Matrix multiplication.cpp

#include<bits/stdc++.h>
using namespace std;

using type=int;// Kieu du lieu cac phan tu trong ma tran

struct Matrix{
	vector <vector <type> > data;
	int row() const{return data.size();}
	int col() const{ return data[0].size();}
	auto & operator[] (int i) { return data[i];}
	const auto & operator[] (int i) const {return data[i];}
	Matrix()=default;
	Matrix(int r, int c): data(r, vector<type> (c)){}
	Matrix(const vector<vector <type> > &d): data(d){}
	
	// in ra matran
	friend ostream & operator<< (ostream &out, const Matrix &d){
		for(auto x: d.data){
			for(auto y: x) out<<y<<' ';
			out<<'\n';
		}
		return out;
	}
	// ma tran don vi
	static Matrix identity(long long n){
		Matrix a= Matrix(n,n);
		while(n--) a[n][n]=1;
		return a;
	}
	// nhan ma tran
	Matrix operator * (const Matrix &b){
		Matrix a=*this;
		assert(a.col()==b.row());
		Matrix c(a.row(), b.col());
		for(int i=0;i<a.row();i++)
			for(int j=0;j<b.col();j++)
				for(int k=0;k<a.col();k++)
					c[i][j]+=a[i][k]*b[k][j];
		return c;
	}
	// luy thua ma tran
	Matrix pow(long long exp){
		assert(row()==col());
		Matrix base=*this,ans=identity(row());
		for(;exp;exp>>=1,base=base*base)
			if(exp&1) ans=ans*base;
		return ans;
	}
};
int main(){
	Matrix a({
		{1, 2},
		{3, 4}}
	);
	Matrix b({
	    {0, 10, 100}, 
	    {1, 1, 10}
	});
	cout<<a*b<<'\n';
	cout<<a.pow(3)<<'\n';
	b=a;
	cout<<b<<'\n';
	b= Matrix::identity(3);
	cout<<b<<'\n';
	b=Matrix(2,3);
	cout<<b<<'\n';
	Matrix c(3,2);
	cout<<c<<'\n';
}