Find minimum value different than zero given some conditions - c++

Question

I've started learning C++ Sets and Iterators and I can't figure if I'm doing this correctly since I'm relatively new to programming.
I've created a Set of a struct with a custom comparator that puts the items in a decreasing order. Before receiving the input I don't know how many items my Set will contain. It can contain any number of items from 0 to 1000.
Here are the Setdefinitions:
typedef struct Pop {
int value_one; int node_value;
} Pop;
struct comparator {
bool operator() (const Pop& lhs, const Pop& rhs) const {
if (rhs.value_one == lhs.value_one) {
return lhs.node_value < rhs.node_value;
} else { return rhs.value_one < lhs.value_one;}
}
};
set<Pop, comparator> pop;
set<Pop>::iterator it;
And this is the algorithm. It should find a minimum value and print that value. If it does not find (the function do_some_work(...) returns 0), it should print "Zero work found!\n":
int minimum = (INT_MAX) / 2; int result;
int main(int argc, char** argv) {
//....
//After reading input and adding values to the SET gets to this part
Pop next;
Pop current;
for (it = pop.begin(); it != pop.end() && minimum != 1; it++) {
current = *it;
temp_it = it;
temp_it++;
if (temp_it != pop.end()) {
next = *temp_it;
// This function returns a integer value that can be any number from 0 to 5000.
// Besides this, it checks if the value found is less that the minimum (declared as global) and different of 0 and if so
// updates the minimum value. Even if the set as 1000 items and at the first iteration the value
// found is 1, minimum is updated with 1 and we should break out of the for loop.
result = do_some_work(current.node_value);
if (result > 0 && next.value_one < current.value_one) {
break;
}
} else {
result = do_some_work(current.node_value);
}
}
if (minimum != (INT_MAX) / 2) {
printf("%d\n", minimum);
} else {
printf("Zero work found!\n");
}
return 0;
}
Here are some possible outcomes.
If the Set is empty it should print Zero work found!
If the Set as one item and do_some_work(current.node_value) returns a value bigger than 0 it should printf("%d\n", minimum); or Zero work found! otherwise.
Imagine I have this Set (first position value_one and second position node_value:
4 2
3 6
3 7
3 8
3 10
2 34
If in the first iteration do_some_work(current.node_value) returns a value bigger than 0, since all other items value_one are smaller, it should break the loop, print the minimum and exit the program.
If in the first iteration do_some_work(current.node_value) returns 0, I advance in the Set and since there are 4 items with value_one as 3 I must analyze this 4 items because any of these can return a possible valid minimum value. If any of these updates the minimum value to 1, it should break the loop, print the minimum and exit the program.
In this case, the last item of the Set is only analysed if all other items return 0 or minimum value is set to 1.
For me this is both an algorithmic problem and a programming problem.
With this code, am I analysing all the possibilities and if minimum is 1, breaking the loop since if 1 is returned there's no need to check any other items?