为了求矩形中的点的数量,首先可以想到的就是二维线段树或者二维树状数组,但是这道题的数据范围比较大,即使离散化之后还有200万多的点,会超空间。所以只能用一维的树状数组,可以先把所有点(包括查询矩形的四个顶点)按照第一关键字Y轴升序排序,第二关键字X轴升序排序。然后离散化,然后再扫一遍,如果是点就插入到树状数组中,如果是查询就求和,其值为右上角为改点,左下角为原点的矩形内的点,每个查询可以通过四个顶点的加减来考虑。有两点要考虑:1.要考虑边界,可以通过给点设值来排序。2.对N=0的情况要特判。
program p1935; const p:array[0..4] of longint=(4,1,3,5,2); type tree=record x,y:longint; end; num=record x,y,sx,pd,ls:longint; end; question=record x1,x2,y1,y2:longint; w:array[0..4] of longint; end; hzb=record x,sx:longint; end; var t:array[1..500000] of tree; q:array[1..500000] of question; x:array[0..3000000] of num; h:array[0..3000000] of longint; c:array[1..3000000] of longint; len,n,m,i,j:longint; procedure add(k1,k2,k3,k4:longint); begin inc(len); x[len].x:=k1; x[len].y:=k2; x[len].sx:=k4; x[len].pd:=k3; end; function bo(k1,k2:longint):boolean; begin if x[k1].y<x[k2].y then exit(true); if x[k1].y>x[k2].y then exit(false); if x[k1].pd<=1 then exit(true); if x[k2].pd<=1 then exit(false); if x[k1].x<x[k2].x then exit(true); if x[k1].x>x[k2].x then exit(false); if x[k1].pd<=x[k2].pd then exit(true); exit(false); end; procedure quick(first,en:longint); var i,j:longint; begin {writeln(first,' ',en);} i:=first; j:=en; x[0]:=x[first]; while i<j do begin {writeln(x[i].x,' ',x[i].y,' ',x[i].pd); writeln(x[j].x,' ',x[j].y,' ',x[j].pd); writeln(x[0].x,' ',x[0].y,' ',x[0].pd);} while (i<j) and (bo(0,j)=true) do dec(j); if i<j then x[i]:=x[j]; while (i<j) and (bo(i,0)=true) do inc(i); if i<j then x[j]:=x[i]; end; x[i]:=x[0]; if i>first+1 then quick(first,i-1); if i<en-1 then quick(i+1,en); end; procedure sort(first,en:longint); var i,j:longint; begin i:=first; j:=en; h[0]:=h[i]; while i<j do begin while (i<j) and ((x[h[j]].x>x[h[0]].x) or ((x[h[j]].x=x[h[0]].x)) and (p[x[h[j]].pd]>=p[x[h[0]].pd])) do dec(j); if i<j then h[i]:=h[j]; while (i<j) and ((x[h[i]].x<x[h[0]].x) or ((x[h[i]].x=x[h[0]].x)) and (p[x[h[i]].pd]<p[x[h[0]].pd])) do inc(i); if i<j then h[j]:=h[i]; end; h[i]:=h[0]; if i>first+1 then sort(first,i-1); if i<en-1 then sort(i+1,en); end; function lowbit(k:longint):longint; begin exit(k and -k); end; procedure add(k:longint); var i,j:longint; begin i:=k; while i<=len do begin inc(c[i]); i:=i+lowbit(i); end; end; function total(k:longint):longint; var i,j,num:longint; begin i:=k; num:=0; while i>0 do begin num:=num+c[i]; i:=i-lowbit(i); end; exit(num); end; begin readln(n,m); len:=0; fillchar(x,sizeof(x),0); for i:=1 to n do begin readln(t[i].x,t[i].y); add(t[i].x,t[i].y,2,i); end; if n=0 then begin for i:=1 to m do writeln(0); exit; end; for i:=1 to m do begin readln(q[i].x1,q[i].y1,q[i].x2,q[i].y2); add(q[i].x1,q[i].y1,1,i); add(q[i].x2,q[i].y2,3,i); add(q[i].x1,q[i].y2,4,i); add(q[i].x2,q[i].y1,0,i); end; quick(1,len); fillchar(c,sizeof(c),0); for i:=1 to len do h[i]:=i; sort(1,len); for i:=1 to len do x[h[i]].ls:=i; for i:=1 to len do if x[i].pd=2 then add(x[i].ls) else q[x[i].sx].w[x[i].pd]:=total(x[i].ls); for i:=1 to m do begin writeln(q[i].w[3]+q[i].w[1]-q[i].w[0]-q[i].w[4]); end; end.