BZOJ 2875: [Noi2012]随机数生成器( 矩阵快速幂 )

矩阵快速幂...+快速乘就OK了

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#include<bits/stdc++.h>

 

using namespace std;

 

typedef long long ll;

 

ll MOD, a, c, x, n, g;

 

ll MUL(ll a, ll b) {

ll ans = 0;

for(; b; b >>= 1) {

if(b & 1) ans += a;

if(ans >= MOD) ans -= MOD;

a <<= 1;

if(a >= MOD) a -= MOD;

}

return ans;

}

 

struct matrix {

ll x[2][2];

matrix() {

memset(x, 0, sizeof x);

}

inline void unit() {

x[0][0] = x[1][1] = 1;

x[0][1] = x[1][0] = 0;

}

matrix operator * (const matrix &o) {

matrix ans;

for(int i = 0; i < 2; i++)

   for(int j = 0; j < 2; j++)

       for(int k = 0; k < 2; k++)

           (ans.x[i][j] += MUL(x[i][k], o.x[k][j])) %= MOD;

return ans;

}

matrix operator = (const matrix &o) {

memcpy(x, o.x, sizeof x);

return *this;

}

matrix operator ^ (ll k) {

matrix ans, p = *this; ans.unit();

for(; k; k >>= 1) {

if(k & 1) ans = ans * p;

p = p * p;

}

return ans;

}

} Q;

 

int main() {

cin >> MOD >> a >> c >> x >> n >> g;

Q.x[0][0] = a; Q.x[0][1] = 0; Q.x[1][0] = c; Q.x[1][1] = 1;

matrix ans = Q ^ n;

cout << (MUL(x, ans.x[0][0]) + ans.x[1][0]) % MOD % g << "\n";

return 0;

}

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2875: [Noi2012]随机数生成器

Time Limit: 10 Sec  Memory Limit: 512 MB
Submit: 1289  Solved: 731
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Description

Input

包含6个用空格分割的m,a,c,X0,n和g，其中a,c,X0是非负整数，m,n,g是正整数。

Output

输出一个数，即Xn mod g

Sample Input

11 8 7 1 5 3

Sample Output

2

HINT

Source