cf 632E FFT+快速幂

Posted 2022-12-04 nervendnig

fft+快速幂,需要不少优化才能过

#include<bits/stdc++.h>
#define ll long long
#define rep(ii,a,b) for(int ii=a;ii<=b;++ii)
#define per(ii,a,b) for(int ii=b;ii>=a;--ii)
#define forn(i,x,g,e) for(int i=g[x];i;i=e[i].next)
#define IO ios::sync_with_stdio(false);cin.tie(0);cout.tie(0)
#define ull unsigned long long
#define fi first
#define se second
#define mp make_pair
#define pii pair<ll,ll>
#define all(x) x.begin(),x.end()
#define show(x) cout<<#x<<"="<<x<<endl
#define showa(a,b) cout<<#a<<‘[‘<<b<<"]="<<a[b]<<endl
#define show2(x,y) cout<<#x<<"="<<x<<" "<<#y<<"="<<y<<endl
#define show3(x,y,z) cout<<#x<<"="<<x<<" "<<#y<<"="<<y<<" "<<#z<<"="<<z<<endl
#define show4(w,x,y,z) cout<<#w<<"="<<w<<" "<<#x<<"="<<x<<" "<<#y<<"="<<y<<" "<<#z<<"="<<z<<endl
#define show5(v,w,x,y,z) cout<<#v<<"="<<v<<" "<<#w<<"="<<w<<" "<<#x<<"="<<x<<" "<<#y<<"="<<y<<" "<<#z<<"="<<z<<endl
#define showa2(x,a,b) cout<<#x<<": ";rep(i,a,b) cout<<x[i]<<‘ ‘;cout<<endl
using namespace std;
int n,k;
const double pi=acos(-1.0);
struct cpdouble x,y;;
inline cp operator*(cp a,cp b)return a.x*b.x-a.y*b.y,a.x*b.y+a.y*b.x;
inline cp operator+(cp a,cp b)return a.x+b.x,a.y+b.y;
inline cp operator-(cp a,cp b)return a.x-b.x,a.y-b.y;
const int maxl=1e6+10;
int la,lb;
bool a[maxl<<2];
bool ret[maxl<<2];
class fourierpublic:
  int rev[maxl<<2],len,pw;
  void init(int n)
    len=1,pw=0;
    while(len<=n) len<<=1,pw++;
    rep(i,0,len-1) rev[i]=0;
    rep(i,0,len-1) rev[i]=(rev[i>>1]>>1)|((i&1)<<(pw-1));
  
  cp c1[maxl<<2],c2[maxl<<2];
  cp wt[maxl<<2];
  void init_0(int ml=maxl)
		for(int mid=1;mid<2*maxl;mid<<=1)
//			wt.resize(mid*2+1);
			cp wn1=cos(pi/mid),sin(pi/mid);
			wt[mid]=(cp)1,0;
			rep(j,1,mid-1) wt[mid+j]=wt[mid+j-1]*wn1;
		
  
  void transform(cp*a,int flag)
    rep(i,0,len-1) if(i<rev[i]) swap(a[i],a[rev[i]]);
    for(int mid=1;mid<len;mid<<=1)
      for(int r=mid<<1,j=0;j<len;j+=r)
        for(int k=0;k<mid;++k)
          cp wn=wt[mid+k];
          if(flag==-1) wn.y=-wn.y;
          cp y=wn*a[mid+j+k];
          a[j+k+mid]=a[j+k]-y,a[j+k]=a[j+k]+y;
        
      
    
    if(flag==-1) rep(i,0,len-1) a[i].x/=len;
  
  void fix1()while(la&&!ret[la-1])--la;
  void fix2()while(lb&&!a[lb-1])--lb;
  //@传入整数,进行卷积@
  void mul(bool *a,bool *b)
    init(la+lb);
    rep(i,0,la-1)c1[i].x=a[i],c1[i].y=0;
    rep(i,la,len-1)c1[i].x=c1[i].y=0;
    rep(i,0,lb-1)c2[i].x=b[i],c2[i].y=0;
    rep(i,lb,len-1)c2[i].x=c2[i].y=0;
    transform(c1,1);transform(c2,1);
    rep(i,0,len-1) c1[i]=c1[i]*c2[i];
    transform(c1,-1);
    la=len;
    rep(i,0,len-1) a[i]=c1[i].x>=0.5;
    fix1();
  
  void sqr(bool *a)
    init(2*lb);
    rep(i,0,lb-1)c1[i].x=a[i],c1[i].y=0;
    rep(i,lb,len-1)c1[i].x=c1[i].y=0;
    transform(c1,1);
    rep(i,0,len-1) c1[i]=c1[i]*c1[i];
    transform(c1,-1);
    lb=len;
    rep(i,0,len-1) a[i]=c1[i].x>=0.5;
    fix2();
  
  void pow(int k)
    fix1();la=1,ret[0]=1;
    while(k)
      if(k&1) mul(ret,a);
      sqr(a);
      k>>=1;
    
  
fft;
int s[2000];
int main()
  ios::sync_with_stdio(false);cin.tie(0);
  cin>>n>>k;
  for(int i=1;i<=n;i++)
    cin>>s[i];
    a[s[i]]=1;
  
  sort(s+1,s+1+n);
  fft.init_0(s[n]*k+1);
  lb=1001;
  fft.pow(k);
  int len=min(la,s[n]*k+1);
  for(int i=k;i<len;i++) if(ret[i]) cout<<i<<" ";