[NOI2012]隨機數生成器
阿新 • • 發佈:2018-12-19
嘟嘟嘟
這題就是一道矩陣加速dp的水題,dp式都給你了,所以矩陣這方面就不說了。
之所以發這篇部落格,是因為兩數相乘可能會爆long long,所以得用快速乘。
現學了一下,感覺和快速冪特別像。
對於兩個數\(a, b\),按位列舉\(b\),如果\(b\)的第\(i\)位為\(1\),答案就加上\(a * 2 ^ i\)。
發一下程式碼。
#include<cstdio> #include<iostream> #include<cmath> #include<algorithm> #include<cstring> #include<cstdlib> #include<cctype> #include<vector> #include<stack> #include<queue> using namespace std; #define enter puts("") #define space putchar(' ') #define Mem(a, x) memset(a, x, sizeof(a)) #define rg register typedef long long ll; typedef double db; const int INF = 0x3f3f3f3f; const db eps = 1e-8; //const int maxn = ; inline ll read() { ll ans = 0; char ch = getchar(), last = ' '; while(!isdigit(ch)) {last = ch; ch = getchar();} while(isdigit(ch)) {ans = (ans << 1) + (ans << 3) + ch - '0'; ch = getchar();} if(last == '-') ans = -ans; return ans; } inline void write(ll x) { if(x < 0) x = -x, putchar('-'); if(x >= 10) write(x / 10); putchar(x % 10 + '0'); } ll mod, a, c, x0, n, g; ll mul(ll a, ll b) //神奇的快速乘 { ll ret = 0; for(; b; b >>= 1, a = (a << 1) % mod) if(b & 1) ret = (ret + a) % mod; return ret; } const int N = 2; struct Mat { ll a[N][N]; Mat operator * (const Mat& oth)const { Mat ret; Mem(ret.a, 0); for(int i = 0; i < N; ++i) for(int j = 0; j < N; ++j) for(int k = 0; k < N; ++k) ret.a[i][j] += mul(a[i][k], oth.a[k][j]), ret.a[i][j] %= mod; return ret; } }F; void init() { Mem(F.a, 0); F.a[0][0] = a; F.a[0][1] = F.a[1][1] = 1; } Mat quickpow(Mat A, ll b) { Mat ret; Mem(ret.a, 0); for(int i = 0; i < N; ++i) ret.a[i][i] = 1; for(; b; b >>= 1, A = A * A) if(b & 1) ret = ret * A; return ret; } int main() { mod = read(), a = read(), c = read(), x0 = read(), n = read(), g = read(); a %= mod; c %= mod; x0 %= mod; init(); Mat A = quickpow(F, n); write((mul(A.a[0][0], x0) + mul(A.a[0][1], c)) % mod % g), enter; return 0; }