题意简述
多次查询区间 \([l,r]\) 的众数，若有多个取数值最小的。强制在线。
\(n\le 4\times10^4,m\le 5\times10^4\)。
分析
考虑分块。
首先预处理出块区间内的众数 \(maj_{l,r}\) 和每种数在某个块的前缀的出现次数 \(cnt_{i,a_i}\)，时空复杂度都是 \(O(n\sqrt n)\) 的。
对于询问区间的整块，直接取出预处理好的众数以及出现次数。
由于散块中只有 \(O(\sqrt n)\) 种数，故直接提取出这 \(O(\sqrt n)\) 个数在整块的出现次数，然后暴力计算这些数的出现次数，找到最终的众数。
时空复杂度 \(O(n\sqrt n)\)。
具体见代码。
点击查看代码
#include<iostream>
#include<cstdio>
#include<cstring>
#include<string>
#include<algorithm>
#include<cmath>
#include<map>
#include<unordered_map>
#include<vector>
#include<queue>
#include<bitset>
#include<set>
#include<ctime>
#include<random>
#define x1 xx1
#define y1 yy1
#define IOS ios::sync_with_stdio(false)
#define ITIE cin.tie(0);
#define OTIE cout.tie(0);
#define FlushIn fread(Fread::ibuf,1,1<<21,stdin)
#define FlushOut fwrite(Fwrite::obuf,1,Fwrite::S-Fwrite::obuf,stdout)
#define PY puts("Yes")
#define PN puts("No")
#define PW puts("-1")
#define P__ puts("")
#define PU puts("--------------------")
#define popc __builtin_popcount
#define pii pair<int,int>
#define mp make_pair
#define fi first
#define se second
#define gc getchar
#define pc putchar
#define pb emplace_back
#define rep(a,b,c) for(int a=(b);a<=(c);a++)
#define per(a,b,c) for(int a=(b);a>=(c);a--)
#define reprange(a,b,c,d) for(int a=(b);a<=(c);a+=d)
#define perrange(a,b,c,d) for(int a=(b);a>=(c);a-=d)
#define graph(i,j,k,l) for(int i=k[j];i;i=l[i].nxt)
#define lowbit(x) (x&-x)
#define lson(x) (x<<1)
#define rson(x) (x<<1|1)
#define mem(x,y) memset(x,y,sizeof x)
//#define double long double
//#define int long long
//#define int __int128
using namespace std;
bool greating(int x,int y){return x>y;}
bool greatingll(long long x,long long y){return x>y;}
bool smallingll(long long x,long long y){return x<y;}
namespace Fread {
const int SIZE=1<<21;
char ibuf[SIZE],*S,*T;
inline char getc(){if(S==T){T=(S=ibuf)+fread(ibuf,1,SIZE,stdin);if(S==T)return '\n';}return *S++;}
}
namespace Fwrite{
const int SIZE=1<<21;
char obuf[SIZE],*S=obuf,*T=obuf+SIZE;
inline void flush(){fwrite(obuf,1,S-obuf,stdout);S=obuf;}
inline void putc(char c){*S++=c;if(S==T)flush();}
struct NTR{~NTR(){flush();}}ztr;
}
/*#ifdef ONLINE_JUDGE
#define getchar Fread::getc
#define putchar Fwrite::putc
#endif*/
inline int rd(){
int x=0,f=1;char ch=getchar();
while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
while(ch>='0'&&ch<='9'){x=x*10+ch-48;ch=getchar();}return x*f;
}
inline void write(int x,char ch='\0'){
if(x<0){x=-x;putchar('-');}
int y=0;char z[40];
while(x||!y){z[y++]=x%10+48;x/=10;}
while(y--)putchar(z[y]);if(ch!='\0')putchar(ch);
}
bool Mbg;
const int maxn=4e4+5,maxm=205,inf=0x3f3f3f3f,BSIZE=300;
const long long llinf=0x3f3f3f3f3f3f3f3f;
int n,Q,a[maxn],b[maxn];
int num;
int cnt[maxm][maxn];
int maj[maxm][maxm];
int tnc[maxn],tim[maxn];
int L[maxm],R[maxm],bel[maxn];
void solve_the_problem(){
n=rd(),Q=rd();
num=(n+BSIZE-1)/BSIZE;
rep(i,1,n)b[i]=a[i]=rd();
sort(b+1,b+n+1);int tot=unique(b+1,b+n+1)-(b+1);
rep(i,1,n)a[i]=lower_bound(b+1,b+tot+1,a[i])-b;
rep(i,1,num){
L[i]=R[i-1]+1,R[i]=min(R[i-1]+BSIZE,n);
rep(j,L[i],R[i])bel[j]=i;
}
rep(i,1,num){
rep(j,1,tot)cnt[i][j]=cnt[i-1][j];
rep(j,L[i],R[i])cnt[i][a[j]]++;
}
rep(i,1,num){
int mx=0;
rep(j,L[i],R[i]){
tnc[a[j]]++;
if(tnc[a[j]]>mx||(tnc[a[j]]==mx&&a[j]<maj[i][i]))mx=tnc[a[j]],maj[i][i]=a[j];
}
rep(j,i+1,num){
maj[i][j]=maj[i][j-1];
rep(k,L[j],R[j]){
tnc[a[k]]++;
if(tnc[a[k]]>mx||(tnc[a[k]]==mx&&a[k]<maj[i][j]))mx=tnc[a[k]],maj[i][j]=a[k];
}
}
rep(j,1,tot)tnc[j]=0;
}
int lstans=0;
rep(_,1,Q){
int l=(rd()+lstans-1)%n+1,r=(rd()+lstans-1)%n+1;
if(l>r)swap(l,r);
int bl=bel[l],br=bel[r];
int res=maj[bl+1][br-1],mx=bl==br?0:cnt[br-1][res]-cnt[bl][res];
rep(i,max(l,L[bl]),min(r,R[bl])){
if(tim[a[i]]<_)tim[a[i]]=_,tnc[a[i]]=bl==br?0:cnt[br-1][a[i]]-cnt[bl][a[i]];
tnc[a[i]]++;
if(tnc[a[i]]>mx||(tnc[a[i]]==mx&&a[i]<res))mx=tnc[a[i]],res=a[i];
}
if(bl^br){
rep(i,max(l,L[br]),min(r,R[br])){
if(tim[a[i]]<_)tim[a[i]]=_,tnc[a[i]]=bl==br?0:cnt[br-1][a[i]]-cnt[bl][a[i]];
tnc[a[i]]++;
if(tnc[a[i]]>mx||(tnc[a[i]]==mx&&a[i]<res))mx=tnc[a[i]],res=a[i];
}
}
write(lstans=b[res],10);
}
}
bool Med;
signed main(){
// freopen(".in","r",stdin);freopen(".out","w",stdout);
// fprintf(stderr,"%.3lfMB\n",(&Mbg-&Med)/1048576.0);
int _=1;while(_--)solve_the_problem();
}
/*
*/