poj1741 bzoj2152

树分治入门

poj1741是男人八题之一，经典的树分治的题目
这里用到的是点分治
核心思想是我们把某个点i作为根，把路径分为过点i和不过点i
先统计过点i这样的路径数，然后在统计其子树中的答案，这样就不断地划分成规模较小子问题。
要使划分最优，我们每次都选的是树的重心

 type node=record
        len,next,po:longint;
      end;

 var e:array[..] of node;
     w,p,d,a,size:array[..] of longint;
     v:array[..] of boolean;
     root,sum,n,t,ans,k,i,x,y,z,len:longint;

 function max(a,b:longint):longint;
   begin
     if a>b then exit(a) else exit(b);
   end;

 procedure sort(l,r: longint);
   var i,j,x,y: longint;
   begin
     i:=l;
     j:=r;
     x:=a[(l+r) div ];
     repeat
       while a[i]<x do inc(i);
       while x<a[j] do dec(j);
       if not(i>j) then
       begin
         y:=a[i];
         a[i]:=a[j];
         a[j]:=y;
         inc(i);
         j:=j-;
       end;
     until i>j;
     if l<j then sort(l,j);
     if i<r then sort(i,r);
   end;

 procedure add(x,y,z:longint);
   begin
     inc(len);
     e[len].po:=y;
     e[len].len:=z;
     e[len].next:=p[x];
     p[x]:=len;
   end;

 procedure getroot(x,fa:longint);  //选择重心
   var i,y:longint;
   begin
     i:=p[x];
     size[x]:=;
     w[x]:=;
     while i<> do
     begin
       y:=e[i].po;
       if (not v[y]) and (y<>fa) then
       begin
         getroot(y,x);
         size[x]:=size[x]+size[y];
         w[x]:=max(w[x],size[y]);
       end;
       i:=e[i].next;
     end;
     w[x]:=max(w[x],sum-size[x]);
     if w[x]<w[root] then root:=x;
   end;

 procedure deep(x,fa:longint);
   var i,y:longint;
   begin
     inc(t);
     a[t]:=d[x];
     i:=p[x];
     while i<> do
     begin
       y:=e[i].po;
       if not v[y] and (y<>fa) then
       begin
         d[y]:=d[x]+e[i].len;
         deep(y,x);
       end;
       i:=e[i].next;
     end;
   end;

 function calc(x,now:longint):longint;
   var i,l,r:longint;
   begin
     t:=;
     d[x]:=now;
     calc:=;
     deep(x,);
     sort(,t);
     l:=;
     r:=t;
     while l<r do
     begin
       if a[l]+a[r]<=k then
       begin
         calc:=calc+r-l;
         inc(l);
       end
       else dec(r);
     end;
   end;

 procedure work(x:longint);
   var i,y:longint;
   begin
     ans:=ans+calc(x,);
     i:=p[x];
     v[x]:=true;
     while i<> do
     begin
       y:=e[i].po;
       if not v[y] then
       begin
         ans:=ans-calc(y,e[i].len);  //之前的计算会导致lca不为root的点对被算入，实际它们的路径不过重心，这里要减去
         sum:=size[y];
         root:=;
         getroot(y,);
         work(root);
       end;
       i:=e[i].next;
     end;
   end;

 begin
   readln(n,k);
   while n<> do
   begin
     len:=;
     fillchar(p,sizeof(p),);
     for i:= to n- do
     begin
       readln(x,y,z);
       add(x,y,z);
       add(y,x,z);
     end;
     fillchar(v,sizeof(v),false);
     sum:=n;
     w[]:=;
     getroot(,);
     ans:=;
     work(root);
     writeln(ans);
     readln(n,k);
   end;
 end.

bzoj2152是更水的树分治……