【UVA11082】Matrix Decompressing（有上下界的网络流）

题意：给出一个矩阵前i列所有元素的和，和前j行所有元素的和，求这个矩阵解压以后的原型。（答案不唯一）

n,m<=20,1<=a[i,j]<=20

思路：这道题把边上的流量作为原先矩阵中的点

把每一行，每一列都看成一个点

S——>i行 a[i]-m

i行——>j列 19

j列——>T b[i]-n

跑最大流，边(i,j+n)上的流量就是a[i,j]的值

为什么容量是a[i]-m,19,b[i]-n？

因为点权（边权）不能为0，所以要先把所有值+1，上限就-1，输出的时候+1即可

 var fan:array[..]of longint;
     head,vet,next,len,gap,dis,a,b,c1,c2:array[..]of longint;
     num:array[..,..]of longint;
     n,m,i,j,tot,s,source,src,cas,v:longint;
 
 procedure add(a,b,c:longint);
 begin
  inc(tot);
  next[tot]:=head[a];
  vet[tot]:=b;
  len[tot]:=c;
  head[a]:=tot;
 
  inc(tot);
  next[tot]:=head[b];
  vet[tot]:=a;
  len[tot]:=;
  head[b]:=tot;
 end;
 
 function min(x,y:longint):longint;
 begin
  if x<y then exit(x);
  exit(y);
 end;
 
 function dfs(u,aug:longint):longint;
 var e,v,t,flow,val:longint;
 begin
  if u=src then exit(aug);
  e:=head[u]; flow:=; val:=s-;
  while e<> do
  begin
   v:=vet[e];
   if len[e]> then
   begin
    if dis[u]=dis[v]+ then
    begin
     t:=dfs(v,min(len[e],aug-flow));
     len[e]:=len[e]-t;
     len[fan[e]]:=len[fan[e]]+t;
     flow:=flow+t;
     if dis[source]>=s then exit(flow);
     if aug=flow then break;
    end;
    val:=min(val,dis[v]);
   end;
   e:=next[e];
  end;
  if flow= then
  begin
   dec(gap[dis[u]]);
   if gap[dis[u]]= then dis[source]:=s;
   dis[u]:=val+;
   inc(gap[dis[u]]);
  end;
  exit(flow);
 end;
 
 function maxflow:longint;
 var ans:longint;
 begin
  fillchar(gap,sizeof(gap),);
  fillchar(dis,sizeof(dis),);
  gap[]:=s; ans:=;
  while dis[source]<s do ans:=ans+dfs(source,maxlongint);
  exit(ans);
 end;
 
 begin
  assign(input,'UVA11082.in'); reset(input);
  assign(output,'UVA11082.out'); rewrite(output);
  for i:= to  do
   if i mod = then fan[i]:=i+
    else fan[i]:=i-;
  readln(cas);
  for v:= to cas do
  begin
   fillchar(head,sizeof(head),); tot:=;
   fillchar(num,sizeof(num),);
   fillchar(len,sizeof(len),);
   readln(n,m);
   for i:= to n do
   begin
    read(a[i]); c1[i]:=a[i]-a[i-];
   end;
   for i:= to m do
   begin
    read(b[i]); c2[i]:=b[i]-b[i-];
   end;
   s:=n+m+; source:=n+m+; src:=n+m+;
   for i:= to n do add(source,i,c1[i]-m);
   for i:= to m do add(i+n,src,c2[i]-n);
   for i:= to n do
    for j:= to m do
    begin
     num[i,j]:=tot+;
     add(i,j+n,);
    end;
   maxflow;
   writeln('Matrix ',v);
   for i:= to n do
   begin
    for j:= to m- do write(len[num[i,j]]+,' ');
    write(len[num[i,m]]+);
    writeln;
   end;
   if v<>cas then writeln;
  end;
 
  close(input);
  close(output);
 end.