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_yolanda

园龄：3年7个月粉丝：11关注：15

📂笔记总结
🔖数据结构总结
2022-08-28 22:19阅读: 67评论: 0推荐: 0

【模板】数据结构

树剖

戳他

平衡树

Splay

模板指路

点击查看代码 
//超级全，啥都有
#include<bits/stdc++.h>
using namespace std;
 
const int N=1e5+5,INF=0x3f3f3f3f;
struct node{
	int son[2],cnt,val,tot,fa;
}tr[N];
int co,root;
 
int read(){
	int sum=0,f=1;char a=getchar();
	while(a<'0' || a>'9'){if(a=='-')	f=-1;a=getchar();}
	while(a>='0' && a<='9')	sum=sum*10+a-'0',a=getchar();
	return sum*f;
}
 
inline void pushup(int x){
	tr[x].tot=tr[tr[x].son[0]].tot+tr[tr[x].son[1]].tot+tr[x].cnt;
}
inline void rotate(int x){
	int y=tr[x].fa,z=tr[y].fa,k=(tr[y].son[1]==x);
	tr[z].son[tr[z].son[1]==y]=x;
//	cout<<"rotate: "<<x<<" "<<z<<" "<<tr[x].val<<" "<<tr[z].val<<endl;
	tr[x].fa=z;
	tr[y].son[k]=tr[x].son[k^1];
	tr[tr[x].son[k^1]].fa=y;
	tr[x].son[k^1]=y;
	tr[y].fa=x;
	pushup(y),pushup(x);
}
void splay(int x,int goal){
	while(tr[x].fa!=goal){
		int y=tr[x].fa,z=tr[y].fa;
		if(z!=goal)
			((tr[y].son[1]==x)^(tr[z].son[1]==y))?rotate(x):rotate(y);
		rotate(x);
	}
	if(!goal)	root=x;
}
void fi(int x){
	int u=root;
	if(!u)	return;
	while(tr[u].son[x>tr[u].val] && tr[u].val!=x)
		u=tr[u].son[x>tr[u].val];
	splay(u,0);
}
void insert(int x){
	int fa=0,u=root;
	while(u && tr[u].val!=x){
		fa=u;
		u=tr[u].son[x>tr[u].val];
	}
//	cout<<"insert : "<<x<<" "<<u<<" "<<fa<<" "<<tr[u].val<<" "<<tr[fa].val<<endl;
	if(u)	tr[u].cnt++;
	else{
		u=++co;
		if(fa)	tr[fa].son[x>tr[fa].val]=u;
		tr[u].fa=fa,tr[u].son[0]=tr[u].son[1]=0;
		tr[u].cnt=1,tr[u].tot=1,tr[u].val=x;
	}
	splay(u,0);
}
int nxt(int x,bool k){
	fi(x);
	int u=root;
	if(tr[u].val>x && k)	return u;
	if(tr[u].val<x && !k)	return u;
	u=tr[u].son[k];
	while(tr[u].son[k^1])	u=tr[u].son[k^1];
	return u;
}
void delet(int x){
	int pre=nxt(x,0),suc=nxt(x,1);
	splay(pre,0),splay(suc,pre);
	int del=tr[suc].son[0];
	if(tr[del].cnt>1){
		tr[del].cnt--;
		splay(del,0);
	}
	else	tr[suc].son[0]=0;
}
int rk(int x){
	fi(x);
	return tr[tr[root].son[0]].tot+1;
}
int kth(int p,int x){
//	cout<<"kth : "<<p<<" "<<tr[p].tot<<" "<<tr[p].val<<" "<<x<<endl;
	if(tr[p].tot<x)	return 0;
	if(tr[tr[p].son[0]].tot>=x)	return kth(tr[p].son[0],x);
	if(tr[tr[p].son[0]].tot+tr[p].cnt>=x)	return tr[p].val;
	return kth(tr[p].son[1],x-tr[tr[p].son[0]].tot-tr[p].cnt);
}
 
int main(){
	
	insert(-INF),insert(INF);
	int n=read(),op,x;
	while(n--){
		op=read(),x=read();
		if(op==1)	insert(x);
		if(op==2)	delet(x);
		if(op==3)	printf("%d\n",rk(x)-1);
		if(op==4)	printf("%d\n",kth(root,x+1));
		if(op==5)	printf("%d\n",tr[nxt(x,0)].val);
		if(op==6)	printf("%d\n",tr[nxt(x,1)].val);
	}
	
	return 0;
}

线段树

单点加减，区间询问

模板 
#include<bits/stdc++.h>
using namespace std;
#define mid ((l+r)>>1)
 
const int N=1e5+5;
int tr[N<<2];
 
