Classis task for splitting weights into 2 trucks (C++) (Dynamic Programming) - c++

Question

I have a task that by given line of weights of cages and I have to split them into 2 trucks. The split should be done like this that |a - b| to have least value where 'a' is the common weight of the cages in the first truck and 'b' is the common weight of the cages of second truck. My program seems to work but when I upload it to hackerrank abort function is called. So where is my fault? Here is the code:
#include <iostream>
#include <vector>
#include <sstream>
#include <cstring>
using namespace std;
int main()
{
string input;
int k;
while (getline(cin, input))
{
/* splitting the input into integers */
vector<int> v;
istringstream iss(input);
while (iss >> k) v.push_back(k);
/* --- II --- */
unsigned long sum = 0;
unsigned i, j;
for (i = 0; i < v.size(); i++)
sum += v[i];
vector<char> can;
can.push_back(1);
for (i = 1; i <= sum; i++)
can[i] = 0;
for (i = 0; i < v.size(); i++)
{
for (j = sum; j+1 > 0; j--)
{
if (can[j])
{
can[j + v[i]] = 1;
}
}
}
for (i = sum / 2; i > 1; i--)
{
if (can[i])
{
if (i <= sum - i)
{
cout << i << " " << sum - i << endl;
break;
}
else
{
cout << "a should be <= b";
break;
}
}
}
}
return 0;
}

Answer 1

How can this work?
You create an empty vector of char, push one single value into it and that try to assign value passed the first:
...
vector<char> can;
can.push_back(1); // can contains one single value
for (i = 1; i <= sum; i++)
can[i] = 0; // Error "vector subscript out of range" in debug mode
If you do not ask the control of vector subscript you will just invoke undefined behaviour.
But if you just want to expand the vector, you can repeatedly can push_back:
for (i = 1; i <= sum; i++)
can.push_back(0);