dijkstra--matlab

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本文详细介绍Dijkstra算法的具体实现过程，并通过实例演示如何寻找加权图中两点间的最短路径。文章提供了一段清晰的MATLAB代码，展示了初始化标签、迭代更新路径及最终获取最短路径的全过程。

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无向：

有向：

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);

%测试数据
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)

%结果
dis =

    13


path =

     1     2     5     6     3     7    10     9    11

B站：https://www.bilibili.com/video/av29474522/?p=6