Codeforces 450B Jzzhu and Sequences(矩阵快速幂)

    f1 = x, f2 = y;
    fi = f(i-1) + f(i+1)
        fi = f(i-1)-f(i-2);

类似于斐波那契构造矩阵

| 1 -1 |

| 1 0 |

代码：

#include
using namespace std;
const int mod = 1000000007;
struct node
{
    int s[2][2];
    node() {}
    node(int a, int b, int c, int d)
    {
        s[0][0] = a;
        s[0][1] = b;
        s[1][0] = c;
        s[1][1] = d;
    }
};

node mul(node a, node b)
{

    node t = node(0, 0, 0, 0);
    for(int i = 0; i < 2; i++)
        for(int j = 0; j < 2; j++)
            for(int k = 0; k < 2; k++)
                t.s[i][j] = (t.s[i][j]+a.s[i][k]*b.s[k][j])%mod;
    return t;
}

node mt_pow(node p, int n)
{
    node q = node(1, 0, 0, 1);
    while(n)
    {

        if(n&1) q = mul(q, p);
        p = mul(p, p);
        n /= 2;
    }
    return q;
}

int main(void)
{
    int f1, f2, n;
    while(cin >> f1 >> f2 >> n)
    {
        if(n == 1) printf("%d\n", (f1%mod+mod)%mod);
        else if(n == 2) printf("%d\n", (f2%mod+mod)%mod);
        else
        {
            node base = node(1, -1, 1, 0);
            node ans = mt_pow(base, n-2);
            int res = (ans.s[0][0]*f2+ans.s[0][1]*f1)%mod;
            if(res < 0) res += mod;
            printf("%d\n", res);
        }
    }
    return 0;
}

A - Jzzhu and Sequences

Time Limit:1000MS     Memory Limit:262144KB     64bit IO Format:%I64d & %I64u

Submit  Status  Practice  CodeForces 450B

Appoint description:  System Crawler  (Oct 7, 2016 3:23:55 PM)

Description

Jzzhu has invented a kind of sequences, they meet the following property:

You are given x and y, please calculate f_n modulo 1000000007 (10⁹ + 7).

Input

The first line contains two integers x and y (|x|, |y| ≤ 10⁹). The second line contains a single integer n (1 ≤ n ≤ 2·10⁹).

Output

Output a single integer representing f_n modulo 1000000007 (10⁹ + 7).

Sample Input

Input

2 3
3

Output

1

Input

0 -1
2

Output

1000000006

Hint

In the first sample, f₂ = f₁ + f₃, 3 = 2 + f₃, f₃ = 1.

In the second sample, f₂ =  - 1;  - 1 modulo (10⁹ + 7) equals (10⁹ + 6).