Josephus Transform（约瑟夫变换 线段树）
https://ac.nowcoder.com/acm/contest/5671/J
题意：
每次操作对序列做，X次K约瑟夫环变换，问最终序列。
一次3约瑟夫环变化后，12345变成31524，就是每数3个数后删掉。
解析：
求出一次变换的结果：
线段树，tr记录sum，当前pos的前缀和为val，下一个就是第一个大于等于val+k的位置。
一次求出来后K次相当于找出环，X%环长后就是这个环转置的次数。
代码：
#include
const int INF = 0x3f3f3f3f, MAXN = 2e5 + 50;
const ll LINF = 0x3f3f3f3f3f3f3f3f, MOD = 998244353;
const db Pi = acos(-1), EPS = 1e-6;
void test(){cerr << "\n";}template<typename T,typename...Args>void test(T x,Args...args){cerr<<x<<" ";test(args...);}
inline ll qpow(ll a, ll b){return b?((b&1)?a*qpow(a*a%MOD,b>>1)%MOD:qpow(a*a%MOD,b>>1))%MOD:1;}
inline ll qpow(ll a, ll b,ll c){return b?((b&1)?a*qpow(a*a%c,b>>1,c)%c:qpow(a*a%c,b>>1,c)) %c:1;}
inline ll gcd(ll a,ll b){return b?gcd(b,a%b):a;}
inline ll cede(ll a,ll b){if(b<0)return cede(-a,-b);if(a<0)return a/b;return (a+b-1)/b;}
inline ll flde(ll a,ll b){if(b<0)return flde(-a,-b);if(a<0)return (a-b+1)/b;return a/b;}
inline int sign(db x){return x<-EPS ? -1:x>EPS;}
inline int dbcmp(db l,db r){return sign(l - r);}
namespace Fast_IO{ //orz laofu
const int MAXL((1 << 18) + 1);int iof, iotp;
char ioif[MAXL], *ioiS, *ioiT, ioof[MAXL],*iooS=ioof,*iooT=ioof+MAXL-1,ioc,iost[55];
char Getchar(){
if (ioiS == ioiT){
ioiS=ioif;ioiT=ioiS+fread(ioif,1,MAXL,stdin);return (ioiS == ioiT ? EOF : *ioiS++);
}else return (*ioiS++);
}
void Write(){fwrite(ioof,1,iooS-ioof,stdout);iooS=ioof;}
void Putchar(char x){*iooS++ = x;if (iooS == iooT)Write();}
inline int read(){
int x=0;for(iof=1,ioc=Getchar();(ioc<'0'||ioc>'9')&&ioc!=EOF;)iof=ioc=='-'?-1:1,ioc=Getchar();
if(ioc==EOF)Write(),exit(0);
for(x=0;ioc<='9'&&ioc>='0';ioc=Getchar())x=(x<<3)+(x<<1)+(ioc^48);return x*iof;
}
inline long long read_ll(){
long long x=0;for(iof=1,ioc=Getchar();(ioc<'0'||ioc>'9')&&ioc!=EOF;)iof=ioc=='-'?-1:1,ioc=Getchar();
if(ioc==EOF)Write(),exit(0);
for(x=0;ioc<='9'&&ioc>='0';ioc=Getchar())x=(x<<3)+(x<<1)+(ioc^48);return x*iof;
}
void Getstr(char *s, int &l){
for(ioc=Getchar();ioc==' '||ioc=='\n'||ioc=='\t';)ioc=Getchar();
if(ioc==EOF)Write(),exit(0);
for(l=0;!(ioc==' '||ioc=='\n'||ioc=='\t'||ioc==EOF);ioc=Getchar())s[l++]=ioc;s[l] = 0;
}
template <class Int>void Print(Int x, char ch = '\0'){
if(!x)Putchar('0');if(x<0)Putchar('-'),x=-x;while(x)iost[++iotp]=x%10+'0',x/=10;
while(iotp)Putchar(iost[iotp--]);if (ch)Putchar(ch);
}
void Putstr(const char *s){for(int i=0,n=strlen(s);i<n;++i)Putchar(s[i]);}
} // namespace Fast_IO
using namespace Fast_IO;
#define rep(i,a,b) for(int i=(int)(a);i<=(int)(b);i++)
const int maxn=2e5+9;
int a[maxn];
#define ls (rt<<1)
#define rs (rt<<1|1)
