【Codevs1227】方格取数2（费用流）

题意：给出一个n*n的矩阵,每一格有一个非负整数Aij,(Aij <= 1000)

现在从(1,1)出发,可以往右或者往下走,最后到达(n,n),每达到一格,把该格子的数取出来,该格子的数就变成0,

这样一共走K次,现在要求K次所达到的方格的数的和最大。

n<=50,k<=10

思路：费用流

将每个点裂成一个出点和一个入点(i,j,1..2)，这个思路与最大流类似

(i,j,1)->(i,j,2) 连两条边：

容量为1，费用为a[i,j]

容量为K，费用为0

(i,j,2)->(i+1,j,1)连容量为K，费用为0的边 (i,j+1)类似

(n,n,2)->T 连流量为K，费用为0的边限制流量

跑最大费用最大流就行了，其实就是SPFA的三角不等式改个方向

 var fan:array[..]of longint;
     q:array[..]of longint;
     head,vet,next,len1,len2:array[..]of longint;
     pre:array[..,..]of longint;
     inq:array[..]of boolean;
     dis:array[..]of longint;
     a:array[..,..]of longint;
     num:array[..,..,..]of longint;
     n,m,k1,i,j,k,tot,s,source,src:longint;
     ans:int64;

 function min(x,y:longint):longint;
 begin
  if x<y then exit(x);
  exit(y);
 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,t,w,i,e,v:longint;
 begin
  for i:= to s do
  begin
   dis[i]:=-maxlongint;
   inq[i]:=false;
  end;
  t:=; w:=; q[]:=source; inq[source]:=true; dis[source]:=;
  while t<w do
  begin
   inc(t); u:=q[t mod (s+)];
   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
     pre[v,]:=u; pre[v,]:=e;
     dis[v]:=dis[u]+len2[e];
     if not inq[v] then
     begin
      inc(w); q[w mod (s+)]:=v;
      inq[v]:=true;
     end;
    end;
    e:=next[e];
   end;
  end;
  if dis[src]=-maxlongint then exit(false)
   else exit(true);
 end;

 procedure mcf;
 var k,e:longint;
     t:int64;
 begin
  k:=src; t:=maxlongint;
  while k<>source do
  begin
   e:=pre[k,]; k:=pre[k,];
   t:=min(t,len1[e]);
  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,'codevs1227.in'); reset(input);
  assign(output,'codevs1227.out'); rewrite(output);
  readln(n,k1);
  for i:= to  do
   if i mod = then fan[i]:=i+
    else fan[i]:=i-;
  for i:= to n do
   for j:= to n do read(a[i,j]);
  for i:= to n do
   for j:= to n do
    for k:= to  do
    begin
     inc(s); num[i,j,k]:=s;
    end;
  for i:= to n do
   for j:= to n do
   begin
    add(num[i,j,],num[i,j,],,a[i,j]);
    add(num[i,j,],num[i,j,],k1,);
    if j+<=n then add(num[i,j,],num[i,j+,],k1,);
    if i+<=n then add(num[i,j,],num[i+,j,],k1,);
   end;
  source:=; src:=s+; inc(s);
  add(num[n,n,],src,k1,);
  while spfa do mcf;
  writeln(ans);
  close(input);
  close(output);
 end.