P2686 Matrix

还是二分图，源点 S 汇点 T ， x[i]->y[i] 流量 1 权值 -cost 作为限制不重点， y[i]->x[i+1] /y[i]->x[i+n]  流量 inf 权值 0 为边， S->x[1] 流量 2 权值 0 为起点， y[n*n]->T 流量 2 权值 0 为终点， x[1]->y[1]/x[n*n]->y[n*n] 流量 1 权值 0 方便回来的时候不重复计算cost。这样的话最短路找增广路，最短路径值的相反数即为最大值，本题是最大费用最大流。

  1 const maxe=1000000; inf=1000000000;
  2 type
  3   node=record
  4     next,t,cap,cost:longint;
  5   end;
  6 var time,n,k,s,t,ans,temp,cnt:longint;
  7 b:array[0..maxe] of node;
  8 head,go,f,d:array[0..maxe] of longint;
  9 p:array[0..maxe] of boolean;
 10 procedure add(u,v,x,y:longint);
 11 begin
 12   inc(cnt);
 13   with b[cnt] do
 14     begin
 15       next:=head[u];
 16       t:=v;
 17       cap:=x;
 18       cost:=y;
 19     end;
 20   head[u]:=cnt;
 21 end;
 22 procedure insert(u,v,x,y:longint);
 23 begin
 24   add(u,v,x,y);
 25   add(v,u,0,-y);
 26 end;
 27 procedure intit;
 28 var i,j,k,now,temp:longint;
 29 begin
 30   cnt:=-1; k:=n*n; s:=0; t:=2*k+1; ans:=0;
 31   fillchar(head,sizeof(head),255);
 32   fillchar(b,sizeof(b),255);
 33   for i:=1 to n do
 34     begin
 35       for j:=1 to n do
 36         begin
 37           read(temp); now:=(i-1)*n+j;
 38           insert(now,now+k,1,-temp);
 39           if i<>n then insert(now+k,now+n,inf,0);
 40           if j<>n then insert(now+k,now+1,inf,0);
 41         end;
 42       readln;
 43     end;
 44   insert(s,1,2,0);
 45   insert(1,k+1,1,0);
 46   insert(k,2*k,1,0);
 47   insert(2*k,t,2,0);
 48   readln(n);
 49 end;
 50 function spfa:longint;
 51 var e,v,l,r,point:longint;
 52 begin
 53   fillchar(p,sizeof(p),true);
 54   fillchar(go,sizeof(go),255);
 55   for l:=s to t do d[l]:=inf;
 56   l:=1; r:=1; f[1]:=s; p[s]:=false; d[s]:=0;
 57   while l<=r do
 58     begin
 59       point:=f[l];
 60       e:=head[point];
 61       while e<>-1 do
 62         begin
 63           v:=b[e].t;
 64           if (d[v]>d[point]+b[e].cost) and (b[e].cap>0) then
 65             begin
 66               d[v]:=d[point]+b[e].cost;
 67               go[v]:=e;
 68               if p[v] then
 69                 begin
 70                   p[v]:=false;
 71                   inc(r);
 72                   f[r]:=v;
 73                 end;
 74             end;
 75           e:=b[e].next;
 76         end;
 77       inc(l);
 78       p[point]:=true;
 79     end;
 80   if d[t]<>inf then exit(-d[t])
 81     else exit(-1);
 82 end;
 83 function min(a,b:longint):longint;
 84 begin if a>b then exit(b) else exit(a); end;
 85 function delete:longint;
 86 var now,flow:longint;
 87 begin
 88   now:=t; flow:=inf;
 89   while go[now]<>-1 do
 90     begin
 91       flow:=min(flow,b[go[now]].cap);
 92       now:=b[go[now] xor 1].t;
 93     end;
 94   now:=t;
 95   while go[now]<>-1 do
 96     begin
 97       dec(b[go[now]].cap,flow);
 98       inc(b[go[now] xor 1].cap,flow);
 99       now:=b[go[now] xor 1].t;
100     end;
101   exit(flow);
102 end;
103 begin
104   readln(n);
105   while not(eof) do
106     begin
107       intit;
108       temp:=spfa;
109       while temp>0 do
110         begin
111           inc(ans,temp*delete);
112           temp:=spfa;
113         end;
114       writeln(ans);
115     end;
116 end.

其实代码里面乘的delete也是不需要的(因为最大流一定为1)。

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