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通过USACO草地排水学习了一下网络流,终于写好了几个模板。
最大流
BFS求增广路径
简述:通过BFS在网络中找出一条最短增广路径并修改流量(前向弧加可改进量X,后向弧则减去X),当不存在增广路径时得出最大流,时间效率O(nm^2)。
{ ID: qty1272 PROG: ditch LANG: PASCAL } program ditch; var c,f:array[0..200,0..200]of longint; path,u:array[0..200]of longint; n,i,m,x,y,z,s,t,max:longint; procedure change(a:longint); var i,w:longint; begin w:=t; repeat i:=w; w:=abs(path[i]); if path[i]<0 then f[i,w]:=f[i,w]-a; if path[i]>0 then f[w,i]:=f[w,i]+a; until w=s; end; function find:longint; var i:longint; begin i:=1; while (i<=n)and not((path[i]<>0)and(u[i]=0)) do inc(i); if i>n then find:=0 else find:=i; end; function ford(var a:longint):boolean; var i,w:longint; begin ford:=true; fillchar(path,sizeof(path),0); fillchar(u,sizeof(u),0); path[s]:=s; while path[t]=0 do begin x:=find; if x=0 then exit; for i:=1 to n do if (path[i]=0)and((c[x,i]<>0)or(c[i,x]<>0)) then begin if f[x,i]<c[x,i] then path[i]:=x; if f[i,x]>0 then path[i]:=-x; end; u[x]:=1; end; w:=t; a:=maxlongint; repeat i:=w; w:=abs(path[i]); if path[i]<0 then x:=f[i,w]; if path[i]>0 then x:=c[w,i]-f[w,i]; if x<a then a:=x; until w=s; ford:=false; end; procedure shuchu; var i:longint; begin max:=0; for i:=1 to n do if f[i,t]<>0 then max:=max+f[i,t]; writeln(max); end; procedure work; var x:longint; g:boolean; begin s:=1; t:=n; repeat g:=ford(x); if g then shuchu else change(x); until g; end; begin assign(input,‘ditch.in‘); reset(input); assign(output,‘ditch.out‘); rewrite(output); readln(m,n); for i:=1 to m do begin readln(x,y,z); c[x,y]:=c[x,y]+z; end; work; close(input); close(output); end.
dinic算法
简述:先BFS弄出层次图,在利用DFS找增广路径,时间效率O(n^2m)。
{ ID: qty1272 PROG: ditch LANG: PASCAL } program ditch; var c,f:array[0..200,0..200]of longint; team,d:array[0..200]of longint; g:array[0..200]of boolean; n,i,m,x,y,z,s,t,max,sum:longint; function min(x,y:longint):longint; begin if x<y then min:=x else min:=y; end; function bfs:boolean; var i,u,head,tail:longint; begin fillchar(g,sizeof(g),false); fillchar(d,sizeof(d),0); head:=0; tail:=1; g[s]:=true; team[1]:=s; while head<tail do begin head:=head+1; u:=team[head]; for i:=1 to n do if (not g[i])and(c[u,i]>f[u,i]) then begin d[i]:=d[u]+1; g[i]:=true; tail:=tail+1; team[tail]:=i; end; end; exit(g[t]); end; function dfs(x,flow:longint):longint; var i,tmp,k:longint; begin tmp:=flow; if x=t then exit(flow); for i:=1 to n do if (c[x,i]>f[x,i])and(d[x]+1=d[i]) then begin k:=dfs(i,min(c[x,i]-f[x,i],flow)); f[x,i]:=f[x,i]+k; f[i,x]:=f[i,x]-k; flow:=flow-k; end; exit(tmp-flow); end; procedure work; begin sum:=0;s:=1; t:=n; while bfs do begin inc(sum,dfs(s,maxlongint)); end; writeln(sum); end; begin assign(input,‘ditch.in‘); reset(input); assign(output,‘ditch.out‘); rewrite(output); readln(m,n); for i:=1 to m do begin readln(x,y,z); c[x,y]:=c[x,y]+z; end; work; close(input); close(output); end.
令人比较疑惑的是DFS后面几句 flow:=flow-k; exit(tmp-flow); 这分明是返回k的值,但为什么要这么做呢,因为k在前面被DFS赋值了,不能直接返回该值,否则错误。
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原文地址:http://www.cnblogs.com/qtyytq/p/4296231.html