void pushup(int node){
	tr[node]=tr[node<<1]+tr[node<<1|1];
}
void change(int node,int l,int r,int x,int y){
	if(l>x || r<x)	return;
	if(l==r && l==x){
		tr[node]+=y;
		return;
	}
	change(node<<1,l,mid,x,y);
	change(node<<1|1,mid+1,r,x,y);
	pushup(node);
}
int ask(int node,int l,int r,int be,int en){
	if(l>en || r<be)	return 0;
	if(l>=be && r<=en)	return tr[node];
	return ask(node<<1,l,mid,be,en)+ask(node<<1|1,mid+1,r,be,en);
}
 
int main(){
	
	int n,m;
	cin>>n>>m;
	while(m--){
		int op,x,y;
		cin>>op>>x>>y;
		if(op)	cout<<ask(1,1,n,x,y)<<endl;
		else	change(1,1,n,x,y);
	}
	
	return 0;
}

区间加减，区间询问

点击查看代码 
#include<bits/stdc++.h>
using namespace std;
#define mid ((l+r)>>1)
#define int long long
 
const int N=1e6+5;
int tr[N<<2],lz[N<<2],len[N<<2];
 
int read(){
	int sum=0,f=1;char a=getchar();
	while(a<'0' || a>'9'){if(a=='-')	f=-1;a=getchar();}
	while(a>='0' && a<='9')	sum=sum*10+a-'0',a=getchar();
	return sum*f;
} 
void print(int x){
	if(x<0) putchar('-'),x=-x;
	if(x>9) print(x/10);
	putchar(x%10+'0');
}
void pushup(int node){
	tr[node]=tr[node<<1]+tr[node<<1|1];
}
void push(int node,int x){
	tr[node]+=len[node]*x,lz[node]+=x;
}
void pushdown(int node){
	if(lz[node]){
		push(node<<1,lz[node]);
		push(node<<1|1,lz[node]);
		lz[node]=0;
	}
}
void build(int node,int l,int r){
	len[node]=r-l+1;
	if(l==r){
		tr[node]=read();
		return;
	}
	build(node<<1,l,mid);
	build(node<<1|1,mid+1,r);
	pushup(node);
} 
void change(int node,int l,int r,int be,int en,int x){
	if(l>en || r<be)	return;
	if(l>=be && r<=en){
		push(node,x);
		return;
	}
	pushdown(node);
	change(node<<1,l,mid,be,en,x);
	change(node<<1|1,mid+1,r,be,en,x);
	pushup(node);
}
int ask(int node,int l,int r,int be,int en){
	if(l>en || r<be)	return 0;
	if(l>=be && r<=en)	return tr[node];
	pushdown(node);
	return ask(node<<1,l,mid,be,en)+ask(node<<1|1,mid+1,r,be,en);
}
 
signed main(){
	
	int n,m;
	n=read(),m=read();
	build(1,1,n);
	while(m--){
		int op,x,y,z;
		op=read(),x=read(),y=read();
		if(op==2)	print(ask(1,1,n,x,y)),puts("");
		else	z=read(),change(1,1,n,x,y,z);
	}
	
	return 0;
}

区间加乘，区间询问

点击查看代码 
#include<bits/stdc++.h>
using namespace std;
#define mid ((l+r)>>1)
#define int long long
 
const int N=1e5+5;
int p;
int tr[N<<2],lz_add[N<<2],lz_mul[N<<2],len[N<<2];
 
int read(){
	int sum=0,f=1;char a=getchar();
	while(a<'0' || a>'9'){if(a=='-')	f=-1;a=getchar();}
	while(a>='0' && a<='9')	sum=sum*10+a-'0',a=getchar();
	return sum*f;
}
void pushup(int node){
	tr[node]=(tr[node<<1]%p+tr[node<<1|1]%p)%p;
}
void push_add(int node,int x){
	tr[node]+=len[node]*x,tr[node]%=p;
	lz_add[node]+=x,lz_add[node]%=p;
}
void push_mul(int node,int x){
	tr[node]*=x,tr[node]%=p;
	lz_mul[node]*=x,lz_mul[node]%=p;
	lz_add[node]*=x,lz_add[node]%=p;
}
void pushdown(int node){
	if(lz_mul[node]!=1){
		push_mul(node<<1,lz_mul[node]);
		push_mul(node<<1|1,lz_mul[node]);
		lz_mul[node]=1;
	}
	if(lz_add[node]){
		push_add(node<<1,lz_add[node]);
		push_add(node<<1|1,lz_add[node]);
		lz_add[node]=0;
	}
}
void build(int node,int l,int r){
	len[node]=r-l+1;
	lz_mul[node]=1;
	if(l==r){
		tr[node]=read()%p;
		return;
	}
	build(node<<1,l,mid);
	build(node<<1|1,mid+1,r);
	pushup(node);
} 
void change_mul(int node,int l,int r,int be,int en,int x){
	if(l>en || r<be)	return;
	if(l>=be && r<=en){
		push_mul(node,x);
		return;
	}
	pushdown(node);
	change_mul(node<<1,l,mid,be,en,x);
	change_mul(node<<1|1,mid+1,r,be,en,x);
	pushup(node);
}
void change_add(int node,int l,int r,int be,int en,int x){
	if(l>en || r<be)	return;
	if(l>=be && r<=en){
		push_add(node,x);
		return;
	}
	pushdown(node);
	change_add(node<<1,l,mid,be,en,x);
	change_add(node<<1|1,mid+1,r,be,en,x);
	pushup(node);
}
int ask(int node,int l,int r,int be,int en){
	if(l>en || r<be)	return 0;
	if(l>=be && r<=en)	return tr[node]%p;
	pushdown(node);
	return (ask(node<<1,l,mid,be,en)+ask(node<<1|1,mid+1,r,be,en))%p;
}
 
