【POJ3680】Intervals（费用流）

题意：有n条线段，每条有起点，终点和一个权值

要求选取一些线段，使它们的权值和最大，并且使每一个点被覆盖不超过k次

1 ≤ K ≤ N ≤ 200

1 ≤ a_i < b_i ≤ 100,000, 1 ≤ w_i ≤ 100,000

思路：RYZ作业

费用流（经典？）模型之一

离散化后对于线段(a[i],b[i],w[i])，从a[i]到b[i]连容量为1,费用为w[i]的边

(i,i+1)之间都连容量为K，费用为0的边，以达到限制max<=k的效果

S——>1和N——>T之间都连容量为K，费用为0的边

跑最大费用最大流

 var head,vet,next,len1,len2,a,b,c,d,fan:array[..]of longint;
     inq:array[..]of boolean;
     q:array[..]of longint;
     pre:array[..,..]of longint;
     dis:array[..]of longint;
     n,m,k,up,i,tot,ans,s,source,src,cas,v,x,y:longint;
 
 procedure swap(var x,y:longint);
 var t:longint;
 begin
  t:=x; x:=y; y:=t;
 end;
 
 procedure qsort(l,r:longint);
 var i,j,mid:longint;
 begin
  i:=l; j:=r; mid:=d[(l+r)>>];
  repeat
   while mid>d[i] do inc(i);
   while mid<d[j] do dec(j);
   if i<=j then
   begin
    swap(d[i],d[j]);
    inc(i); dec(j);
   end;
  until i>j;
  if l<j then qsort(l,j);
  if i<r then qsort(i,r);
 end;
 
 function min(x,y:longint):longint;
 begin
  if x<y then exit(x);
  exit(y);
 end;
 
 function hash(x:longint):longint;
 var l,r,mid:longint;
 begin
  l:=; r:=up;
  while l<=r do
  begin
   mid:=(l+r)>>;
   if d[mid]=x then exit(mid);
   if d[mid]<x then l:=mid+
    else r:=mid-;
  end;
 end;
 
 procedure add(a,b,c,d:longint);
 begin
  inc(tot);
  next[tot]:=head[a];
  vet[tot]:=b;
  len1[tot]:=c;
  len2[tot]:=d;
  head[a]:=tot;
 
  inc(tot);
  next[tot]:=head[b];
  vet[tot]:=a;
  len1[tot]:=;
  len2[tot]:=-d;
  head[b]:=tot;
 end;
 
 function spfa:boolean;
 var u,e,v,i,top:longint;
 begin
  for i:= to s do
  begin
   dis[i]:=-(maxlongint>>);
   inq[i]:=false;
  end;
  top:=; q[]:=source; dis[source]:=; inq[source]:=true;
  while top> do
  begin
   u:=q[top]; dec(top); inq[u]:=false;
   e:=head[u];
   while e<> do
   begin
    v:=vet[e];
    if (len1[e]>)and(dis[u]+len2[e]>dis[v]) then
    begin
     dis[v]:=dis[u]+len2[e];
     pre[v,]:=u;
     pre[v,]:=e;
     if not inq[v] then
     begin
      inc(top); q[top]:=v; inq[v]:=true;
     end;
    end;
    e:=next[e];
   end;
  end;
  if dis[src]=-(maxlongint>>) then exit(false);
  exit(true);
 end;
 
 procedure mcf;
 var k,e,t:longint;
 begin
  k:=src; t:=maxlongint;
  while k<>source do
  begin
   t:=min(t,len1[pre[k,]]);
   k:=pre[k,];
  end;
  k:=src;
  while k<>source do
  begin
   e:=pre[k,];
   len1[e]:=len1[e]-t;
   len1[fan[e]]:=len1[fan[e]]+t;
   ans:=ans+t*len2[e];
   k:=pre[k,];
  end;
 end;
 
 begin
  assign(input,'poj3680.in'); reset(input);
  assign(output,'poj3680.out'); rewrite(output);
  readln(cas);
  for i:= to  do
   if i and = then fan[i]:=i+
    else fan[i]:=i-;
  for v:= to cas do
  begin
   for i:= to s do head[i]:=;
   s:=; tot:=; ans:=;
   //fillchar(head,sizeof(head),);
   read(n,k); m:=;
   for i:= to n do
   begin
    read(a[i],b[i],c[i]);
    inc(m); d[m]:=a[i];
    inc(m); d[m]:=b[i];
   end;
   qsort(,m);
   up:=;
   for i:= to m do
    if d[i]<>d[up] then begin inc(up); d[up]:=d[i]; end;
   for i:= to n do
   begin
    x:=hash(a[i]); y:=hash(b[i]);
    add(x,y,,c[i]);
   end;
   source:=up+; src:=up+; s:=up+;
   add(source,,k,);
   add(up,src,k,);
   for i:= to up- do add(i,i+,k,);
   while spfa do mcf;
   writeln(ans);
  end;
  close(input);
  close(output);
 end.