zoukankan      html  css  js  c++  java
  • 洛谷 P1939 矩阵加速(数列)

    题意简述

    (a[1]=a[2]=a[3]=1)
    (a[x]=a[x−3]+a[x−1](x>3))
    求a数列的第n项对1000000007取余的值。

    题解思路

    矩阵加速
    设$$ F=egin{bmatrix} 0&0&11&0&0&1&1end{bmatrix}, G=egin{bmatrix} 111end{bmatrix}$$
    则$$ egin{bmatrix} a[n-3]a[n-2]a[n-1]end{bmatrix} = G * F ^ {n-3} (n > 3)$$

    代码

    #include <cstdio>
    typedef long long ll;
    const int mod = 1000000007;
    int n, T, N;
    struct Matrix
    {
    	int a[4][4];
    	Matrix& operator =(const Matrix& x)
    	{
    		for (register int i = 1; i <= N; ++i)
    			for (register int j = 1; j <= N; ++j)
    				a[i][j] = x.a[i][j];
    		return *this;
    	}
    };
    Matrix a, b, c;
    Matrix Mul(const Matrix& x, const Matrix& y)
    {
    	Matrix s;
    	for (register int i = 1; i <= N; ++i)
    		for (register int j = 1; j <= N; ++j)
    			s.a[i][j] = 0;
    	for (register int i = 1; i <= N; ++i)
    		for (register int j = 1; j <= N; ++j)
    			for (register int k = 1; k <= N; ++k)
    				s.a[i][j] = (s.a[i][j] + (ll)x.a[i][k] * y.a[k][j] % mod) % mod;
    	return s;
    }
    Matrix _pow(Matrix x, int y)
    {
    	Matrix s;
    	for (register int i = 1; i <= N; ++i)
    		for (register int j = 1; j <= N; ++j)
    			s.a[i][j] = (i == j);
    	for (; y; y >>= 1, x = Mul(x, x)) if (y & 1) s = Mul(s, x);
    	return s;
    }
    int main()
    {
    	N = 3;
    	scanf("%d", &T);
    	while (T--)
    	{
    		c.a[1][1] = c.a[1][2] = c.a[1][3] = 1;
    		a.a[1][3] = a.a[2][1] = a.a[3][2] = a.a[3][3] = 1;
    		scanf("%d", &n);
    		if (n <= 3) {printf("1
    "); continue; }
    		b = Mul(c, _pow(a, n - 3));
    		printf("%d
    ", b.a[1][3]);
    	}
    }
    
  • 相关阅读:
    Android--adb
    Android 爬坑之路
    Android倒计时实现
    Android Studio常用设置
    Java Web开发——MySQL数据库的安装与配置
    DOS命令(系统错误5,拒绝访问)的解决方法
    Java EE开发环境——MyEclipse2017破解 和 Tomcat服务器配置
    设计模式-工厂模式
    设计模式-简单工厂模式
    设计模式简介
  • 原文地址:https://www.cnblogs.com/xuyixuan/p/9800426.html
Copyright © 2011-2022 走看看