signed main(){
	
	int n,m;
	n=read(),p=read();
	build(1,1,n);
	m=read();
	while(m--){
		int op,x,y,z;
		op=read(),x=read(),y=read();
		if(op==1)	z=read(),change_mul(1,1,n,x,y,z);
		if(op==2)	z=read(),change_add(1,1,n,x,y,z);
		if(op==3)	printf("%lld\n",ask(1,1,n,x,y));
	}
	
	return 0;
}

扫描线

点击查看代码 
#include<bits/stdc++.h>
using namespace std;
#define int long long
#define mid ((l+r)>>1)
 
const int N=2e5+5;
int ly[N];
struct seg{
	int x,y[2];
	int val;
}a[N];
int len[N<<4],tr[N<<4],sum[N<<4];
 
inline int read(){
	int sum=0,f=1;char a=getchar();
	while(a<'0' || a>'9'){if(a=='-') 	f=-1;a=getchar();}
	while(a>='0' && a<='9') 	sum=sum*10+a-'0',a=getchar();
	return sum*f;
}
bool cmp(seg _,seg __){
	return _.x<__.x;
}
 
void build(int node,int l,int r){
	len[node]=ly[r+1]-ly[l];
	if(l==r)    return;
	build(node<<1,l,mid);
	build(node<<1|1,mid+1,r);
}
void pushup(int node){
	if(sum[node])
		tr[node]=len[node];
	else
		tr[node]=tr[node<<1]+tr[node<<1|1];
}
void change(int node,int l,int r,int be,int en,int x){
	if(l>en || r<be)    return;
	if(l>=be && r<=en){
		sum[node]+=x;
		pushup(node);
		return;
	}
	change(node<<1,l,mid,be,en,x);
	change(node<<1|1,mid+1,r,be,en,x);
	pushup(node);
}
 
signed main(){
	
	int n=read();
	for(int i=1;i<=n;++i){
		a[i].x=read(),a[i].y[0]=a[i+n].y[0]=ly[i]=read();
		a[i+n].x=read(),a[i].y[1]=a[i+n].y[1]=ly[i+n]=read();
		a[i].val=1,a[i+n].val=-1;
	}
	n*=2;
	sort(a+1,a+n+1,cmp);
	sort(ly+1,ly+n+1);
	int co=unique(ly+1,ly+n+1)-ly-1;
	ly[co+1]=0x3f3f3f3f;
	build(1,1,co);
	
	int ans=0;
	for(int i=1;i<n;++i){
		int y=lower_bound(ly+1,ly+co+1,a[i].y[0])-ly;
		int y1=lower_bound(ly+1,ly+co+1,a[i].y[1])-ly-1;
		
		//cout<<y<<" "<<y1<<endl;
		
		change(1,1,co,y,y1,a[i].val);
		ans+=tr[1]*(a[i+1].x-a[i].x);
		//cout<<a[i].x<<" "<<a[i].val<<" "<<ans<<endl;
	}
	printf("%lld",ans);
	
	return 0;
}

树状数组

区间加减，区间询问

点击查看代码 
#include<bits/stdc++.h>
using namespace std;
const int N=1e6+5;
#define int long long
int read(){
	int sum=0,f=1;char a=getchar();
	while(a<'0'||a>'9'){if(a=='-')f=-1;a=getchar();}
	while(a>='0'&&a<='9')sum=sum*10+a-'0',a=getchar();
	return sum*f;
}
int n,q;int a[N];
struct bit{
	int a[N];
	bit(){memset(a,0,sizeof a);}
	void add(int x,int y){for(int i=x;i<=n;i+=(i&-i))a[i]+=y;}
	int ask(int x){
		if(x<=0)return 0;int res=0;
		for(int i=x;i;i-=(i&-i))res+=a[i];
		return res;
	}
}b,c;
int ask(int x){return (x+1)*b.ask(x)-c.ask(x);}
signed main(){
	
