FFT学习
看了一天的多项式的内容，看博客的时候好像还是那么回事，一看题，哇塞，发现我其实连卷积是啥都没看懂。
qtdydb，背板子。 不知道卷积是啥就很伤了。
P3803 【模板】多项式乘法（FFT）
#include<iostream> #include<cstdio> #include<cmath> #include<cstring> #include<algorithm> #include<queue> using namespace std; typedef long long LL; inline int read() { char c=getchar();int num=0,f=1; for(;!isdigit(c);c=getchar()) f=c=='-'?-1:f; for(;isdigit(c);c=getchar()) num=num*10+c-'0'; return num*f; } const int N=4e6+5; const double pi=acos(-1); int n,m,bit,len=1; int rev[N]; struct Complex { double x,y; Complex(double xx=0,double yy=0){x=xx,y=yy;} Complex operator + (const Complex &A){return Complex(x+A.x,y+A.y);} Complex operator - (const Complex &A){return Complex(x-A.x,y-A.y);} Complex operator * (const Complex &A){return Complex(x*A.x-y*A.y,x*A.y+y*A.x);} }a[N],b[N]; void fft(Complex *A,int dft) { for(int i=0;i<len;++i) if(i<rev[i]) swap(A[i],A[rev[i]]); for(int step=1;step<len;step<<=1) { Complex wn(cos(pi/step),dft*sin(pi/step)); for(int j=0;j<len;j+=(step<<1)) { Complex wnk(1,0); for(int k=j;k<step+j;++k) { Complex x=A[k],y=wnk*A[k+step]; A[k]=x+y,A[k+step]=x-y; wnk=wnk*wn; } } } if(dft==1) return; for(int i=0;i<=n+m;++i) A[i].x/=len; } int main() { n=read(),m=read(); for(int i=0;i<=n;++i) a[i].x=read(); for(int i=0;i<=m;++i) b[i].x=read(); while(len<=n+m) len<<=1,++bit; for(int i=0;i<len;++i) rev[i]=(rev[i>>1]>>1)|((i&1)<<(bit-1)); fft(a,1),fft(b,1); for(int i=0;i<=len;++i) a[i]=a[i]*b[i]; fft(a,-1); for(int i=0;i<=n+m;++i) cout<<(int)(a[i].x+0.5)<<' '; return 0; }
P3338 [ZJOI2014]力
不会，抄的
#include<iostream> #include<cstdio> #include<cmath> #include<cstring> #include<algorithm> #include<queue> using namespace std; typedef long long LL; inline int read() { char c=getchar();int num=0,f=1; for(;!isdigit(c);c=getchar()) f=c=='-'?-1:f; for(;isdigit(c);c=getchar()) num=num*10+c-'0'; return num*f; } const int N=4e5+5; const double pi=acos(-1); int n,m,bit,len=1,rev[N]; struct Complex { double x,y; Complex(double xx=0,double yy=0){x=xx,y=yy;} Complex operator + (const Complex &A){return Complex(x+A.x,y+A.y);} Complex operator - (const Complex &A){return Complex(x-A.x,y-A.y);} Complex operator * (const Complex &A){return Complex(x*A.x-y*A.y,x*A.y+y*A.x);} }a[N],b[N],c[N]; void fft(Complex *A,int dft) { for(int i=0;i<len;++i) if(i<rev[i]) swap(A[i],A[rev[i]]); for(int i=1;i<len;i<<=1) { Complex wn(cos(pi/i),dft*sin(pi/i)); for(int j=0,t=i*2;j<len;j+=t) { Complex wnk(1,0); for(int k=j;k<i+j;++k) { Complex x=A[k],y=wnk*A[k+i]; A[k]=x+y,A[k+i]=x-y; wnk=wnk*wn; } } } if(dft==1) return; for(int