remove_if

I'm looking at the example for the function object predicate. Here is the example that show what you should not do with the predicate

Code:

#include <iostream>
#include <list>
#include <algorithm>
#include <iterator>
using namespace std;

class Nth
{
private:
  int nth;
  int count;
public:
  Nth ( int n) : nth(n) , count(0) {}
  bool operator() (int) // need in input, empty input field yield errors
  {
     return ++count == nth;
  }
};

int main()
{
    list<int> coll;
    // insert elements from 1 to 9
    for ( int i = 0 ; i <= 9 ; ++i)
    {
        coll.push_back(i);
    }

    copy(coll.begin(),coll.end(),
                      ostream_iterator<int>(cout," ") );
    cout << endl;

    list<int>::iterator pos;
    pos = remove_if(coll.begin(),coll.end(),Nth(3));

    coll.erase(pos,coll.end());
    copy(coll.begin(),coll.end(),
                       ostream_iterator<int>(cout," ") );
	pos = find_if(coll.begin() , coll.end() , Nth(3));
	cout << endl;
    cout << *pos << endl;

    cout << endl;
}

Code:

// output
1 2 3 4 5 6 7 8 9 10
1 2 4 5 7 8 9 10

The author didn't explain it perfectly clear how that function fails. He only mentioned the use of find_if in the template of remove_if. But that wouldn't have cause the problem, would it?
I thought it gives the wrong answer because of using remove_copy_if after the use of find_if becuase remove_copy_if uses another copy of the predicate to move the rest of the range.

Am I on the right track here?

The idea is that the function object is copied from the original passed-in value when the algorithm restarts, rather than the "current" copy where count is 3. IOW, when you pass a function object with internal state into an algorithm, you can't rely on all the calls being done "in order"; the algorithm can decide to go back to the original version passed in (and therefore the original internal state) at a whim. In this case, it happens when it finds the first item to remove is found and the remove_if calls remove_copy_if -- a new copy of Nth(3) is started at that time. Since remove_copy_if doesn't restart, you only lose 3 and 6 (rather than 3, 6, and 9).

thank you for the concise explanation, tabstop.