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多项式取模优化k阶常系数线性递推的模板

刚才的板子改了一下，wa了，，，先码这吧，下次再改。

 1 //Achen
 2 #include<algorithm>
 3 #include<iostream>
 4 #include<cstring>
 5 #include<cstdlib>
 6 #include<vector>
 7 #include<cstdio>
 8 #include<queue>
 9 #include<cmath>
10 #include<set>
11 #include<map>
12 #define Formylove return 0
13 #define For(i,a,b) for(int i=(a);i<=(b);i++)
14 #define Rep(i,a,b) for(int i=(a);i>=(b);i--)
15 const int N=4007,p=1000000007;
16 typedef long long LL;
17 typedef double db;
18 using namespace std;
19 LL a[N],f[N],n,k;
20 
21 template<typename T>void read(T &x)  {
22     char ch=getchar(); x=0; T f=1;
23     while(ch!='-'&&(ch<'0'||ch>'9')) ch=getchar();
24     if(ch=='-') f=-1,ch=getchar();
25     for(;ch>='0'&&ch<='9';ch=getchar()) x=x*10+ch-'0'; x*=f;
26 }
27 
28 LL rs[N],bs[N];
29 void mul(LL a[],LL b[],LL c[]) {
30     static LL tp[N];
31     int up=(k<<1);
32     For(i,0,up) tp[i]=0;
33     For(i,0,k-1) For(j,0,k-1)
34         (tp[i+j]+=a[i]*b[j]%p)%=p; 
35     Rep(i,up,k) { 
36         For(j,1,k) (tp[i-j]+=f[j]*tp[i]%p)%=p;
37         tp[i]=0;
38     }
39     For(i,0,up) c[i]=tp[i]; 
40 }
41 
42 void ksm(LL b) {
43     while(b) {
44         if(b&1) mul(rs,bs,rs);
45         mul(bs,bs,bs);
46         b>>=1;    
47     }
48 }
49 
50 //#define ANS
51 int main() {
52 #ifdef ANS
53     freopen("shanghai.in","r",stdin);
54     freopen("shanghai.out","w",stdout);
55 #endif
56     read(n); read(k);
57     For(i,1,k) read(f[i]);
58     For(i,1,k) { read(a[i]); (a[i]+=p)%=p; }
59     if(n<k) { 
60         printf("%lld\n",a[n+1]); 
61         return 0;
62     }
63     rs[0]=1; bs[1]=1;
64     ksm(n);
65     LL ans=0;
66     For(i,0,k-1) (ans+=rs[i]*a[i+1]%p)%=p;
67     printf("%lld\n",ans);
68     Formylove;
69 }
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posted @ 2018-08-20 20:19  啊宸  阅读(203)  评论(0)  编辑  收藏  举报