i=0;i<=len;++i) A[i].x/=len; } int main() { n=read(); for(int i=1;i<=n;++i) scanf("%lf",&a[i].x),b[n-i+1].x=a[i].x; for(int i=1;i<=n;++i) c[i].x=1.0/(1ll*i*i); while(len<=(n<<1)) ++bit,len<<=1; for(int i=0;i<len;++i) rev[i]=(rev[i>>1]>>1)|((i&1)<<(bit-1)); fft(a,1),fft(b,1),fft(c,1); for(int i=0;i<=len;++i) a[i]=a[i]*c[i],b[i]=b[i]*c[i]; fft(a,-1),fft(b,-1); for(int i=1;i<=n;++i) printf("%.3lf\n",a[i].x-b[n-i+1].x); return 0; }
2194: 快速傅立叶之二
不会，抄的。 好像知道fft/卷积一拉子是干什么的了。
#include<iostream> #include<cstdio> #include<cmath> #include<cstring> #include<algorithm> #include<queue> using namespace std; typedef long long LL; inline int read() { char c=getchar();int num=0,f=1; for(;!isdigit(c);c=getchar()) f=c=='-'?-1:f; for(;isdigit(c);c=getchar()) num=num*10+c-'0'; return num*f; } const int N=4e5+5; const double pi=acos(-1); int n,bit,len=1,rev[N]; struct Complex { double x,y; Complex(double a=0,double b=0){x=a,y=b;} Complex operator + (const Complex &A){return Complex(x+A.x,y+A.y);} Complex operator - (const Complex &A){return Complex(x-A.x,y-A.y);} Complex operator * (const Complex &A){return Complex(x*A.x-y*A.y,x*A.y+y*A.x);} }a[N],b[N]; void fft(Complex *A,int dft) { for(int i=0;i<len;++i) if(i<rev[i]) swap(A[i],A[rev[i]]); for(int i=1;i<len;i<<=1) { Complex wn(cos(pi/i),dft*sin(pi/i)); for(int j=0,t=i<<1;j<len;j+=t) { Complex wnk(1,0); for(int k=j;k<i+j;++k) { Complex x=A[k],y=wnk*A[k+i]; A[k]=x+y,A[k+i]=x-y; wnk=wnk*wn; } } } if(dft==1) return; for(int i=0;i<len;++i) A[i].x/=len; } int main() { n=read(); for(int i=0;i<n;++i) { a[n-i-1].x=read(); b[i].x=read(); } while(len<=(n<<1)) len<<=1,++bit; for(int i=0;i<len;++i) rev[i]=(rev[i>>1]>>1)|((i&1)<<(bit-1)); fft(a,1),fft(b,1); for(int i=0;i<=len;++i) a[i]=a[i]*b[i]; fft(a,-1); for(int i=0;i<n;++i) printf("%d\n",(int)(a[n-i-1].x+0.5)); return 0; }
3513: [MUTC2013]idiots
不会，抄的。还是不知道fft/卷积一拉子是干什么的。
#include<iostream> #include<cstdio> #include<cmath> #include<cstring> #include<algorithm> #include<queue> using namespace std; typedef long long LL; inline int read() { char c=getchar();int num=0,f=1; for(;!isdigit(c);c=getchar()) f=c=='-'?-1:f; for(;isdigit(c);c=getchar()) num=num*10+c-'0'; return num*f; } const int N=4e5+5; const double pi=acos(-1); int n,bit,len=1,rev[N]; LL g[N],t[N]; struct Complex { double x,y; Complex(double a=0,double b=0){x=a,y=b;} Complex operator + (const Complex &A){return Complex(x+A.x,y+A.y);} Complex operator - (const Complex &A){return Complex(x-A.x,y-A.y);} Complex operator * (const Complex &A){return Complex(x*A.x-y*A.y,x*A.y+y*A.x);} }f[N]; void fft(Complex *A,int dft) { for(int i=0;i<len;++i) if(i<rev[i]) swap(A[i],A[rev[i]]); for(int i=1;i<len;i<<=1) { Complex wn(cos(pi/i),dft*sin(pi/i)); for(int j=0,t=i<<1;j<len;j+=t) { Complex wnk(1,0); for(int k=j;k<i+j;++k) { Complex x=A[k],y=wnk*A[k+i]; A[k]=x+y,A[k+i]=x-y; wnk=wnk*wn; } } } if(dft==1) return; for(int i=0;i<=len;++i) A[i].x/=len; } int main() { int T=read(); while(T--) { memset(g,0,sizeof(g)),memset(t,0,sizeof(t)); memset(f,0,sizeof(f)); n=read();int mx=0;LL sum; for(int i=1,a;i<=n;++i) { a=read();mx=max(mx,a); --g[a<<1],++t[a],++f[a].x; } for(int i=mx;i;--i) t[i]+=t[i+1]; mx<<=1,sum=1ll*n*(n-1)*(n-2)/6; len=1,bit=0;while(len<=mx) len<<=1,++bit; for(int i=0;i<=len;++i) rev[i]=(rev[i>>1]>>1)|((i&1)<<(bit-1)); fft(f,1); for(int i=0;i<=len;++i) f[i]=f[i]*f[i]; fft(f,-1); for(int i=0;i<=len;++i) g[i]+=1ll*(f[i].x+0.5); LL ans=0; for(int i=0;i<=len;++i) ans+=(g[i]/2)*t[i]; ans=sum-ans; printf("%.7lf\n",1.0*ans/sum); } return 0; }
不会，抄的。
#include<iostream> #include<cstdio> #include<cmath> #include<cstring> #include<algorithm> #include<queue> using namespace std; typedef long long LL; inline int read() { char c=getchar();int num=0,f=1; for(;!isdigit(c);c=getchar()) f=c=='-'?-1:f; for(;isdigit(c);c=getchar()) num=num*10+c-'0'; return num*f; } const int N=3e5+5; const double pi=acos(-1); int n,m,len=1,bit,rev[N]; struct Complex { double x,y; Complex(double a=0,double b=0){x=a,y=b;} Complex operator + (const Complex &A){return Complex(x+A.x,y+A.y);} Complex operator - (const Complex &A){return Complex(x-A.x,y-A.y);} Complex operator * (const Complex &A){return Complex(x*A.x-y*A.y,x*A.y+y*A.x);} }a[N],b[N]; void fft(Complex *A,int dft) { for(int i=0;i<len;++i) if(i<rev[i]) swap(A[i],A[rev[i]]); for(int i=1;i<len;i<<=1) { Complex wn(cos(pi/i),dft*sin(pi/i)); for(int j=0,t=i<<1;j<len;j+=t) { Complex wnk(1,0); for(int k=j;k<i+j;++k) { Complex x=A[k],y=wnk*A[k+i]; A[k]=x+y,A[k+i]=x-y; wnk=wnk*wn; } } } if(dft==1) return; for(int i=0;i<=len;++i) A[i].x=A[i].x/len+0.5; } int main() { n=read(),m=read();LL a1=0,a2=0,b1=0,b2=0; for(int i=1;i<=n;++i) { a[i].x=a[n+i].x=read(); a1+=a[i].x*a[i].x,a2+=a[i].x; } for(int i=1;i<=n;++i) { b[n-i+1].x=read(); b1+=b[n-i+1].x*b[n-i+1].x,b2+=b[n-i+1].x; } while(len<=(n*3)) len<<=1,++bit; for(int i=0;i<len;++i) rev[i]=(rev[i>>1]>>1)|((i&1)<<(bit-1)); fft(a,1),fft(b,1); for(int i=0;i<=len;++i) a[i]=a[i]*b[i]; fft(a,-1); LL ans=1ll<<60,sum=ans; for(int j=-m;j<=m;++j) sum=min(sum,a1+b1+n*j*j+2ll*j*(a2-b2)); for(int i=1;i<=n;++i) ans=min(ans,sum-2ll*(LL)a[n+i].x); cout<<ans; return 0; }
真tm难啊