#define mid (l+r>>1)
#define root int rt,int l,int r
#define lson ls,l,mid
#define rson rs,mid+1,r
int tr[maxn<<2];
void build(root){
if(l==r){
tr[rt]=1;
return;
}
build(lson);build(rson);
tr[rt]=tr[ls]+tr[rs];
}
void update(root,int pos,int val){
if(l==r){
tr[rt]+=val;
return;
}
if(pos<=mid)
update(lson,pos,val);
else
update(rson,pos,val);
tr[rt]=tr[ls]+tr[rs];
}
int queryPre(root,int pos){
if(l==r){
return tr[rt];
}
int ans=0;
if(pos>mid)
ans=tr[ls]+queryPre(rson,pos);
else
ans=queryPre(lson,pos);
return ans;
}
int queryLowerbound(root,int value){
if(l==r)return l;
if(tr[ls]>=value)
return queryLowerbound(lson,value);
else
return queryLowerbound(rson,value-tr[ls]);
}
void Once(int n,int k){
build(1,1,n);
int val=0;
rep(i,1,n){
int K=k;
int pos;
if(val!=0 && val+K>tr[1]){
K-=tr[1]-val;
}
else{
K=val+K;
}
K%=tr[1];
if(K==0)K=tr[1];
pos=queryLowerbound(1,1,n,K);
a[i]=pos;
update(1,1,n,pos,-1);
val=queryPre(1,1,n,pos);
}
// rep(i,1,n){
// printf("%d%c",a[i]," \n"[i==n]);
// }
}
const int N=2e5+50;
int tmpH[N],huan[N];
bool vis[MAXN];
void change(int *arr,int len,int x)// indexed from 1 to len
{
for(int i=1;i<=len;i++)vis[i]=0;
for(int i=1;i<=len;i++)
{
if(vis[i])continue;
int now=i,nxt=arr[i],cntH=0;
vis[now]=1;huan[cntH++]=now;
while(!vis[nxt])
{
huan[cntH++]=nxt;
now=nxt;nxt=arr[now];vis[now]=1;
}
int QAQ=x%cntH;
for(int j=0;j<cntH;j++)tmpH[huan[j]]=huan[(j+QAQ)%cntH];
}
for(int i=1;i<=len;i++)arr[i]=tmpH[i];
}
int changa(int *arr,int len)
{
for(int i=1;i<=len;i++)
{
tmpH[arr[i]]=i;
}
for(int i=1;i<=len;i++)arr[i]=tmpH[i];
}
int changc(int *arr,int *brr,int len)
{
for(int i=1;i<=len;i++)tmpH[brr[i]]=arr[i];
for(int i=1;i<=len;i++)arr[i]=tmpH[i];
}
int now[MAXN];
void work()
{
int n,m;
scanf("%d%d",&n,&m);
for(int i=1;i<=n;i++)now[i]=i;
for(int i=1;i<=m;i++)
{
int k,x;scanf("%d%d",&k,&x);
Once(n,k);
// printf("GETa :");for(int j=1;j<=n;j++)printf("%d%c",a[j]," \n"[j==n]);
changa(a,n);
//printf("changa :");for(int j=1;j<=n;j++)printf("%d%c",a[j]," \n"[j==n]);
//for(int i=1;i<=n;i++)tmpnow[i]=a[i];
//changc(now,a,n);
// printf("changc :");for(int j=1;j<=n;j++)printf("%d%c",now[j]," \n"[j==n]);
change(a,n,x);
// printf("change :");for(int j=1;j<=n;j++)printf("%d%c",a[j]," \n"[j==n]);
changc(now,a,n);
//printf("change :");for(int j=1;j<=n;j++)printf("%d%c",now[j]," \n"[j==n]);
}
for(int i=1;i<=n;i++)printf("%d%c",now[i]," \n"[i==n]);
}
int main()
{
//std::ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
//int T=read();for(int cas=1;cas<=T;cas++)
//int T;scanf("%d",&T);for(int i=1;i<=T;i++)
work();
// Write();
}