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%ej.4.10仓库选址
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clc; clear; close all; format long g;
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a=zeros(6);
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a(1,[2,5])=[20,15];
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a(2,[1,3,4,5])=[20,20,60,25];
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a(3,[2,4,5])=[20,30,18];
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a(4,[2,3])=[60,30];
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a(5,[1,2,3,6])=[15,25,18,15];
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a(6,5)=15;
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s = cellstr(strcat('销售点',int2str([1:6]')));
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G=graph(a,s);
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P = plot(G,'layout','force','EdgeColor','k','NodeFontSize',12);
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D=[];
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for i=1:6
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temp=0;
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for j=1:6
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[path,d]=shortestpath(G,i,j);
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if d>temp;
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temp=d;
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end
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end
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D=[D,temp];
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end
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[minVal,minInd]=min(D);
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disp('仓库应建在销售点');
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disp(minInd);
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%答案版
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clc; clear; close all;
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% 初始化邻接矩阵
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a = zeros(6);
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a(1, [2, 5]) = [20, 15];
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a(2, 3:5) = [20, 60, 25];
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a(3, [4, 5]) = [30, 18];
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a(5, 6) = 15;
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% 创建节点标签
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s = cellstr(strcat('V', int2str([1:6]')));
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% 创建图
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G = graph(a, s, 'upper');
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% 计算所有节点之间的最短路径距离矩阵
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d = distances(G);
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% 计算从每个节点到其他节点的最大最短路径距离
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D = max(d, [], 2)'; %第三个参数 2 指定沿着矩阵的第二个维度（即列）进行操作。
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% 找到最大最短路径距离中的最小值及其下标
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[minD, minIndex] = min(D);
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% 绘制图
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plot(G, 'EdgeLabel', G.Edges.Weight, 'Layout', 'force');%设置边的标签
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% 显示结果
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fprintf('从每个节点到任意其他节点的最大最短路径距离: \n');
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disp(D);
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fprintf('最大最短路径距离中的最小值为: %f\n', minD);
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fprintf('对应的节点为: V%d\n', minIndex);
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%设备更新问题；
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clc;clear;close all;
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a=zeros(6);
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a(1,[2:6])=[15,20,27,37,54];
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a(2,[3:6])=[15,20,27,37];
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a(3,[4:6])=[16,21,28];
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a(4,[5:6])=[16,21];
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a(5,6)=17;
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s=cellstr(strcat(int2str((1:6)'),'年初'));
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G=digraph(a,s);
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P = plot(G,'layout','force','EdgeColor','k','NodeFontSize',12);
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[path,d]=shortestpath(G,1,6);%注意参数个数
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highlight(P,path,"EdgeColor","red",'LineWidth',3.5);
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%最小生成树
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clc;clear;
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a=zeros(9);
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a(1,[2:9])=[2 1 3 4 4 2 5 4]; % 顶点1到其他顶点的边的权重
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a(2,[3 9])=[4 1]; % 顶点2到顶点3、顶点9的边的权重
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a(3,4)=1; % 同上。因为写过1到3，和2到3的边的权重，无需重复设
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a(4,5)=1;
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a(5,6)=5;
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a(6,7)=2;
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a(7,8)=3;
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a(8,9)=5;
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s=cellstr(strcat('节点',int2str([1:9]')));
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G=graph(a,s,'upper');
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P=plot(G,'layout','force');
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T=minspantree(G,'Method','sparse');
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L=sum(T.Edges.Weight);
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highlight(P,T,"EdgeColor","red",'LineWidth',2.5);
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