最短路+网络流/sgu 185 Two shortest

题意

　　求一个无向图中没有重边的两条最短路，并输出方案

分析

　　注意，是两条最短路！不是一条最短一条次短！所以先来个dijkstra/spfa来算一下最短路

　　根据dijkstra/spfa求出的dist[i]数组，建立一个新图，上面只有所有满足最短路的边构成的图

　　这样，建图就Ok了，下面如何解决没有重边呢？

　　很显然，设立一个源点和汇点，在源点出放出2的值。然后把刚刚建好的新图，边的权值设为1，相当于只能允许一个人经过。这样，如果在汇点得到了2的值，说明这样的两条路是存在的，再利用一个dfs求出即可。

　　注意dinic需要加上当前弧优化，不然会tle at #17

Accepted Code

{
        PROBLEM：sgu185
        AUTHER:Rinyo
        MEMO:最短路 网络流  
}
Program sgu185;
Const
  Infile = 'sgu185.in';
  Outfile = '';
Type
  Rec = Record
    y,s,flow:Longint;
  End;
Var
  map:Array[0..160000]Of REc;
  a:Array[0..430,0..430]Of Longint;
  dist,q,num,next,p:Array[0..430]Of Longint;
  v:Array[0..430]Of Boolean;
  maxflow,i,j,n,m,l:Longint;
  flag:Boolean;
Function min(a,b:Longint):Longint;
Begin
  if a<b Then min:=a Else min:=b;
End;
Procedure init;
Var
  x,y,w:Longint;
Begin
  ReadLn(n,m);
  For i:=1 To m Do Begin
    ReadLn(x,y,w);
    a[x,y]:=w;
    a[y,x]:=w;
  End;
End;
Procedure dijkstra;
Var
  j,k,mink:Longint;
begin
  Fillchar(dist,sizeof(dist),100);
  dist[1]:=0;
  For i:=1 To n-1 Do Begin
    mink:=maxlongint;
    For j:=1 To n Do
      If (not v[j]) And (dist[j]<mink) Then Begin
        mink:=dist[j];
        k:=j;
      End;
    v[k]:=true;
    For j:=1 To n Do
      If (a[k,j]>0) And (dist[j]>mink+a[k,j]) Then dist[j]:=mink+a[k,j];
  End;
End;

Function dfs(now,value:Longint):Longint;
Var
  v1,i,x,ff:Longint;
begin
  if now=n Then Begin
    dfs:=value;
    Exit;
  End;
  v1:=value;
  ff:=p[now];
  While ff>-1 Do Begin
    i:=map[ff].y;
    If (map[ff].flow>0) And (num[i]=num[now]+1) Then begin
      x:=dfs(i,min(value,map[ff].flow));
      map[ff].flow:=map[ff].flow-x;
      value:=value-x;
      If odd(ff) Then map[ff+1].flow:=map[ff+1].flow+x
                 Else map[ff-1].flow:=map[ff-1].flow+x;
    End;
    ff:=map[ff].s;
    If value=0 then break;
  End;
  p[now]:=ff;
  dfs:=v1-value;
End;

Procedure bfs;
Var
  head,tail,now,ff,v:Longint;
Begin
  Fillchar(q,sizeof(q),0);
  Fillchar(num,sizeof(num),0);
  head:=0;tail:=1;q[1]:=1;num[1]:=1;flag:=false;
  While head<tail Do begin
    Inc(head);
    now:=q[head];
    ff:=next[now];
    While ff<>-1 Do Begin
      v:=map[ff].y;
      If (map[ff].flow>0) And (num[v]=0) Then Begin
        num[v]:=num[now]+1;
        Inc(tail);
        q[tail]:=v;
        If v=n Then Begin
          flag:=true;
          Exit;
        End;
      End;
      ff:=map[ff].s;
    End;
  End;
End;

Procedure answer(x:Longint);
Var
  ff,v:Longint;
Begin
  If (x=n) Then Begin
    WriteLn(n);
    Exit;
  End;
  ff:=next[x];
  While ff<>-1 Do Begin
    v:=map[ff].y;
    If (map[ff].flow=0) And (a[x,v]+dist[x]=dist[v]) Then begin
      Write(x,' ');
      answer(v);
      map[ff].flow:=1;
      Exit;
    End;
    ff:=map[ff].s;
  End;
End;

Begin
  Assign(input,infile);Reset(input);
  Assign(output,outfile);Rewrite(output);
  init;
  dijkstra;
  l:=0;
  Fillchar(next,sizeof(next),$ff);
  For i:=1 To n Do
    For j:=1 To n Do
      If (i<>j) And (a[i,j]>0) Then
        If dist[i]+a[i,j]=dist[j] Then Begin
          Inc(l);map[l].y:=j;map[l].flow:=1;map[l].s:=next[i];next[i]:=l;
          Inc(l);map[l].y:=i;map[l].flow:=0;map[l].s:=next[j];next[j]:=l;
        End;
  flag:=true;
  While flag Do Begin
    BFS;
    p:=next;
    maxflow:=maxflow+dfs(1,2);
  End;
  //WriteLn(maxflow);
  If maxflow<2 Then Begin
    WriteLn('No solution');
  End Else Begin
    answer(1);
    answer(1);
  End;
  Close(input);Close(output);
End.