【POJ2482】Stars in Your Window（线段树，扫描线）

题意：在二维坐标系中有一些带权值的点，要求用一个长宽指定不能互换的框套住其中的一些，使得它们的权值和最大。

n<=10000 x,y<=2^31

思路：首先按X排序，将Y坐标离散化，X坐标用扫描线框定，每个点(x,y)在x中只对y有a[i]的贡献，y+h有-a[i]的贡献，线段树（树状数组更好写）维护最大子段和即可。

 var t:array[..]of record
                            l,r,s,m:int64;
                           end;
     x,y,c,a,h:array[..]of int64;
     n,m,i,j,tt,ww,up,w1,h1:longint;
     ans:int64;

 procedure swap(var x,y:int64);
 var t:int64;
 begin
  t:=x; x:=y; y:=t;
 end;

 procedure qsort(l,r:longint);
 var i,j,mid1,mid2:longint;
 begin
  i:=l; j:=r; mid1:=x[(l+r)>>]; mid2:=y[(l+r)>>];
  repeat
   while (mid1>x[i])or((mid1=x[i])and(mid2>y[i])) do inc(i);
   while (mid1<x[j])or((mid1=x[j])and(mid2<y[j])) do dec(j);
   if i<=j then
   begin
    swap(x[i],x[j]);
    swap(y[i],y[j]);
    swap(a[i],a[j]);
    inc(i); dec(j);
   end;
  until i>j;
  if l<j then qsort(l,j);
  if i<r then qsort(i,r);
 end;

 procedure qsort2(l,r:longint);
 var i,j:longint;
     mid:int64;
 begin
  i:=l; j:=r; mid:=c[(l+r)>>];
  repeat
   while mid>c[i] do inc(i);
   while mid<c[j] do dec(j);
   if i<=j then
   begin
    swap(c[i],c[j]);
    inc(i); dec(j);
   end;
  until i>j;
  if l<j then qsort2(l,j);
  if i<r then qsort2(i,r);
 end;

 function max(x,y:int64):int64;
 begin
  if x>y then exit(x);
  exit(y);
 end;

 procedure pushup(p:longint);
 var ls,rs:longint;
 begin
  ls:=p<<; rs:=ls+;
  t[p].l:=max(t[ls].l,t[ls].s+t[rs].l);
  t[p].r:=max(t[rs].r,t[rs].s+t[ls].r);
  t[p].m:=max(t[ls].r+t[rs].l,max(t[ls].m,t[rs].m));
 end;

 procedure update(l,r,x,v,p:longint);
 var mid:longint;
 begin
  if l=r then
  begin
   t[p].s:=t[p].s+v;
   t[p].l:=t[p].s; t[p].r:=t[p].s; t[p].m:=t[p].s;
   exit;
  end;
  mid:=(l+r)>>;
  if x<=mid then update(l,mid,x,v,p<<)
   else update(mid+,r,x,v,p<<+);
  t[p].s:=t[p].s+v;
  pushup(p);
 end;

 function hash(x:int64):longint;
 var l,r,mid,last:longint;
 begin
  l:=; r:=up; last:=;
  while l<=r do
  begin
   mid:=(l+r)>>;
   if x=h[mid] then begin last:=mid; r:=mid-; end;
   if x<h[mid] then r:=mid-;
   if x>h[mid] then l:=mid+;
  end;
  exit(last);
 end;

 begin
  assign(input,'poj2482.in'); reset(input);
  assign(output,'poj2482.out'); rewrite(output);
  while not eof do
  begin
   readln(n,w1,h1);
   if n= then break;
   for i:= to n do read(x[i],y[i],a[i]);
   qsort(,n);
   m:=;
   for i:= to n do
   begin
    inc(m); c[m]:=y[i];
    inc(m); c[m]:=y[i]+h1;
   end;
   qsort2(,m);
   up:=; h[]:=c[];
   for i:= to m do
    if c[i]>c[i-] then
    begin
     if c[i]=c[i-]+ then begin inc(up); h[up]:=c[i]; end
      else
      begin
       inc(up); h[up]:=c[i-];
       inc(up); h[up]:=c[i];
      end;
    end;
   ans:=-maxlongint;
   tt:=; ww:=;
   while ww<n do
   begin
    inc(ww);
    while (tt<=n)and(x[tt]+w1-<x[ww]) do
    begin
     update(,up,hash(y[tt]),-a[tt],);
     update(,up,hash(y[tt]+h1),a[tt],);
     inc(tt);
    end;
    update(,up,hash(y[ww]),a[ww],);
    update(,up,hash(y[ww]+h1),-a[ww],);
    ans:=max(ans,t[].m);
   end;
   writeln(ans);
   for i:= to up<< do
   begin
    t[i].s:=; t[i].l:=; t[i].r:=; t[i].m:=;
   end;
  end;
  close(input);
  close(output);
 end.