BZOJ 2300

题目传送门

凸包 动态删点并询问当前凸包周长

这道题在线应该也可以,但离线一下就比较好想了,动态删点变成了动态加点

先离线并记录哪些城市始终需要保护,然后把初始的三个点加进去,再把始终要保护的城市加进去并维护

然后倒着来依次加点(别人都用Treap Set神马的,尼玛真短…只会SBT…),每次加点的步骤如下:

       1.找到在凸包中的前驱节点(左边的点)l与后继节点(右边的点)r,用叉积判断如果在直线lr内侧就说明在凸包内侧然后跳出,否则说明lr这条边一定要删然后删掉并继续

       2.找到l的前驱ll,如果当前要插入的点在lll连线的外侧说明lll的线段将被覆盖(也就是说l将被覆盖),删掉l这个点,更新答案,从ll继续往下找,重复以上步骤直到找到最左端结点或发现不能覆盖节点l,然后将新连的边加入答案

       3.右端的操作类似

       4.将当前点加入肯德基豪华午餐,仅需15元凸包

Tips

如果每次修改都重新计算一遍凸包周长肯定慢死,所以开一个全局变量记录当前凸包周长修改时改这个就好了,反正一步步修改每一步只改一条边

求前驱和后继一定注意要找与当前点不同的,要不然不存在直线的

叉积真是个好东西…

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program bzoj_2300;
type point=record x,y:longint; end;
var p:array[1..100000]of point;
q:array[1..200000]of longint;
ans:array[1..200000]of extended;
curans:extended;
n,m,query,i,k,tot,root:longint;
cap:point;
s:array[0..100000]of record lc,rc,size,x,y:longint; end;
flag:array[1..100000]of boolean;
function sml(x1,y1,x2,y2:longint):boolean;
begin
if (x1<>x2) then exit(x1<x2);
exit(y1<y2);
end;
function dis(x1,y1,x2,y2:longint):extended;
begin
exit(sqrt(sqr(x2-x1)+sqr(y2-y1)));
end;
function cross(x1,y1,x2,y2:longint):longint;
begin
exit(x1*y2-x2*y1);
end;
procedure l_rotate(var t:longint);
var k:longint;
begin
k:=s[t].rc;
s[t].rc:=s[k].lc;
s[k].lc:=t;
s[k].size:=s[t].size;
s[t].size:=s[s[t].lc].size+s[s[t].rc].size+1;
t:=k;
end;
procedure r_rotate(var t:longint);
var k:longint;
begin
k:=s[t].lc;
s[t].lc:=s[k].rc;
s[k].rc:=t;
s[k].size:=s[t].size;
s[t].size:=s[s[t].lc].size+s[s[t].rc].size+1;
t:=k;
end;
procedure maintain(var t:longint;flag:boolean);
begin
if not flag then
if s[s[s[t].lc].lc].size>s[s[t].rc].size then r_rotate(t) else
if s[s[s[t].lc].rc].size>s[s[t].rc].size then
begin
l_rotate(s[t].lc);
r_rotate(t);
end else exit;
if flag then
if s[s[s[t].rc].rc].size>s[s[t].lc].size then l_rotate(t) else
if s[s[s[t].rc].lc].size>s[s[t].lc].size then
begin
r_rotate(s[t].rc);
l_rotate(t);
end else exit;
maintain(s[t].lc,false);
maintain(s[t].rc,true);
maintain(t,false);
maintain(t,true);
end;
procedure insert(var t:longint;x,y:longint);
begin
if t=0 then
begin
inc(tot);
t:=tot;
s[t].x:=x;
s[t].y:=y;
s[t].size:=1;
exit;
end;
inc(s[t].size);
if sml(x,y,s[t].x,s[t].y) then
begin
insert(s[t].lc,x,y);
maintain(t,false);
end else
begin
insert(s[t].rc,x,y);
maintain(t,true);
end;
end;
function pred(t,x,y:longint):point;
begin
pred.x:=0;
pred.y:=0;
while t<>0 do
if sml(x,y,s[t].x,s[t].y)or((s[t].x=x)and(s[t].y=y)) then t:=s[t].lc else
begin
pred.x:=s[t].x;
pred.y:=s[t].y;
t:=s[t].rc;
end;
end;
function succ(t,x,y:longint):point;
begin
succ.x:=n;
succ.y:=0;
while t<>0 do
if sml(s[t].x,s[t].y,x,y)or((s[t].x=x)and(s[t].y=y)) then t:=s[t].rc else
begin
succ.x:=s[t].x;
succ.y:=s[t].y;
t:=s[t].lc;
end;
end;
function delete(var t:longint;x,y:longint):longint;
var d:longint;
begin
dec(s[t].size);
if ((s[t].x=x)and(s[t].y=y))or(sml(x,y,s[t].x,s[t].y)and(s[t].lc=0))or(sml(s[t].x,s[t].y,x,y)and(s[t].rc=0)) then
begin
delete:=t;
if (s[t].lc=0)or(s[t].rc=0) then t:=s[t].lc+s[t].rc else
begin
d:=delete(s[t].lc,x,y+1);
s[t].x:=s[d].x;
s[t].y:=s[d].y;
end;
end else
if sml(x,y,s[t].x,s[t].y) then exit(delete(s[t].lc,x,y)) else exit(delete(s[t].rc,x,y));
end;
procedure addpoint(x,y:longint);
var l,r,ll,rr:point;
begin
l:=pred(root,x,y);
r:=succ(root,x,y);
if cross(x-l.x,y-l.y,r.x-l.x,r.y-l.y)>=0 then exit;
curans:=curans-dis(l.x,l.y,r.x,r.y);
while (l.x<>0)and(l.y<>0) do
begin
ll:=pred(root,l.x,l.y);
if cross(x-l.x,y-l.y,ll.x-l.x,ll.y-l.y)>=0 then
begin
curans:=curans-dis(l.x,l.y,ll.x,ll.y);
delete(root,l.x,l.y);
l:=ll;
end else break;
end;
curans:=curans+dis(l.x,l.y,x,y);
while (r.x<n)and(r.y<>0) do
begin
rr:=succ(root,r.x,r.y);
if cross(x-r.x,y-r.y,rr.x-r.x,rr.y-r.y)<=0 then
begin
curans:=curans-dis(r.x,r.y,rr.x,rr.y);
delete(root,r.x,r.y);
r:=rr;
end else break;
end;
curans:=curans+dis(r.x,r.y,x,y);
insert(root,x,y);
end;
begin
readln(n,cap.x,cap.y);
readln(m);
for i:=1 to m do read(p[i].x,p[i].y);
readln(query);
fillchar(q,sizeof(q),0);
root:=0;
tot:=0;
fillchar(s,sizeof(s),0);
insert(root,0,0);
insert(root,n,0);
insert(root,cap.x,cap.y);
curans:=dis(0,0,cap.x,cap.y)+dis(n,0,cap.x,cap.y);
fillchar(flag,sizeof(flag),true);
for i:=1 to query do
begin
read(k);
if k=2 then continue;
read(q[i]);
flag[q[i]]:=false;
end;
for i:=1 to m do if flag[i] then addpoint(p[i].x,p[i].y);
fillchar(ans,sizeof(ans),0);
for i:=query downto 1 do if q[i]=0 then ans[i]:=curans else addpoint(p[q[i]].x,p[q[i]].y);
for i:=1 to query do if ans[i]<>0 then writeln(ans[i]:0:2);
end.