- 加法、減法：若 A 為 m×n 矩陣，B 為 m×n 矩陣，則 A + B 和 A – B 還是一個 m×n 矩陣。
- 乘法：若 A 為 m×n 矩陣，B 為 n×p 矩陣，則他們的乘積 AB (或記做A · B)會是一個 m×p 矩陣。
- 【範例】ZeroJudge d481: 矩陣乘法【題解】
- 【練習】ZeroJudge a451: 10229 – Modular Fibonacci【題解】
【實作】struct
#include <iostream>
#include <vector>
using namespace std;
struct Matrix{
int row, col;
vector <vector <int> > data;
//constructor
Matrix(int r, int c): row(r), col(c), data(r, vector<int>(c)) {}
Matrix operator + (const Matrix &B) const{
Matrix ret(row, col);
for (int i = 0; i < row; i++){
for (int j = 0; j < col; j++){
ret.data[i][j] = data[i][j] + B.data[i][j];
}
}
return ret;
}
Matrix operator - (const Matrix &B) const{
Matrix ret(row, col);
for (int i = 0; i < row; i++){
for (int j = 0; j < col; j++){
ret.data[i][j] = data[i][j] - B.data[i][j];
}
}
return ret;
}
Matrix operator * (const Matrix &B) const{
Matrix ret(row, B.col);
for (int i = 0; i < row; i++){
for (int j = 0; j < B.col; j++){
for (int k = 0; k < col; k++){
ret.data[i][j] = (ret.data[i][j] + data[i][k] * B.data[k][j]);
}
}
}
return ret;
}
};
void printMatrix (Matrix A){
//print Matrix
for (int i = 0; i < A.row; i++){
for (int j = 0; j < A.col; j++){
cout << A.data[i][j] << " ";
}
cout << "\n";
}
}
int main(){
int a, b, c, d;
cin >> a >> b >> c >> d;
Matrix A(a, b);
Matrix B(c, d);
for (int i = 0; i < a; i++){
for (int j = 0; j < b; j++){
cin >> A.data[i][j];
}
}
for (int i = 0; i < c; i++){
for (int j = 0; j < d; j++){
cin >> B.data[i][j];
}
}
A = A * B;
printMatrix(A);
return 0;
}
【實作】class
#include <iostream>
#include <cstring>
#include <vector>
using namespace std;
class Matrix{
public:
int row, col;
vector <vector <int> > data;
Matrix(int r=0, int c=0): row(r), col(c), data(r, vector<int>(c)) {}
void InputMatrix(){
for (int i = 0; i < row; i++)
for (int j = 0; j < col; j++)
cin >> data[i][j];
}
void OutputMatrix(){
for (int i = 0; i < row; i++){
for (int j = 0; j < col; j++)
cout << data[i][j] << " ";
cout << "\n";
}
}
Matrix Add(const Matrix &B){
Matrix ret(row, col);
for (int i = 0; i < row; i++)
for (int j = 0; j < col; j++)
ret.data[i][j] = data[i][j] + B.data[i][j];
return ret;
}
Matrix Sub(const Matrix &B){
Matrix ret(row, col);
for (int i = 0; i < row; i++)
for (int j = 0; j < col; j++)
ret.data[i][j] = data[i][j] - B.data[i][j];
return ret;
}
Matrix Mult(const Matrix &B){
Matrix ret(row, B.col);
for (int i = 0; i < row; i++)
for (int j = 0; j < B.col; j++)
for (int k = 0; k < col; k++)
ret.data[i][j] = (ret.data[i][j] + data[i][k] * B.data[k][j]);
return ret;
}
};
int main(){
int a, b, c, d;
cin >> a >> b >> c >> d;
Matrix A(a, b);
Matrix B(c, d);
cout << "\n";
A.InputMatrix();
B.InputMatrix();
cout << "\n";
Matrix C = A.Add(B);
C.OutputMatrix();
cout << "\n";
Matrix D = A.Sub(B);
D.OutputMatrix();
cout << "\n";
A = A.Mult(B);
A.OutputMatrix();
return 0;
}
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