LUOGU P4088 [USACO18FEB]Slingshot(线段树)
解题思路
推了推式子发现是个二维数点，想了想似乎排序加线段树难写，就写了个树套树，结果写完看见空间才\(128M\)。。各种奇技淫巧卡空间还是\(MLE\)到天上。后来只好乖乖的写排序+线段树。做法就是把式子写出来，然后把绝对值分类讨论成四种情况，发现这就是二维数点，然后讨论每种情况排序算最小值。
代码1(树套树 30pts)
#include<iostream>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<cstdlib>
#include<algorithm>
using namespace std;
typedef long long LL;
const int N=200005;
const int M=N*20;
inline int rd(){
int x=0,f=1; char ch=getchar();
while(!isdigit(ch)) f=ch=='-'?0:1,ch=getchar();
while(isdigit(ch)) x=(x<<1)+(x<<3)+ch-'0',ch=getchar();
return f?x:-x;
}
int n,m,xx[N<<2],yy[N<<2],tt[N],cnt,u,tot,cpy[N<<2],rt,num;
LL ans=1e18;
struct Segment_Tree_in{
int rt[N<<2],ls[M],rs[M];
LL Min[M];
inline void init(){
memset(Min,0x3f,sizeof(Min));
}
void update(int &x,int l,int r,int pos,LL w){
if(!x) x=++tot; Min[x]=min(Min[x],w);
if(l==r) return; int mid=(l+r)>>1;
if(pos<=mid) update(ls[x],l,mid,pos,w);
else update(rs[x],mid+1,r,pos,w);
}
LL query(int x,int l,int r,int L,int R){
if(!x) return 1e18;
if(L<=l && r<=R) return Min[x];
int mid=(l+r)>>1; LL ret=1e18;
if(L<=mid) ret=min(ret,query(ls[x],l,mid,L,R));
if(mid<R) ret=min(ret,query(rs[x],mid+1,r,L,R));
return ret;
}
}tree2[2];
struct Segment_Tree_out{
int ls[N<<2],rs[N<<2];
void update(int &x,int l,int r,int i,int op){
if(!x) x=++num;
tree2[0].update(tree2[0].rt[x],1,u,yy[i],1ll*cpy[xx[i]]*op+cpy[yy[i]]+tt[i]);
tree2[1].update(tree2[1].rt[x],1,u,yy[i],1ll*cpy[xx[i]]*op-cpy[yy[i]]+tt[i]);
if(l==r) return; int mid=(l+r)>>1;
if(xx[i]<=mid) update(ls[x],l,mid,i,op);
else update(rs[x],mid+1,r,i,op);
}
LL query(int x,int l,int r,int x1,int x2,int y1,int y2,int op){
if(!x) return 1e18;
if(x1<=l && r<=x2) return tree2[op].query(tree2[op].rt[x],1,u,y1,y2);
int mid=(l+r)>>1; LL ret=1e18;
if(x1<=mid) ret=min(ret,query(ls[x],l,mid,x1,x2,y1,y2,op));
if(mid<x2) ret=min(ret,query(rs[x],mid+1,r,x1,x2,y1,y2,op));
return ret;
}
}tree1[2];
//0+ 1-
int main(){
tree2[0].init(); tree2[1].init();
n=rd(),m=rd(); int x,y,t,X,Y;
for(int i=1;i<=n;i++){
x=rd(),y=rd(),t=rd();
xx[i]=x; yy[i]=y; tt[i]=t;
cpy[++cnt]=x; cpy[++cnt]=y;
}
for(int i=1;i<=m;i++){
x=rd(),y=rd();
cpy[++cnt]=x; cpy[++cnt]=y;
xx[i+n]=x; yy[i+n]=y;
}
sort(cpy+1,cpy+1+cnt);
u=unique(cpy+1,cpy+1+cnt)-cpy-1;
for(int i=1;i<=n;i++){
xx[i]=lower_bound(cpy+1,cpy+1+u,xx[i])-cpy;
yy[i]=lower_bound(cpy+1,cpy+1+u,yy[i])-cpy;
tree1[0].update(rt,1,u,i,1);
tree1[1].update(rt,1,u,i,-1);
}
for(int i=1;i<=m;i++){
x=lower_bound(cpy+1,cpy+1+u,xx[i+n])-cpy;
y=lower_bound(cpy+1,cpy+1+u,yy[i+n])-cpy;
ans=abs(cpy[x]-cpy[y]);
ans=min(ans,tree1[0].query(1,1,u,x+1,u,y+1,u,0)-cpy[x]-cpy[y]);
ans=min(ans,tree1[0].query(1,1,u,x+1,u,1,y,1)-cpy[x]+cpy[y]);
ans=min(ans,tree1[1].query(1,1,u,1,x,y+1,u,0)+cpy[x]-cpy[y]);
ans=min(ans,tree1[1].query(1,1,u,1,x,1,y,1)+cpy[x]+cpy[y]);
printf("%lld\n",ans);
}
return 0;
}
代码2