	n=read(),q=read();
	for(int i=1;i<=n;++i)a[i]=read();
	for(int i=1;i<=n;++i)b.add(i,a[i]-a[i-1]),c.add(i,(a[i]-a[i-1])*i);
	while(q--){
		int opt=read(),l=read(),r=read(),x;
		if(opt==1){
			x=read();
			b.add(l,x),b.add(r+1,-x);
			c.add(l,x*l),c.add(r+1,-x*(r+1));
		}
		else printf("%lld\n",ask(r)-ask(l-1));
	}
	
	return 0;
}

字典树

可持久化 01 Trie

模板

点击查看代码 
#include<bits/stdc++.h>
using namespace std;
 
const int N=6e5+5;
struct node{
	int cnt,s[2];
}t[N*35];
int co;
int rt[N];
void insert(int p,int q,int x){
	for(int i=30;i>=0;--i){
		t[p].cnt=t[q].cnt+1;
		bool w=(x&(1<<i));
		if(!t[p].s[w])	t[p].s[w]=++co;
		t[p].s[w^1]=t[q].s[w^1];
		p=t[p].s[w],q=t[q].s[w];
	}
	t[p].cnt=t[q].cnt+1;
}
int ask(int p,int q,int x){
	int res=0;
	for(int i=30;i>=0;--i){
		bool w=(x&(1<<i));
		if(t[t[p].s[w^1]].cnt-t[t[q].s[w^1]].cnt>0)
			p=t[p].s[w^1],q=t[q].s[w^1],res+=(1<<i);
		else	p=t[p].s[w],q=t[q].s[w];
	}
	return res;
}
int sum[N];
 
int main(){
 
	int n,m;cin>>n>>m;
	for(int i=1;i<=n;++i)	cin>>sum[i],sum[i]=sum[i-1]^sum[i];
	for(int i=1;i<=n;++i)	rt[i]=++co,insert(rt[i],rt[i-1],sum[i]);
	while(m--){
		char opt;cin>>opt;
		if(opt=='A'){
			int x;cin>>x;
			++n;sum[n]=sum[n-1]^x;
			rt[n]=++co,insert(rt[n],rt[n-1],sum[n]);
		}
		else{
			int l,r,x;cin>>l>>r>>x;--l,--r;
			if(!l)	cout<<max(sum[n]^x,ask(rt[r],rt[0],sum[n]^x))<<"\n";
			else	cout<<ask(rt[r],rt[l-1],sum[n]^x)<<"\n";
		}
	}
 
	return 0;
}

本文作者：_yolanda

本文链接：https://www.cnblogs.com/yolanda-yxr/p/16634167.html

版权声明：本作品采用知识共享署名-非商业性使用-禁止演绎 2.5 中国大陆许可协议进行许可。

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  2. 2 像鸟儿一样（Live） 周深
  3. 3 Rubia 周深
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Rubia - 周深
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Rubia (崩坏3《渡尘》动画短片印象曲) - 周深

词：TetraCalyx

曲：蔡近翰Zoe(HOYO-MiX)

编曲：宫奇Gon(HOYO-MiX)/杨启翔Frex(HOYO-MiX)

Life blooms like a flower

Far away or by the road

Waiting for the one

To find the way back home

Rain falls a thousand times

No footprints of come-and-go

You who once went by

Where will you belong

I feel your sigh and breath

In the last blow of wind

Not yet for the story on the last page

It's not the end

Life blooms like a flower

Far away or by the road

Waiting for the one

To find the way back home

Time flows across the world

There is always a longer way to go

Till I reach your arms

A Madder there for you

Up against the stream

Waterways will join as one

Tracing to the source

No more strayed or lost

You will see petals fly

When lament becomes carol

Could you please hear my voice

That hungers for a duo

Life blooms like a flower

Far away or by the road

Waiting for the one

To find the way back home

Time flows across the world

There is always a longer way to go

Till I reach your arms

A Madder there for you

Life blooms like a flower

Far away or by the road

Waiting for the one

To find the way back home

Time flows across the world

There is always a longer way to go

Till I reach your arms

A Madder there for you

人声录音 Recording：徐威Aaron Xu

混音/母带 Mixing&Mastering Engineer：宫奇Gon(HOYO-MiX)

制作人 Producer：蔡近翰Zoe(HOYO-MiX)

特别鸣谢 Special Thanks：周深工作室

出品 Produced by：HOYO-MiX