p4841 城市规划

分析

https://www.luogu.org/blog/DRA/solution-p4841

代码(似乎附赠了一个全家桶呢)

#pragma GCC optimize(2)
#pragma GCC optimize(3)
#pragma GCC optimize("Ofast")
#pragma GCC optimize("inline")
#pragma GCC optimize("-fgcse")
#pragma GCC optimize("-fgcse-lm")
#pragma GCC optimize("-fipa-sra")
#pragma GCC optimize("-ftree-pre")
#pragma GCC optimize("-ftree-vrp")
#pragma GCC optimize("-fpeephole2")
#pragma GCC optimize("-ffast-math")
#pragma GCC optimize("-fsched-spec")
#pragma GCC optimize("unroll-loops")
#pragma GCC optimize("-falign-jumps")
#pragma GCC optimize("-falign-loops")
#pragma GCC optimize("-falign-labels")
#pragma GCC optimize("-fdevirtualize")
#pragma GCC optimize("-fcaller-saves")
#pragma GCC optimize("-fcrossjumping")
#pragma GCC optimize("-fthread-jumps")
#pragma GCC optimize("-funroll-loops")
#pragma GCC optimize("-fwhole-program")
#pragma GCC optimize("-freorder-blocks")
#pragma GCC optimize("-fschedule-insns")
#pragma GCC optimize("inline-functions")
#pragma GCC optimize("-ftree-tail-merge")
#pragma GCC optimize("-fschedule-insns2")
#pragma GCC optimize("-fstrict-aliasing")
#pragma GCC optimize("-fstrict-overflow")
#pragma GCC optimize("-falign-functions")
#pragma GCC optimize("-fcse-skip-blocks")
#pragma GCC optimize("-fcse-follow-jumps")
#pragma GCC optimize("-fsched-interblock")
#pragma GCC optimize("-fpartial-inlining")
#pragma GCC optimize("no-stack-protector")
#pragma GCC optimize("-freorder-functions")
#pragma GCC optimize("-findirect-inlining")
#pragma GCC optimize("-frerun-cse-after-loop")
#pragma GCC optimize("inline-small-functions")
#pragma GCC optimize("-finline-small-functions")
#pragma GCC optimize("-ftree-switch-conversion")
#pragma GCC optimize("-foptimize-sibling-calls")
#pragma GCC optimize("-fexpensive-optimizations")
#pragma GCC optimize("-funsafe-loop-optimizations")
#pragma GCC optimize("inline-functions-called-once")
#pragma GCC optimize("-fdelete-null-pointer-checks")
#include<bits/stdc++.h>
using namespace std;
#define int long long
const int g = ;
const int mod = ;
int G,a[],b[],c[],len,r[],a1[],b1[],ib[],ans[],ans2[];
inline int pw(int x,int p){
    int res=;
    while(p){if(p&)res=res*x%mod;x=x*x%mod,p>>=;}
    return res;
}
#define pi acos(-1.0)
struct node {
    double x,y;
};
node A[],B[];
inline node operator + (const node x,const node y){return (node){x.x+y.x,x.y+y.y};}
inline node operator - (const node x,const node y){return (node){x.x-y.x,x.y-y.y};}
inline node operator * (const node x,const node y){return (node){x.x*y.x-x.y*y.y,x.x*y.y+x.y*y.x};}
inline void fft(node a[],int f,int n){
    int i,j,k;
    for(i=;i<n;i++)if(i<r[i])swap(a[i],a[r[i]]);
    for(i=;i<n;i<<=){
          node wn=(node){cos(pi/i),f*sin(pi/i)};
