浮波那契 51Nod - 1358

https://www.51nod.com/onlineJudge/questionCode.html#!problemId=1358

看了题解才想到。。

f(n)=f(n-1)+(fn-3.4) => g(n)=g(n-10)+g(n-34) g(10*n)=f(n)

要求f(n)等价于求g(10*n) g(i)=1 1<=i<=40

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll mod=1e9+7;

ll mat[35][35],ans[35][35];

void getmul(ll a[][35],ll b[][35])
{
    ll c[35][35];
    int i,j,k;
    for(i=1;i<=34;i++)
    {
        for(j=1;j<=34;j++)
        {
            c[i][j]=0;
            for(k=1;k<=34;k++) c[i][j]=(c[i][j]+(a[i][k]*b[k][j])%mod)%mod;
        }
    }
    memcpy(a,c,sizeof(c));
}

ll quickpow(ll n)
{
    ll res;
    int i;
    for(i=1;i<=33;i++) mat[i][i+1]=1;
    mat[10][1]=1,mat[34][1]=1;
    for(i=1;i<=34;i++) ans[i][i]=1;
    while(n>0)
    {
        if(n%2) getmul(ans,mat);
        getmul(mat,mat),n/=2;
    }
    res=0;
    for(i=1;i<=34;i++) res=(res+ans[i][1])%mod;
    return res;
}

int main()
{
    ll n;
    scanf("%lld",&n);
    if(n<=4) printf("1\n");
    else printf("%lld\n",quickpow(10*(n-4)));
    return 0;
}