数学 习题
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#include<iostream> #include<cstring> #include<cstdio> #include<algorithm> #include<cassert> using namespace std; #define MOD 100000007 struct matrix { static const int maxn = 2; int n,m; int mat[maxn][maxn]; matrix() { memset(mat,0,sizeof(mat)); } void initEye(int n) { this->n = this->m = n; memset(mat,0,sizeof(mat)); for (int i=0;i<n;i++) mat[i][i] = 1; } void initStart() { this->n = 2; this->m = 1; memset(mat,0,sizeof(mat)); mat[0][0] = mat[1][0] = 1; } void initFib() { this->n = this->m = 2; mat[0][0] = 0; mat[1][0] = mat[0][1] = mat[1][1] = 1; } void print() { cout<<"MATRIX "<<n<<" "<<m<<endl; for (int i=0;i<n;i++) { for (int j=0;j<m;j++) { cout<<mat[i][j]<<"\t"; } cout<<endl; } } }; matrix operator* (const matrix& m1,const matrix& m2) { assert(m1.m == m2.n); matrix res; res.n = m1.n; res.m = m2.m; for (int i=0;i<m1.n;i++) { for (int j=0;j<m2.m;j++) { for (int k=0;k<m1.m;k++) { res.mat[i][j] = (res.mat[i][j] + (long long)m1.mat[i][k]*m2.mat[k][j])%MOD; } } } return res; } matrix pow_mod(matrix x,int y) { matrix res; res.initEye(2); while(y) { if (y&1) res = res * x; x = x*x; y>>=1; } return res; } int main() { matrix x; matrix T; x.initStart(); x.print(); T.initFib(); T.print(); (pow_mod(T,60000000)*x).print(); while (1); } |
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#include<iostream> #include<cstring> #include<cstdio> #include<algorithm> #include<cassert> #include<cmath> using namespace std; #define MOD 100000007 #define eps 1e-7 struct matrix { static const int maxn = 20; int n,m; double mat[maxn][maxn]; matrix() { memset(mat,0,sizeof(mat)); } void print() { cout<<"MATRIX "<<n<<" "<<m<<endl; for (int i=0;i<n;i++) { for (int j=0;j<m;j++) { cout<<mat[i][j]<<"\t"; } cout<<endl; } } void random(int n) { this->n = n; this->m = n; for (int i=0;i<n;i++) for (int j=0;j<n;j++) mat[i][j] = rand()%100; } void initSquare() { this->n = 4; this->m = 4; memset(mat,0,sizeof(mat)); mat[0][1] = mat[0][3] = 1; mat[1][0] = mat[1][2] = 1; mat[2][1] = mat[2][3] = 1; mat[3][0] = mat[3][2] = 1; mat[0][0] = mat[1][1] = mat[2][2] = mat[3][3] = -2; this->n --;//去一行 this->m --;//去一列 } double gauss() { double ans = 1; for (int i=0;i<n;i++) { int sid = -1; for (int j=i;j<n;j++) if (abs(mat[j][i]) > eps) { sid = j; break; } if (sid == -1) continue; if (sid != i) { for (int j=0;j<n;j++) { swap(mat[sid][j],mat[i][j]); ans = - ans; } } for (int j=i+1;j<n;j++) { double ratio = mat[j][i]/mat[i][i]; for (int k=0;k<n;k++) { mat[j][k] -= mat[i][k] * ratio; } } //print(); } for (int i=0;i<n;i++) ans *= mat[i][i]; return abs(ans); } }; int main() { srand(1); matrix T; //T.random(2); T.initSquare(); T.print(); double ans = T.gauss(); T.print(); cout<<ans<<endl; } |