【LOJ】#2670. 「NOI2012」随机数生成器

题解

矩阵乘法，注意需要快速乘

矩阵2*2

a c

0 1

代码

#include <iostream>
#include <algorithm>
#include <cstdio>
#include <cstring>
#define enter putchar('\n')
#define space putchar(' ')
#define MAXN 70005
//#define ivorysi
using namespace std;
typedef long long int64;
template<class T>
void read(T &res) {
    res = 0;char c = getchar();T f = 1;
    while(c < '0' || c > '9') {
	if(c == '-') f = -1;
	c = getchar();
    }
    while(c >= '0' && c <= '9') {
	res = res * 10 + c - '0';
	c = getchar();
    }
    res = res * f;
}
template<class T>
void out(T x) {
    if(x < 0) {x = -x;putchar('-');}
    if(x >= 10) out(x / 10);
    putchar('0' + x % 10);
}
int64 M,a,c,X0,N,G;
int64 inc(int64 a,int64 b) {
    return a + b >= M ? a + b - M : a + b;
}
int64 mul(int64 a,int64 b) {
    int64 res = 0,t = a;
    while(b) {
	if(b & 1) res = inc(res,t);
	t = inc(t,t);
	b >>= 1;
    }
    return res;
}
struct Matrix {
    int64 f[2][2];
    Matrix() {memset(f,0,sizeof(f));}
    friend Matrix operator * (const Matrix &a,const Matrix &b) {
	Matrix c;
	for(int i = 0 ; i <= 1 ; ++i) {
	    for(int j = 0 ; j <= 1 ; ++j) {
		for(int k = 0 ; k <= 1 ; ++k) {
		    c.f[i][j] = inc(c.f[i][j],mul(a.f[i][k],b.f[k][j]));
		}
	    }
	}
	return c;
    }
}A,ans;
void fpow(int64 c) {
    Matrix t = A;
    while(c) {
	if(c & 1) ans = ans * t;
	t = t * t;
	c >>= 1;
    }
}
void Solve() {
    read(M);read(a);read(c);read(X0);read(N);read(G);
    ans.f[0][0] = ans.f[1][1] = 1;
    A.f[0][0] = inc(a % M,M);A.f[0][1] = inc(c % M,M);
    A.f[1][1] = 1;
    fpow(N);
    int64 res = inc(mul(ans.f[0][0],X0),ans.f[0][1]);
    res = res % G;
    out(res);enter;
}
int main() {
#ifdef ivorysi
    freopen("f1.in","r",stdin);
#endif
    Solve();
}