      for(j=;j<n;j+=(i<<)){
          node w=(node){,},p,q;
          for(k=;k<i;k++,w=w*wn){
            p=a[j+k],q=a[i+j+k]*w;
            a[j+k]=p+q,a[i+j+k]=p-q;
        }
      }
    }
    if(f==-)for(i=;i<n;i++)a[i].x=a[i].x/n;
    return;
}
inline void get_fft_mul(node A[],node B[],int n){
    int N=;
    for(N=;N<=n;N<<=)len++;
    for(int i=;i<N;i++)r[i]=((r[i>>]>>)|((i&)<<(len-)));
    fft(A,,N),fft(B,,N);
    for(int i=;i<N;i++)A[i]=A[i]*B[i];
    fft(A,-,N);
    for(int i=;i<N;i++)ans[i]=(int)(A[i].x+0.5);
    return;
}
inline void fwt_or(int a[],int f,int n){
    int i,j,k;
    for(i=;i<n;i<<=)
      for(j=;j<n;j+=(i<<))
        for(k=;k<i;k++){
          if(f==)a[i+j+k]=(a[j+k]+a[i+j+k])%mod;
            else a[i+j+k]=(a[i+j+k]+mod-a[j+k])%mod;
        }
}
inline void fwt_and(int a[],int f,int n){
    int i,j,k;
    for(i=;i<n;i<<=)
      for(j=;j<n;j+=(i<<))
        for(k=;k<i;k++){
          if(f==)a[j+k]=(a[j+k]+a[i+j+k])%mod;
            else a[j+k]=(a[j+k]+mod-a[i+j+k])%mod;
        }
}
inline void fwt_xor(int a[],int f,int n){
    int i,j,k,inv2=pw(,mod-);
    for(i=;i<n;i<<=)
      for(j=;j<n;j+=(i<<))
        for(k=;k<i;k++){
          int x=a[j+k],y=a[i+j+k];
          a[j+k]=(x+y)%mod;a[i+j+k]=(x+mod-y)%mod;
        }
    if(f==-)for(i=;i<n;i++)a[i]=a[i]*inv2%mod;
}
inline void ntt(int a[],int opt,int n){
    int i,j,k,inv=pw(n,mod-),now,wn,w,p,q;
    for(i=;i<n;i++)if(i<r[i])swap(a[i],a[r[i]]);
    for(i=;i<n;i<<=){
      now=(opt==?g:G),wn=pw(now,(mod-)/(i<<));
      for(j=;j<n;j+=(i<<))
        for(k=,w=;k<i;k++,w=w*wn%mod)
          p=a[j+k],q=a[i+j+k]*w%mod,a[j+k]=(p+q)%mod,a[i+j+k]=(p-q+mod)%mod;
    }
    if(opt==-)for(i=;i<n;i++)a[i]=a[i]*inv%mod;
    return;
}
inline void cdq_fft(int le,int ri){
    if(le==ri){
      //.....
      return;
    }
    int i,j,k,n,m=ri-le,mid=(le+ri)>>;len=;
    cdq_fft(le,mid);
    for(n=;n<=*(m+);n<<=)len++;
    for(i=;i<n;i++)a1[i]=b1[i]=;
    for(i=;i<n;i++)r[i]=((r[i>>]>>)|((i&)<<(len-)));
    //for(i=0;i<=mid-le;i++)b1[i]=b[i+le];
    //for(i=0;i<=m;i++)a1[i]=a[i];
    ntt(a1,,n),ntt(b1,,n);
    //for(i=0;i<n;i++)b1[i]=a1[i]*b1[i]%mod;
    ntt(b1,-,n);
    for(i=mid+;i<=ri;i++)b[i]=(b[i]+b1[i-le])%mod;
    cdq_fft(mid+,ri);
    return;
}
inline void get_inv(int x,int a[],int b[]){
    if(x==){b[]=pw(a[],mod-);return;}
    int i,j,k,n;get_inv((x+)>>,a,b);len=;
    for(n=;n<(x<<);n<<=)len++;
    for(i=;i<n;i++)r[i]=((r[i>>]>>)|((i&)<<(len-)));
    for(i=;i<x;i++)c[i]=a[i];for(i=x;i<n;i++)c[i]=;
    ntt(b,,n),ntt(c,,n);
    for(i=;i<n;i++)b[i]=(-c[i]*b[i]%mod+mod)%mod*b[i]%mod;
    ntt(b,-,n);for(i=x;i<n;i++)b[i]=;return;
}
inline void get_dao(int n,int a[],int b[]){