#include<iostream>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<cstdlib>
#include<algorithm>
using namespace std;
typedef long long LL;
const int N=400005;
inline int rd(){
int x=0,f=1; char ch=getchar();
while(!isdigit(ch)) f=ch=='-'?0:1,ch=getchar();
while(isdigit(ch)) x=(x<<1)+(x<<3)+ch-'0',ch=getchar();
return f?x:-x;
}
int n,m,xx[N<<2],yy[N<<2],tt[N],cnt,u,cpy[N<<2];
LL ans[N];
struct Segment_Tree{
LL Min[N<<2];
inline void init(){
memset(Min,0x3f,sizeof(Min));
}
void update(int x,int l,int r,int pos,LL w){
Min[x]=min(Min[x],w);
if(l==r) return; int mid=(l+r)>>1;
if(pos<=mid) update(x<<1,l,mid,pos,w);
else update(x<<1|1,mid+1,r,pos,w);
}
LL query(int x,int l,int r,int L,int R){
if(L<=l && r<=R) return Min[x];
int mid=(l+r)>>1; LL ret=1e18;
if(L<=mid) ret=min(ret,query(x<<1,l,mid,L,R));
if(mid<R) ret=min(ret,query(x<<1|1,mid+1,r,L,R));
return ret;
}
}tree;
struct Node{
int x,y,t,op,id;
Node(int _x=0,int _y=0,int _t=0,int _op=0,int _id=0){
x=_x; y=_y; t=_t; op=_op; id=_id;
}
}node[N];
inline bool cmp1(Node A,Node B){
return (A.x==B.x)?A.y<B.y:A.x<B.x;
}
inline bool cmp2(Node A,Node B){
return (A.x==B.x)?A.y>B.y:A.x<B.x;
}
inline bool cmp3(Node A,Node B){
return (A.x==B.x)?A.y<B.y:A.x>B.x;
}
inline bool cmp4(Node A,Node B){
return (A.x==B.x)?A.y>B.y:A.x>B.x;
}
int main(){
n=rd(),m=rd(); int x,y,t,pos;
for(int i=1;i<=n;i++){
x=rd(),y=rd(),t=rd();
xx[i]=x; yy[i]=y; tt[i]=t;
cpy[++cnt]=x; cpy[++cnt]=y;
}
for(int i=1;i<=m;i++){
x=rd(),y=rd(); ans[i]=abs(x-y);
cpy[++cnt]=x; cpy[++cnt]=y;
xx[i+n]=x; yy[i+n]=y;
}
sort(cpy+1,cpy+1+cnt);
u=unique(cpy+1,cpy+1+cnt)-cpy-1;
for(int i=1;i<=n;i++) {
xx[i]=lower_bound(cpy+1,cpy+1+u,xx[i])-cpy;
yy[i]=lower_bound(cpy+1,cpy+1+u,yy[i])-cpy;
node[i]=Node(xx[i],yy[i],tt[i],0,0);
}
for(int i=1;i<=m;i++){
x=lower_bound(cpy+1,cpy+1+u,xx[i+n])-cpy;
y=lower_bound(cpy+1,cpy+1+u,yy[i+n])-cpy;
node[i+n]=Node(x,y,0,1,i);
}
tree.init();
sort(node+1,node+1+n+m,cmp1);
for(int i=1;i<=n+m;i++){
x=node[i].x,y=node[i].y;
if(!node[i].op) tree.update(1,1,u,y,-cpy[x]-cpy[y]+node[i].t);
else ans[node[i].id]=min(ans[node[i].id],tree.query(1,1,u,1,y)+cpy[x]+cpy[y]);
}
tree.init();
sort(node+1,node+1+n+m,cmp2);
for(int i=1;i<=n+m;i++){
x=node[i].x,y=node[i].y;
if(!node[i].op) tree.update(1,1,u,y,-cpy[x]+cpy[y]+node[i].t);
else ans[node[i].id]=min(ans[node[i].id],tree.query(1,1,u,y+1,u)+cpy[x]-cpy[y]);
}
tree.init();
sort(node+1,node+1+n+m,cmp3);
for(int i=1;i<=n+m;i++){
x=node[i].x,y=node[i].y;
if(!node[i].op) tree.update(1,1,u,y,cpy[x]-cpy[y]+node[i].t);
else ans[node[i].id]=min(ans[node[i].id],tree.query(1,1,u,1,y)-cpy[x]+cpy[y]);
}
tree.init();
sort(node+1,node+1+n+m,cmp4);
for(int i=1;i<=n+m;i++){
x=node[i].x,y=node[i].y;
if(!node[i].op) tree.update(1,1,u,y,cpy[x]+cpy[y]+node[i].t);
else ans[node[i].id]=min(ans[node[i].id],tree.query(1,1,u,y+1,u)-cpy[x]-cpy[y]);
}
for(int i=1;i<=m;i++) printf("%lld\n",ans[i]);
return 0;
}
