矩阵类中的运算符重载函数有什么问题

Question

I had to create this class to add two matrixes, using operator overloading. I don't want to use pointers in this problem because I don't understand them fully yet, I'm just trying to learn operator overloading. the error it shows is a segmentation fault (core dumped).

#include <cmath>
#include <cstdio>
#include <vector>
#include <iostream>
#include <algorithm>
using namespace std;

class Matrix {
    public : 
        vector<vector<int> >a;
        Matrix(){}
        Matrix operator+( Matrix m ){
            Matrix sum;
            for (int i=0; i<a.size(); i++ ){
                for(int j=0;j<a[i].size(); j++){
                    sum.a[i][j] = a[i][j] + m.a[i][j];
                }
            } 
            return sum;
        }
};
int main () {
   int cases,k;
   cin >> cases;
   for(k=0;k<cases;k++) {
      Matrix x;
      Matrix y;
      Matrix result;
      int n,m,i,j;
      cin >> n >> m;
      for(i=0;i<n;i++) {
         vector<int> b;
         int num;
         for(j=0;j<m;j++) {
            cin >> num;
            b.push_back(num);
         }
         x.a.push_back(b);
      }
      for(i=0;i<n;i++) {
         vector<int> b;
         int num;
         for(j=0;j<m;j++) {
            cin >> num;
            b.push_back(num);
         }
         y.a.push_back(b);
      }
      result = x+y;
      for(i=0;i<n;i++) {
         for(j=0;j<m;j++) {
            cout << result.a[i][j] << " ";
         }
         cout << endl;
      }
   }  
   return 0;
}

Answer 1

The vector inside your Matrix sum has zero size.
SO using operator[] will cause undefined behavior.

        Matrix sum;                                 // sum.a.size() is zero
        for (int i=0; i<a.size(); i++ ){
            for(int j=0;j<a[i].size(); j++){
                sum.a[i][j] = a[i][j] + m.a[i][j];  // broken
            }                                       // sum.a[0][0] does not exist
        } 

There are a couple of solutions.
Easiest is to resize the array so that it has the required number of rows/cols

Answer 2

You did not initialize the vector for the matrix defined on this line:

Matrix sum;

Your entire approach could use a rethink. Making the callers responsible for managing the internal representation of your matrix breaks the principle of encapsulation.

Furthermore, using vector<vector<int>> is inefficient for non-sparse matrix representations. You would be better off using a single block of contiguous memory.

Either way, I recommend defining a constructor for Matrix that accepts a size. Make the internal data private and define operator[] or similar to access the data

Answer 3

Inside the operator you created an object of the type Matrix that has an empty vector

Matrix sum;

So you may not use the subscript operator in the expression

sum.a[i][j]

You could after creating the object sum set appropriate sizes for the vector.

For example

Matrix sum;
sum.a.assign( a.size(), std::vector<int>( a[0].size() ) );

Pay attention to that it is much better to declare the operator the following way

Matrix operator+( const Matrix &m ) const;

because neither operand of the operator is changed in the operator.