数学建模实验报告-第十一章-最短路问题.docx

实验名称： 第十一章 最短路问题 一、实验内容与要求掌握Dijkstra算法和Floyd算法，并运用这两种算法求一些最短路径的问题。二、实验软件MATLAB7.0三、实验内容1、在一个城市交通系统中取出一段如图所示，其入口为顶点v1，出口为顶点v8，每条弧段旁的数字表示通过该路段所需时间，每次转弯需要附加时间为3，求v1到 v8的最短时间路径。V1 1 V2 3 V3 1 V5 6 V62 23 V4 2 V7 4 V8程序：function y=bijiaodaxiao(f1,f2,f3,f4)v12=1;v23=3;v24=2;v35=1;v47=2;v57=2;v56=6;v68=3;v78=4;turn=3;f1=v12+v23+v35+v56+turn+v68;f2=v12+v23+v35+turn+v57+turn+v78;f3=v12+turn+v24+turn+v47+v78;f4=v12+turn+v24+v47+turn+v57+turn+v56+turn+v68;min=f1;if f2min min=f2;endif f3min min=f3;endif f4min min=f4;endminf1f2f3f4实验结果：v1到v8的最短时间路径为15，路径为1-2-4-7-8.2、求如图所示中每一结点到其他结点的最短路。 V1 10 V3 V5 9 V636 4 5 3 4 V2 5 V4 10 V7 6 V8floy.m中的程序：functionD,R=floyd(a)n=size(a,1);D=afor i=1:n for j=1:n R(i,j)=j; endendRfor k=1:n for i=1:n for j=1:n if D(i,k)+D(k,j) a=0 3 10 inf inf inf inf inf;3 0 inf 5 inf inf inf inf;10 inf 0 6 inf inf inf inf;inf 5 6 0 4 inf 10 inf ;inf inf inf 4 0 9 5 inf ;inf inf inf inf 9 0 3 4;inf inf inf 10 5 3 0 6;inf inf inf inf inf 4 6 0;D,R=floyd(a)实验结果：D = 0 3 10 Inf Inf Inf Inf Inf 3 0 Inf 5 Inf Inf Inf Inf 10 Inf 0 6 Inf Inf Inf Inf Inf 5 6 0 4 Inf 10 Inf Inf Inf Inf 4 0 9 5 Inf Inf Inf Inf Inf 9 0 3 4 Inf Inf Inf 10 5 3 0 6 Inf Inf Inf Inf Inf 4 6 0R = 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8k = 1D = 0 3 10 Inf Inf Inf Inf Inf 3 0 13 5 Inf Inf Inf Inf 10 13 0 6 Inf Inf Inf Inf Inf 5 6 0 4 Inf 10 Inf Inf Inf Inf 4 0 9 5 Inf Inf Inf Inf Inf 9 0 3 4 Inf Inf Inf 10 5 3 0 6 Inf Inf Inf Inf Inf 4 6 0R = 1 2 3 4 5 6 7 8 1 2 1 4 5 6 7 8 1 1 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8k = 2D = 0 3 10 8 Inf Inf Inf Inf 3 0 13 5 Inf Inf Inf Inf 10 13 0 6 Inf Inf Inf Inf 8 5 6 0 4 Inf 10 Inf Inf Inf Inf 4 0 9 5 Inf Inf Inf Inf Inf 9 0 3 4 Inf Inf Inf 10 5 3 0 6 Inf Inf Inf Inf Inf 4 6 0R = 1 2 3 2 5 6 7 8 1 2 1 4 5 6 7 8 1 1 3 4 5 6 7 8 2 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8k = 3D = 0 3 10 8 Inf Inf