Priority Queues

Min-heap means that I have to store the vector in a heap that has the lowest number first,  I want to execute the character with the lowest time in my programm

Then sort (http://www.sgi.com/tech/stl/sort.html) the vector first:

vector<int> v;

//... fill vector

sort(v.begin(),v.size());

priority_queue<int> q(v.begin(),v.end());

Will it be the lowest value be on top of the priority queue or do I need some type of compare function?

Yes, see check the 'sort' example on http://www.sgi.com/tech/stl/sort.html

int A[] = {1, 4, 2, 8, 5, 7};
const int N = sizeof(A) / sizeof(int);
sort(A, A + N);
copy(A, A + N, ostream_iterator<int>(cout, " "));
// The output is " 1 2 4 5 7 8".

Thanks that really helped