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codechef Random Number Generator - ShinriiTin's Blog - 博主是sb

hdu4914 Linear recursive sequence

codeforces round290 Div1 E Fox And Polygon

codechef Random Number Generator

ShinriiTin posted @ 2015年6月12日 17:41 in 未分类 with tags FFT 常系数齐次递推 , 511 阅读

题意:求常系数齐次递推数列的第n项

当递推系数非零项很多的时候暴力复位一次是O(k²)的

构造特征矩阵M的特征多项式f(x)=x^k-∑_i c_i*xⁱ

由f(M)=0,那么我们复位时只需要mod f(x)就好

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154	`#include <stdio.h>` `#include <string.h>` `#include <algorithm>` `#define g() getchar()` `template<class` `Q>void` `Scan(Q&x){` `char` `c;` `while(c=g(),c<48\|\|c>57);` `for(x=0;c>47&&c<58;c=g())x=10x+c-48;` `}` `#define G 3` `#define maxn 65536` `#define DFT(a,n) fft(a,n,0)` `#define IDFT(a,n) fft(a,n,1)` `#define INV(x) qpow(x,P-2)` `#define rep(i,a,b) for(int i=a;i<(b);++i)` `using` `namespace` `std;` `const` `int` `MAXN=(1<<16)+5;` `const` `int` `P=104857601;` `typedef` `long` `long` `ll;` `inline` `ll qpow(ll x,int` `k){` `ll ans=1;` `for(;k;x=xx%P,k>>=1)` `if(k&1)ans=ansx%P;` `return` `ans;` `}` `int` `r[MAXN],w[2][MAXN],rn;` `inline` `void` `init_fft(int` `n,int` `b){` `rn=INV(n);` `rep(i,1,n){` `r[i]=(r[i>>1]>>1)\|((i&1)<<(b-1));` `}` `}` `inline` `void` `fft(inta,int` `n,int` `t){` `rep(i,1,n)if(i<r[i])swap(a[i],a[r[i]]);` `for(int` `i=2;i<=n;i<<=1)` `for(int` `j=0;j<n;j+=i)` `for(int` `k=0;k<i>>1;++k){` `int` `re=1lla[(i>>1)+j+k]w[t][maxn/ik]%P;` `a[(i>>1)+j+k]=(a[j+k]+P-re)%P;` `a[j+k]=(a[j+k]+re)%P;` `}` `if(t)rep(i,0,n)a[i]=1lla[i]rn%P;` `}` `int` `k,len,bit;` `inline` `void` `inv(inta,intb){` `static` `int` `c[MAXN],l;` `b[0]=1,b[1]=0,l=1;` `rep(j,1,bit+1){` `l<<=1;` `rep(i,0,l)c[i]=a[i];` `rep(i,l,l<<1)b[i]=c[i]=0;` `init_fft(l<<1,j+1);` `DFT(b,l<<1),DFT(c,l<<1);` `rep(i,0,l<<1){` `b[i]=1llb[i](2+P-1llb[i]c[i]%P)%P;` `}` `IDFT(b,l<<1);` `rep(i,l,l<<1)b[i]=0;` `}` `}` `int` `m[MAXN],dm[MAXN],im[MAXN];` `int` `ta[MAXN],ra[MAXN];` `inline` `void` `mod(inta){` `DFT(ta,len),DFT(a,len);` `rep(i,0,len)a[i]=1lla[i]ta[i]%P;` `IDFT(a,len);` `rep(i,0,k-1)ra[i]=a[(k-1<<1)-i];` `rep(i,k-1,len)ra[i]=0;` `DFT(ra,len);` `rep(i,0,len)ra[i]=1llra[i]im[i]%P;` `IDFT(ra,len);` `rep(i,0,k-1)ta[i]=ra[k-2-i];` `rep(i,k-1,len)ta[i]=0;` `DFT(ta,len);` `rep(i,0,len)ta[i]=1llta[i]dm[i]%P;` `IDFT(ta,len);` `rep(i,0,k)a[i]=(a[i]+P-ta[i])%P;` `rep(i,k,len)a[i]=0;` `}` `inline` `void` `Init(){` `int` `n=maxn;` `int` `g=qpow(G,(P-1)/n);` `w[0][0]=w[0][n]=1;` `rep(i,1,n)w[0][i]=1llw[0][i-1]g%P;` `rep(i,0,n+1)w[1][i]=w[0][n-i];` `}` `ll n;` `int` `a[MAXN],ans[MAXN],x[MAXN];` `int` `main(){` `Init();` `Scan(k),Scan(n),--n;` `len=k+1,bit=1;` `while(1<<bit<len)++bit;` `len=1<<bit;` `rep(i,0,k)Scan(a[i]);` `for(int` `i=k-1;~i;--i){` `Scan(m[i]),m[i]=(P-m[i])%P;` `}` `if(k==1){` `int` `res=qpow((P-m[0])%P,n%(P-1))a[0]%P;` `printf("%d\n",res);` `return` `0;` `}` `m[k]=1;` `rep(i,0,k+1)dm[i]=m[k-i];` `inv(dm,im);` `len<<=1,++bit;` `rep(i,0,k+1)dm[i]=m[i];` `rep(i,k+1,len)dm[i]=im[i]=0;` `DFT(dm,len),DFT(im,len);` `for(ans[0]=x[1]=1;n;n>>=1){` `if(n&1){` `rep(i,0,len)ta[i]=x[i];` `mod(ans);` `}` `rep(i,0,len)ta[i]=x[i];` `mod(x);` `}` `int` `res=0;` `rep(i,0,k){` `res=(res+1lla[i]*ans[i])%P;` `}` `printf("%d\n",res);` `return` `0;` `}`

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