijkstra(w,start,terminal) n=size(w,1); label(start)=0; f(start)=start; for i=1:n if i~=start label(i)=inf; end, end s(1)=start; u=start; while length(s)<n for i=1:n ins=0; for j=1:length(s) if i==s(j) ins=1; end, end if ins==0 v=i; if label(v)>(label(u)+w(u,v)) label(v)=(label(u)+w(u,v)); f(v)=u; end, end, end v1=0; k=inf; for i=1:n ins=0; for j=1:length(s) if i==s(j) ins=1; end, end if ins==0 v=i; if k>label(v) k=label(v); v1=v; end, end, end s(length(s)+1)=v1; u=v1; end min=label(terminal); path(1)=terminal; i=1; while path(i)~=start path(i+1)=f(path(i)); i=i+1 ; end path(i)=start; L=length(path); path=path(L:-1:1);
3、输入数据格式:
[0 2 8 1 Inf Inf Inf Inf Inf Inf Inf; 2 0 6 Inf 1 Inf Inf Inf Inf Inf Inf; 8 6 0 7 5 1 2 Inf Inf Inf Inf; 1 Inf 7 0 Inf Inf 9 Inf Inf Inf Inf; Inf 1 5 Inf 0 3 Inf 2 9 Inf Inf; Inf Inf 1 Inf 3 0 4 Inf 6 Inf Inf; Inf Inf 2 9 Inf 4 0 Inf 3 1 Inf; Inf Inf Inf Inf 2 Inf Inf 0 7 Inf 9; Inf Inf Inf Inf 9 6 3 7 0 1 2; Inf Inf Inf Inf Inf Inf 1 Inf 1 0 4; Inf Inf Inf Inf Inf Inf Inf 9 2 4 0;] [0 8 Inf Inf Inf Inf 7 8 Inf Inf Inf; Inf 0 3 Inf Inf Inf Inf Inf Inf Inf Inf; Inf Inf 0 5 6 Inf 5 Inf Inf Inf Inf; Inf Inf Inf 0 1 Inf Inf Inf Inf Inf 12; Inf Inf 6 Inf 0 2 Inf Inf Inf Inf 10; Inf Inf Inf Inf 2 0 9 Inf 3 Inf Inf; Inf Inf Inf Inf Inf 9 0 Inf Inf Inf Inf; 8 Inf Inf Inf Inf Inf Inf 0 9 Inf Inf; Inf Inf Inf Inf 7 Inf Inf 9 0 2 Inf; Inf Inf Inf Inf Inf Inf Inf Inf 2 0 2; Inf Inf Inf Inf 10 Inf Inf Inf Inf Inf 0;];