2019雅礼集训 D1T3 math [咕咕咕]

题目描述：

样例：

input:
2
3 5 0.01
3 6 0.02

output:
+2
+4

数据范围：

标签： 数学，矩阵乘法

题解：

标程：

#include<cstring>
#include<algorithm>
#include<cstdio>
#include<cmath>
#define fo(i,a,b) for(i=a;i<=b;i++)
const int maxn=60+5;
int i,j,n,m,t,k;
struct ar{
    double a[maxn][maxn];
} a,c;
double x;
ar ch(ar a,ar b){
    ar c;
    memset(c.a,0,sizeof(c.a));
    fo(i,1,m*2)
    fo(j,1,m*2)
    fo(k,1,m*2) c.a[i][j]=c.a[i][j]+a.a[i][k]*b.a[k][j];
    return c;
}
int main(){
    freopen("math.in","r",stdin);freopen("math.out","w",stdout);
    scanf("%d",&t);
    while (t){
        t--;
        scanf("%d%d%lf",&m,&n,&x);
        memset(a.a,0,sizeof(a.a));
        memset(c.a,0,sizeof(c.a));
        fo(i,m+1,m*2){
            a.a[i][i-m]=1,a.a[i-m][i]=-1;
            a.a[i][i]=2*cos(x);if (i<m*2)a.a[i][i+1]=sin(x);
        }
        c.a[1][1]=sin(x);c.a[1][m+1]=sin(2*x);c.a[1][m+2]=sin(x)*sin(x);
        n--;
        while (n){
            if (n%2)c=ch(c,a);
            a=ch(a,a);
            n/=2;
        }
        double s=c.a[1][m];
        if (s>0) printf("+");else printf("-");
        s=fabs(s);
        if (s<1){
            double s1=0.1;
            while (1) if (s>s1) {printf("%d\n",(int)(s/s1));break;}else s1*=0.1;
        }else{
            while (s)if (s<10) {printf("%d\n",(int)s);break;}else s/=10;
            
        }
    }
}