hlg2148Resident Evil【矩阵快速幂】

这个矩阵比较好找 

#include <iostream>
#include <cstdio>
#include <cstring>
using namespace std;
#define sc scanf
#define pr printf
#define re return
#define me(a, b) memset(a, b, sizeof(a));
#define fr(i, j, k) for(int i = j; i <= k; i++)
#define f(i, j, k) for(int i = j; i < k; i++)
#define co continue

const int N = 2;
struct Mat {
    double mat[N][N];
};

Mat operator * (Mat a, Mat b) {
    Mat c;
    for(int i = 0; i < N; i++) {
        for(int j = 0; j < N; j++) {
            c.mat[i][j] = 0;
            for(int k = 0; k < N; k++) {
                c.mat[i][j] += a.mat[i][k] * b.mat[k][j];
            }
        }
    }
    return c;
}

Mat operator ^ (Mat a, int k) {
    Mat c;
    int i, j;
    for(i = 0; i < N; i++) {
        for(j = 0; j < N; j++) {
            c.mat[i][j] = (i == j);
        }
    }
    for(; k; k >>= 1) {
        if(k & 1) c = c * a;
        a = a * a;
    }
    return c;
}

int main() {
    double a, b; int n;
    double p1, p2; int d;
    Mat m1, m2;
    while(EOF != sc("%lf %lf %d",&a, &b, &n) ) {
        m1.mat[0][0] = a; m1.mat[0][1] = b;
        m1.mat[1][0] = 0; m1.mat[1][1] = 0;
        fr(i, 1, n) {
            sc("%lf %lf %d",&p1, &p2, &d);
            m2.mat[0][0] = 1 - p1; m2.mat[0][1] = p1;
            m2.mat[1][0] = p2; m2.mat[1][1] = 1 - p2;
            if(d == 0) {
                printf("%d
", (int) (b + 1e-8) );
                co;
            }
            m2 = m2^d;
            m2 = m1 * m2;
            printf("%d
",(int) ( m2.mat[0][1] + 1e-8) );
        }
    }
    re 0;
}

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
using namespace std;

#define sc scanf
#define pr printf
#define re return
#define me(a, b) memset(a, b, sizeof(a));
#define fr(i, j, k) for(int i = j; i <= k; i++)
#define f(i, j, k) for(int i = j; i < k; i++)
#define co continue

const int maxn = 1005;

double st[1][2];
double xx[2][2];
double mid[2][2];
double end[1][2];

void xiangcheng(double a[1][2], double b[2][2], double c[1][2]) {
    f(i, 0, 1) {
        f(j, 0, 2) {
            c[i][j] = 0;
            f(k, 0, 2) {
                c[i][j] += a[i][k] * b[k][j];
            }
        }
    }
}

void haha(double a[2][2], double b[2][2], double c[2][2]) {
    f(i, 0, 2) {
        f(j, 0, 2) {
            c[i][j] = 0;
            f(k, 0, 2) {
                c[i][j] += a[i][k] * b[k][j];
            }
        }
    }
}

void jisuan(double a[2][2], int x, double b[2][2]) {
    if(x == 1) {
        f(i, 0, 2) {
            f(j, 0, 2) {
                b[i][j] = a[i][j];
            }
        }
        re;
    }
    double c[2][2];
    if(x % 2 == 1) {
        jisuan(a, x - 1, c);
        haha(c, xx, b);
    } else {
        jisuan(a, x / 2, c);
        haha(c, c, b);
    }
}
        
int main() {
    double a, b; int n;
    double p1, p2; int d;
    while(EOF != sc("%lf %lf %d",&a, &b, &n) ) {
        st[0][0] = a; st[0][1] = b;
        fr(i, 1, n) {
            sc("%lf %lf %d",&p1, &p2, &d);
            xx[0][0] = 1 - p1; xx[0][1] = p1;
            xx[1][0] = p2; xx[1][1] = 1 - p2;
            if(d == 0) {
                printf("%d
", (int) (b + 1e-8) );
                co;
            }
            jisuan(xx, d, mid);
            xiangcheng(st, mid, end);
            printf("%d
",(int) ( end[0][1] + 1e-8) );
        }
    }
    re 0;
}