Inf Inf 3 0 13 5 Inf Inf Inf Inf 10 13 0 6 Inf Inf Inf Inf 8 5 6 0 4 Inf 10 Inf Inf Inf Inf 4 0 9 5 Inf Inf Inf Inf Inf 9 0 3 4 Inf Inf Inf 10 5 3 0 6 Inf Inf Inf Inf Inf 4 6 0R = 1 2 3 2 5 6 7 8 1 2 1 4 5 6 7 8 1 1 3 4 5 6 7 8 2 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8k = 4D = 0 3 10 8 12 Inf 18 Inf 3 0 11 5 9 Inf 15 Inf 10 11 0 6 10 Inf 16 Inf 8 5 6 0 4 Inf 10 Inf 12 9 10 4 0 9 5 Inf Inf Inf Inf Inf 9 0 3 4 18 15 16 10 5 3 0 6 Inf Inf Inf Inf Inf 4 6 0R = 1 2 3 2 2 6 2 8 1 2 4 4 4 6 4 8 1 4 3 4 4 6 4 8 2 2 3 4 5 6 7 8 4 4 4 4 5 6 7 8 1 2 3 4 5 6 7 8 4 4 4 4 5 6 7 8 1 2 3 4 5 6 7 8k = 5D = 0 3 10 8 12 21 17 Inf 3 0 11 5 9 18 14 Inf 10 11 0 6 10 19 15 Inf 8 5 6 0 4 13 9 Inf 12 9 10 4 0 9 5 Inf 21 18 19 13 9 0 3 4 17 14 15 9 5 3 0 6 Inf Inf Inf Inf Inf 4 6 0R = 1 2 3 2 2 2 2 8 1 2 4 4 4 4 4 8 1 4 3 4 4 4 4 8 2 2 3 4 5 5 5 8 4 4 4 4 5 6 7 8 5 5 5 5 5 6 7 8 5 5 5 5 5 6 7 8 1 2 3 4 5 6 7 8k = 6D = 0 3 10 8 12 21 17 25 3 0 11 5 9 18 14 22 10 11 0 6 10 19 15 23 8 5 6 0 4 13 9 17 12 9 10 4 0 9 5 13 21 18 19 13 9 0 3 4 17 14 15 9 5 3 0 6 25 22 23 17 13 4 6 0R = 1 2 3 2 2 2 2 2 1 2 4 4 4 4 4 4 1 4 3 4 4 4 4 4 2 2 3 4 5 5 5 5 4 4 4 4 5 6 7 6 5 5 5 5 5 6 7 8 5 5 5 5 5 6 7 8 6 6 6 6 6 6 7 8k = 7D = 0 3 10 8 12 20 17 23 3 0 11 5 9 17 14 20 10 11 0 6 10 18 15 21 8 5 6 0 4 12 9 15 12 9 10 4 0 8 5 11 20 17 18 12 8 0 3 4 17 14 15 9 5 3 0 6 23 20 21 15 11 4 6 0R = 1 2 3 2 2 2 2 2 1 2 4 4 4 4 4 4 1 4 3 4 4 4 4 4 2 2 3 4 5 5 5 5 4 4 4 4 5 7 7 7 7 7 7 7 7 6 7 8 5 5 5 5 5 6 7 8 7 7 7 7 7 6 7 8k = 8D = 0 3 10 8 12 20 17 23 3 0 11 5 9 17 14 20 10 11 0 6 10 18 15 21 8 5 6 0 4 12 9 15 12 9 10 4 0 8 5 11 20 17 18 12 8 0 3 4 17 14 15 9 5 3 0 6 23 20 21 15 11 4 6 0R = 1 2 3 2 2 2 2 2 1 2 4 4 4 4 4 4 1 4 3 4 4 4 4 4 2 2 3 4 5 5 5 5 4 4 4 4 5 7 7 7 7 7 7 7 7 6 7 8 5 5 5 5 5 6 7 8 7 7 7 7 7 6 7 8D = 0 3 10 8 12 20 17 23 3 0 11 5 9 17 14 20 10 11 0 6 10 18 15 21 8 5 6 0 4 12 9 15 12 9 10 4