【Codeforces】450 B(div2)

题目链接：http://codeforces.com/problemset/problem/450/B

 

题意：

求这个的第n项。

 

题解：$f_{i+1} = f_i - f_{i-1} $

egin{pmatrix} 1 & 1\ -1 & 0 end{pmatrix} *

egin{pmatrix} f(n)& f(n-1) end{pmatrix} =

egin{pmatrix} f(n) - f(n-1) & f(n) end{pmatrix}=

egin{pmatrix} f(n+1) & f(n) end{pmatrix}

 

代入前两项即可。

代码：

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
#define ll long long
const int maxn = 3;
const ll mod = 1e9+7;

ll n,p;

struct Matrix{
    ll a[maxn][maxn];
    void init(){ 
        memset(a, 0, sizeof(a));
        for(int i = 1; i <= maxn;i++){
            a[i][i] = 1;
        }
    }
};

//矩阵乘法 
Matrix mul(Matrix a, Matrix b){
    Matrix ans;
    for(int i = 1;i <= 2;++i){
        for(int j = 1;j <= 2;++j){
            ans.a[i][j] = 0;
            for(int k = 1;k <= 2;++k){
                ans.a[i][j] = ans.a[i][j] % mod + a.a[i][k] * b.a[k][j] % mod;
                ans.a[i][j] %= mod;
            }
        }
    } 
    return ans;
}

//矩阵快速幂 
Matrix qpow(Matrix a,ll b){
    Matrix ans;
    ans.init();
    while(b){
        if(b & 1)
            ans = mul(ans,a);
        a = mul(a,a);
        b >>= 1;
    }
    return ans;
}

void print(Matrix a){
    for(int i = 1; i <= n;++i){
        for(int j = 1;j <= n;++j){
            cout << a.a[i][j]%mod<< " ";
        }
        cout << endl;
    }
}

int main(){
    Matrix base;
    Matrix ans;
    int x,y,n;
    cin>>x>>y>>n;
    if(n == 1){
        cout<<(mod + x) % mod<<endl;
        return 0;
    }
    if( n == 2){
        cout<<(mod + y) % mod<<endl;
        return 0;
    }

    ans.a[1][1] = y;ans.a[1][2] = x;
    base.a[1][1] = 1;base.a[1][2] = 1;
    base.a[2][1] = -1;base.a[2][2] = 0;
    
    ans = mul(ans,qpow(base,n-2));
    ll res = (mod + ans.a[1][1]) % mod;
    cout<<res<<endl;
    return 0;
}