[bzoj4161]Shlw loves matrixI

来源：互联网发布：u盘数据丢失恢复编辑：程序博客网时间：2024/05/21 21:39

题目大意

常系数齐次递推

生成函数

构造特征多项式
然后用快速幂做多项式取模
多项式乘法暴力即可

#include<cstdio>#include<algorithm>#define fo(i,a,b) for(i=a;i<=b;i++)#define fd(i,a,b) for(i=a;i>=b;i--)using namespace std;typedef long long ll;const int maxn=4000+10,mo=1000000007;int a[maxn],b[maxn],c[maxn],d[maxn],e[maxn],f[maxn],o[maxn],ans[maxn],one[maxn],sta[80];int i,j,k,l,t,n,m,top,num;void FFT(int *a,int *b,int *c){    int i,j;    fo(i,0,k-1) e[i]=a[i],f[i]=b[i];    fo(i,0,2*k-2) o[i]=0;    fo(i,0,k-1)        fo(j,0,k-1)            o[i+j]=(o[i+j]+(ll)a[i]*b[j])%mo;    fd(i,2*k-2,k){        fo(j,1,k) o[i-j]=(o[i-j]-(ll)o[i]*d[k-j])%mo;        o[i]=0;    }    fo(i,0,k-1) c[i]=o[i];}int main(){    scanf("%d%d",&n,&k);    fo(i,1,k) scanf("%d",&c[i]);    fo(i,0,k-1) scanf("%d",&a[i]);    d[k]=1;    fd(i,k-1,0) d[i]=-c[k-i];    b[1]=1;    ans[0]=1;    while (n){        sta[++top]=n%2;        n/=2;    }    while (top){        FFT(ans,ans,ans);        if (sta[top]) FFT(ans,b,ans);        top--;    }    fo(i,0,k-1) num=(num+(ll)ans[i]*a[i])%mo;    (num+=mo)%=mo;    printf("%d\n",num);}

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