Since k <= 10 and |ai| ≤ 1000 the largest answer is 10001: let use -11000..11000 to be sure.

Since the end of each segment is an integer such that on one side inequality holds and on the other it is not, the solution is trivial: just find all such points. Still the following program gives WA4. Any hint?

#define I(x) int x; cin >> x
#define FA(i,c) for(auto& i: c)
#define FE(i,a,b) for(int i = (a); i <= (b); ++i)
typedef vector<int> V;

V a;
bool in(double x){
  FA(ai,a) x = fabs(x-ai);
  return x < 1;
}

int main(){
  I(k); a.resize(k); FA(ai,a) cin >> ai;
  V b;
  FE(ix,-11000,11000)
    if(in(ix-0.1) != in(ix+0.1))
      b.push_back(ix);
  cout << b.size()/2 << endl;
  for(size_t i = 0; i < b.size(); i += 2)
    cout << b[i] << ' ' << b[i+1] << endl;
}

<https://en.wikipedia.org/wiki/Line_segment>:
a line segment is a part of a line that is bounded by two distinct end points

In this problem, the end points of a "segment" are not required to be distinct (first occurrence in test 4).