program dijkstra;
const maxvex=100; { 图的最大顶点数 }
type
costtype=dword; { 权值类型为无符号整型 }
graph=record
cost:array[1..maxvex,1..maxvex]of costtype; { 代价矩阵 }
vexnum:word; { 图的顶点数 }
end;
var
dist:array[1..maxvex]of costtype; { 到各顶点的最短路径数值 }
path:array[1..maxvex,0..maxvex]of word; { 每行记录最短路径,其中path[i,0]为到顶点i的路径长度 }
i,j,v1:word;
g:graph;
procedure creat_graph(var g:graph); { 建立图的存储结构 }
var i,j,k,edge:word; w:costtype;
begin
read(g.vexnum,edge); { 输入图的顶点数和边数 }
{ 初始化邻接矩阵 }
for i:=1 to g.vexnum do
for j:=1 to g.vexnum do
g.cost[i,j]:=maxlongint;
for i:=1 to g.vexnum do
g.cost[i,i]:=0; { 主对角线为0 }
for k:=1 to edge do
begin
read(i,j,w); { 输入起点号 边号 权值 }
g.cost[i,j]:=w;
g.cost[j,i]:=w;
end;
end;
procedure shortpath(g:graph; v:word); { 顶点V到其他顶点最短路径的算法,V为顶点序号 }
var i,j,k,k2:word;
minqz:costtype;
s:array[1..maxvex]of boolean;
begin
for i:=1 to maxvex do s[i]:=false; { 初始化,表示到顶点i的最短路径是否已经求得 }
s[v]:=true;
for i:=1 to g.vexnum do { 初始化dist数组和path数组 }
begin
dist[i]:=g.cost[v,i];
if (dist[i]<maxlongint) then
begin path[i,1]:=i; path[i,0]:=1; end {******}
else path[i,0]:=0;
end;
{ 输出dist分量值，以显示求解过程 }
for k:=1 to g.vexnum do
if dist[k]<>maxlongint then write(dist[k]:5)
else write('∞':5);
writeln;
for i:=1 to g.vexnum-1 do
begin { 求顶点v的一条最短路径 }
minqz:=maxlongint; j:=v;
for k:=1 to g.vexnum do
if (not s[k]) and ( dist[k]<minqz) then
begin j:=k; minqz:=dist[k]; end;
s[j]:=true; { 顶点j加入s }
{ 由新求得的路径修改dist数组各分量 }
for k:=1 to g.vexnum do
if g.cost[j,k]<>maxlongint then {本程序这条语句可省，如果costtype为longint,则不能省，否则会溢出 }
if ((not s[k]) and ((dist[j]+g.cost[j,k])<dist[k])) then
begin
dist[k]:=dist[j]+g.cost[j,k];
for k2:=1 to path[j,0] do
path[k,k2]:=path[j,k2];
path[k,k2+1]:=k;
path[k,0]:=path[j,0]+1;
end;
for k:=1 to g.vexnum do
if dist[k]<>maxlongint then write(dist[k]:5)
else write('∞':5);
writeln;
end;
end;
begin
assign(input,'dj.in'); reset(input);
assign(output,'dj.out'); rewrite(output);
creat_graph(g);
read(v1); { 输入开始顶点号 }
close(input);
shortpath(g,v1);
writeln;
{ 输出顶点V1到其他顶点的最短路径 }
writeln('v1 to else');
writeln;
for i:=1 to g.vexnum do write(dist[i]:5);
writeln;
for i:=1 to g.vexnum do
begin
writeln;
write(i:5,':',v1:5);
for j:=1 to path[i,0] do write(path[i,j]:5);
end;
close(output);
end.
--------------------------------------------------------------------------------
输入样例：
7 8
1 2 6
1 4 5
1 6 8
2 3 3
3 5 4
4 3 2
4 6 4
5 7 1
1
输出：
0 6 ∞ 5 ∞ 8 ∞
0 6 7 5 ∞ 8 ∞
0 6 7 5 ∞ 8 ∞
0 6 7 5 11 8 ∞
0 6 7 5 11 8 ∞
0 6 7 5 11 8 12
0 6 7 5 11 8 12
v1 to else
0 6 7 5 11 8 12
1: 1 1
2: 1 2
3: 1 4 3
4: 1 4
5: 1 4 3 5
6: 1 6
7: 1 4 3 5 7
