[pdf-embedder url=”https://mhy12345.xyz/wp-content/uploads/securepdfs/2018/07/数学-讲义-v1.1.pdf” title=”数学 讲义 v1.1″]
[pdf-embedder url=”https://mhy12345.xyz/wp-content/uploads/securepdfs/2018/07/数学-习题.pdf” title=”数学 习题”]
#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);
}
#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;
}