    for(int i=;i<n;i++)b[i]=a[i+]*(i+)%mod;
    b[n-]=;return;
}
inline void get_ji(int n,int a[],int b[]){
    for(int i=n-;i>;i--)b[i]=a[i-]*pw(i,mod-)%mod;
    b[]=;return;
}
inline void get_mul(int n,int a[],int b[]){
    int i,j,k;
    ntt(a,,n),ntt(b,,n);
    for(i=;i<n;i++)a[i]=a[i]*b[i]%mod;
    ntt(a,-,n);return;
}
inline void get_ln(int n,int a[],int b[]){
    for(int i=;i<(n<<);i++)b[i]=;
    get_inv(n,a,b);
    int N;len=;
    for(N=;N<(n<<);N<<=)len++;
    for(int i=;i<N;i++)r[i]=((r[i>>]>>)|((i&)<<(len-)));
    get_dao(N,a,a1);
    get_mul(N,a1,b);
    get_ji(N,a1,b);
    for(int i=;i<N;i++)a1[i]=;
    return;
}
inline void get_exp(int n,int a[],int b[]){
    if(n==){b[]=;return;}
    get_exp((n+)>>,a,b);
    get_ln(n,b,b1);
    b1[]=(a[]+-b1[]+mod)%mod;
    for(int i=;i<n;i++)b1[i]=(a[i]-b1[i]+mod)%mod;
    int N;len=;
    for(N=;N<(n<<);N<<=)len++;
    for(int i=;i<N;i++)r[i]=((r[i>>]>>)|((i&)<<(len-)));
    for(int i=n;i<N;i++)b[i]=b1[i]=;
    ntt(b,,N),ntt(b1,,N);
    for(int i=;i<N;i++)b[i]=b[i]*b1[i]%mod;
    ntt(b,-,N);
    for(int i=n;i<N;i++)b[i]=b1[i]=;
}
inline int read_pw(){
    int x=;char s=getchar();
    while(!isdigit(s))s=getchar();
    while(isdigit(s))x=((x<<)+(x<<)+(s-''))%mod,s=getchar();
    return x;
}
inline void get_pw(int n,int a[],int b[],int k){
    get_ln(n,a,b);
    for(int i=;i<n;i++)b[i]=b[i]*k%mod;
    get_exp(n,b,ans);
    return;
}
inline void get_div(int n,int m,int a1[],int b1[]){
    int i,j,k;
    for(i=;i<n;i++)a[i]=a1[n--i];
    for(i=;i<m;i++)b[i]=b1[m--i],ib[i]=;
    for(i=n-m+;i<m;i++)b[i]=;
    get_inv(n-m+,b,ib);
    int N;len=;
    for(N=;N<(n<<);N<<=)len++;
    for(int i=;i<N;i++)r[i]=((r[i>>]>>)|((i&)<<(len-)));
    get_mul(N,a,ib);
    int _n=n-m+;
    for(i=;i<_n;i++)ans[i]=a[_n--i],printf("%lld ",ans[i]);
    for(i=;i<m;i++)b[i]=b1[m--i];
    for(i=m;i<N;i++)b[i]=;
    puts("");
    get_mul(N,ans,b1);
    for(i=;i<m-;i++)ans2[i]=(a1[i]-ans[i]+mod)%mod,printf("%lld ",ans2[i]);
    puts("");
    return;
}
int fac[],inv[];
signed main(){
    G=pw(g,mod-);
    int n,m,i,k;
    scanf("%lld",&n);
    //k=read_pw();
    k=;
    fac[]=;
    for(i=;i<=n;i++)fac[i]=fac[i-]*i%mod;
    inv[n]=pw(fac[n],mod-);
    for(i=n-;i>=;i--)inv[i]=inv[i+]*(i+)%mod;
    for(i=;i<=n;i++)a[i]=pw(,i*(i-)/)*inv[i]%mod;
    get_inv(n+,a,b);
    int N;len=;
    for(N=;N<=n+;N<<=)len++;
    for(i=;i<N;i++)r[i]=((r[i>>]>>)|((i&)<<(len-)));
    for(i=;i<N;i++)a[i]=;
    for(i=;i<=n;i++)a[i]=pw(,i*(i-)/)*inv[i-]%mod;
    get_mul(N,a,b);a[]=;
    for(i=;i<N;i++)a[i]=a[i]*fac[i-]%mod*inv[i]%mod;
    for(i=N;i<=;i++)a[i]=;
    memset(b,,sizeof(b));
    get_pw(n+,a,b,k);
    printf("%lld\n",ans[n]*fac[n]%mod);
    return ;
}