LUOGU P4088 [USACO18FEB]Slingshot(线段树)

传送门

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
",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
",ans[i]);
	return 0;
}