分块算法板子luogu1903

https://www.luogu.org/problemnew/show/1903

用pre[i]数组记录上一次和当前i同色的位置

查询[l,r]，若pre[i]<r，则说明在[l,i)区间内没用和i同色的，则++ans

于是就可以大胆地分块

对于每一块按照pre[i]排序，再进行二分了

复杂度O(qsqrt(n)log(n)).

#include<stdio.h>
#include<math.h>
#include<algorithm>
#define FOR(i,s,t) for(register int i=s;i<=t;++i)
using std::sort;
using std::lower_bound;
const int N=10011;
const int M=1000011;
inline int min(int a,int b){
	return a<b?a:b;
}
int n,q,m,blo;
int c[N],pos[N],pre[N],b[N],last[M];
inline int find(int x,int v){
	int l=(x-1)*blo+1,r=min(x*blo,n);
	return lower_bound(pre+l,pre+r+1,v)-pre-l;
}
inline void reset(int x){
	int l=(x-1)*blo+1,r=min(x*blo,n);
	FOR(i,l,r)pre[i]=b[i];
	sort(pre+l,pre+r+1);
}
inline void build(){
	FOR(i,1,n){
		b[i]=last[c[i]];
		last[c[i]]=i;
		pos[i]=(i-1)/blo+1;
	}
	FOR(i,1,m)reset(i);
}
inline int ask(int l,int r){
	int ans=0;
	if(pos[l]==pos[r]){
		FOR(i,l,r)if(b[i]<l)++ans;
		return ans;
	}
	for(register int i=l;i<=blo*pos[l];++i)if(b[i]<l)++ans;
	for(register int i=blo*(pos[r]-1)+1;i<=r;++i)if(b[i]<l)++ans;
	for(register int i=pos[l]+1;i<pos[r];++i)ans+=find(i,l);
	return ans;
}
inline void change(int x,int v){
	FOR(i,1,n)last[c[i]]=0;
	c[x]=v;
	FOR(i,1,n){
		int t=b[i];
		b[i]=last[c[i]];
		if(t!=b[i])reset(pos[i]);
		last[c[i]]=i;
	}
}
int main(){
	scanf("%d%d",&n,&q);
	FOR(i,1,n)scanf("%d",c+i);
	blo=int(sqrt(n));
	m=n%blo?(n/blo+1):n/blo;
	build();
	char ch[5];int x,y;
	while(q--){
		scanf("%s%d%d",ch,&x,&y);
		if(ch[0]=='Q')printf("%d
",ask(x,y));
		else change(x,y);
	}
	return 0;
}

　　

补一份带修莫队板子

#include<stdio.h>
#include<math.h>
#include<algorithm>
#define FOR(i,s,t) for(register int i=s;i<=t;++i)
using std::swap;
using std::sort;
const int N=10011,M=300011;
int blo,times,n,m,l,r,tot,now,res;
struct qs{
	int l,r,t,id;
	inline bool operator<(qs A)const{
		if(l/blo!=A.l/blo)return l<A.l;
		if(r/blo!=A.r/blo)return r<A.r;
		if(t/blo!=A.t/blo)return t<A.t;
		return id<A.id;
	}
}q[N];
struct cg{int p,x;}c[N];
int a[N],ans[N],hv[M];
char Q[5];
inline void add(int x){if(!hv[x])++res;++hv[x];}
inline void del(int x){--hv[x];if(!hv[x])--res;}
inline void change(int x,int i){
	if(c[x].p>=q[i].l&&c[x].p<=q[i].r){
		--hv[a[c[x].p]];if(!hv[a[c[x].p]])--res;
		if(!hv[c[x].x])++res;++hv[c[x].x];
	}
	swap(c[x].x,a[c[x].p]);
}
int main(){
	scanf("%d%d",&n,&m);blo=pow(n,2.00/3.00);
	FOR(i,1,n)scanf("%d",a+i);
	FOR(i,1,m){
		scanf("%s%d%d",Q,&l,&r);
		if(Q[0]=='Q')
			q[++tot]=(qs){l,r,times,tot};
		else c[++times]=(cg){l,r};
	}
	sort(q+1,q+tot+1);
	l=1;r=0;now=0;
	FOR(i,1,m){
		while(l<q[i].l)del(a[l++]);while(q[i].l<l)add(a[--l]);
		while(r<q[i].r)add(a[++r]);while(q[i].r<r)del(a[r--]);
		while(now<q[i].t)change(++now,i);while(q[i].t<now)change(now--,i);
		ans[q[i].id]=res;
	}
	FOR(i,1,tot)printf("%d
",ans[i]);
	return 0;
}

　　

线段树+bitset

#include<stdio.h>
#include<bitset>
#include<algorithm>
#define FOR(i,s,t) for(register int i=s;i<=t;++i)
using std::bitset;
using std::sort;
using std::unique;
using std::lower_bound;
const int N=10011;
bitset<N>s[N<<2],ans;
int a[N];
int b[N<<2];
inline void build(int k,int l,int r){
    if(l==r){
        s[k][a[l]]=1;
        return ;
    }
    int mid=(l+r)>>1;
    build(k<<1,l,mid);
    build(k<<1|1,mid+1,r);
    s[k]=s[k<<1]|s[k<<1|1];
}
int n,m,cnt;
inline void change(int k,int l,int r,int x,int v){
    if(l==r){
        s[k][a[l]]=0;
        s[k][a[l]=v]=1;
        return;
    }
    int mid=(l+r)>>1;
    x<=mid?change(k<<1,l,mid,x,v):change(k<<1|1,mid+1,r,x,v);
    s[k]=s[k<<1]|s[k<<1|1];
}
inline void query(int k,int l,int r,int x,int y){
    if(x<=l&&r<=y){
        ans|=s[k];
        return;
    }
    int mid=(l+r)>>1;
    if(x<=mid) query(k<<1,l,mid,x,y);
    if(mid<y) query(k<<1|1,mid+1,r,x,y);
    
}
struct question{
    char c;
    int x;
    int y;
}q[N];
inline void disc_init(){
    sort(b+1,b+cnt+1);
    cnt=unique(b+1,b+cnt+1)-b-1;
}
inline int read(){
    char c;while(c=getchar(),c==' '||c=='
');int data=c-48;
    while(c=getchar(),c>='0'&&c<='9')data=(data<<1)+(data<<3)+c-48;return data;
}
int main(){
    scanf("%d%d
",&n,&m);
    FOR(i,1,n)b[++cnt]=a[i]=read();
    scanf("
");
    FOR(i,1,m){
        q[i].c=getchar();
        q[i].x=read();q[i].y=read();
        scanf("
");
        if(q[i].c=='R')b[++cnt]=q[i].y;
    }
    disc_init();
    FOR(i,1,n)a[i]=lower_bound(b+1,b+cnt+1,a[i])-b;
    build(1,1,n);
    FOR(i,1,m){
        if(q[i].c=='Q'){
            ans.reset();
            query(1,1,n,q[i].x,q[i].y);
            printf("%d
",ans.count());
        }
        else{
            q[i].y=lower_bound(b+1,b+cnt+1,q[i].y)-b;
            change(1,1,n,q[i].x,q[i].y);
        }
    }
    return 0;
}