【51Nod】1126 - 求递推数列的第N项（矩阵快速幂 & C++运算符重载）

题目链接：点击打开题目

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代码如下：

#include <cstdio>
#include <cstring>
#include <queue>
#include <cmath>
#include <stack>
#include <vector>
#include <algorithm>
using namespace std;
#define INF 0x3f3f3f3f
#define CLR(a,b) memset(a,b,sizeof(a))
#define PI acos(-1.0)
#define LL long long
const int MOD = 7;
struct Matrix
{
    int h,w;
    int m[3][3];
    void init(int op)
    {
        if (op == 0)        //初始化矩阵 
            CLR(this->m,0);
        else if (op == 1)       //初始化为单位矩阵 
        {
            this->h = this->w = 2;
            CLR(this->m,0);
            this->m[1][1] = this->m[2][2] = 1;
        }
        else if (op == 2)       //初始化为初始矩阵 
        {
            this->h = 1;
            this->w = 2;
            CLR(this->m,0);
            this->m[1][1] = this->m[1][2] = 1;
        }
    }
    void init(int A,int B)
    {
        this->w = this->h = 2;
        CLR(this->m,0);
        this->m[1][1] = A;
        this->m[2][1] = B;
        this->m[1][2] = 1;
    }
    Matrix operator * (Matrix a)
    {
        Matrix t;
        t.h = this->h;
        t.w = a.w;
        t.init(0);
        for (int i = 1 ; i <= this->h ; i++)
        {
            for (int j = 1 ; j <= a.w ; j++)
            {
                if (this->m[i][j])
                    for (int k = 1 ; k <= this->w ; k++)
                    {
                        t.m[i][k] = (t.m[i][k] + this->m[i][j] * a.m[j][k] % MOD) % MOD;
                    }
            }
        }
        return t;
    }
    Matrix quickMod(int n)
    {
        Matrix t;
        t.init(1);
        while (n)
        {
            if (n & 1)
                t = t * (*this);
            *this = (*this) * (*this);
            n >>= 1;
        }
        return t;
    }
};

int main()
{
    int A,B,n;
    scanf ("%d %d %d",&A,&B,&n);
    if (n == 1 || n == 2)
        puts("1");
    else
    {
        Matrix pr,ans,ori;
        pr.init(2);
        ori.init(A,B);
        ori = ori.quickMod(n-2);
        ans = pr * ori;
        printf ("%d\n",(ans.m[1][1] % MOD + MOD) % MOD);
    }
    return 0;
}