bzoj1937

这道题没弄明白

初始模型很好想，是用到了最小生成树的性质

加入非树边后树上形成的环，非树边一定大于等于任意树边

然后考虑树边一定是缩小，非树边一定是增大

有di+wi>=dj-wj wi+wj>=dj-di（j是加入i形成的环上的边）

然后不知道为什么求∑wi最小就是跑最大费用可行流

求神犇指教

 type node=record
        po,next,cost,flow:longint;
      end;

 var e:array[..] of node;
     v,f:array[..] of boolean;
     a:array[..,..] of longint;
     d,pre,cur,w,p:array[..] of longint;
     q:array[..] of longint;
     x,y,len,i,j,n,m,t,k:longint;

 procedure add(x,y,f,c:longint);
   begin
     inc(len);
     e[len].po:=y;
     e[len].next:=p[x];
     e[len].cost:=c;
     e[len].flow:=f;
     p[x]:=len;
   end;

 procedure build(x,y,f,c:longint);
   begin
     add(x,y,f,c);
     add(y,x,,-c);
   end;

 function dfs(x:longint):boolean;
   var i:longint;
   begin
     f[x]:=true;
     if x=j then
     begin
       q[]:=-;
       exit;
     end;
     for i:= to n do
       if not f[i] and v[a[x,i]] then
       begin
         inc(t);
         q[t]:=a[x,i];
         dfs(i);
         if q[]=- then exit;
         q[t]:=;
         dec(t);
       end;
   end;

 function spfa:boolean;
   var f,r,y,i,j,x:longint;
   begin
     f:=;
     r:=;
     q[]:=;
     d[]:=;
     for i:= to t do
       d[i]:=-;
     fillchar(v,sizeof(v),false);
     while f<=r do
     begin
       x:=q[f];
       v[x]:=false;
       i:=p[x];
       while i<>- do
       begin
         y:=e[i].po;
         if e[i].flow> then
           if d[y]<d[x]+e[i].cost then
           begin
             d[y]:=d[x]+e[i].cost;
             pre[y]:=x;
             cur[y]:=i;
             if not v[y] then
             begin
               v[y]:=true;
               inc(r);
               q[r]:=y;
             end;
           end;
         i:=e[i].next;
       end;
       inc(f);
     end;
     if d[t]>= then exit(true) else exit(false);
   end;

 function maxcost:longint;
   var i,j:longint;
   begin
     maxcost:=;
     while spfa do
     begin
       i:=t;
       while i<> do
       begin
         j:=cur[i];
         dec(e[j].flow);
         inc(e[j xor ].flow);
         i:=pre[i];
       end;
       maxcost:=maxcost+d[t];
     end;
   end;

 begin
   len:=-;
   fillchar(p,sizeof(p),);
   readln(n,m);
   for i:= to m do
   begin
     readln(x,y,w[i]);
     a[x,y]:=i;
     a[y,x]:=i;
   end;
   for i:= to n- do
   begin
     readln(x,y);
     k:=a[x,y];
     v[k]:=true;
     build(,k,,);
   end;
   for i:= to n do
     for j:=i+ to n do
       if (a[i,j]>) and not v[a[i,j]] then
       begin
         build(a[i,j],m+,,);
         fillchar(f,sizeof(f),false);
         t:=; q[]:=;
         dfs(i);
         for k:= to t do
           if w[q[k]]>w[a[i,j]] then build(q[k],a[i,j],,w[q[k]]-w[a[i,j]]);
       end;
   t:=m+;
   writeln(maxcost);
 end.