C++: Data structure for efficient insertion and retrieval of custom data

I'm having a situation in C++ (on Windows) where I need to keep a set of pair of int: pair where start values are unique (we need not be concerned with this). The operations required are:

insert pair

retrieve pair X: this should return the pair Y where Y's start < X's start < X's end < Y's end. If Y doesn't exist, return false.

The basic solution is to simply keep a set of pairs. For retrieval, we'll iterate sequentially through the set to check. This is O(n).

I'm looking for a better solution. I currently see 2 candidate data structures:

Sorted vector

STL's set (internally implemented as binary search tree?)

Sorted Vector: Pros: can customize the binary search to support the retrieval operation. This is O(logn) Cons: how to efficiently insert a new pair to maintain the sorted order. How to avoid a re-sorting cost of O(nlogn)?

Set: Pros: Easy insertion using the standard insert method. This is O(1)? Cons: How to avoid the sequential search? How to do better than O(n)?

Thanks for your advice.

I'm also open to any other structures that can efficiently (1st criterion is speed; 2nd is memory) support the 2 operations mentioned above.

---

It isn't clear whether the ranges can overlap, but if they can't, then this should work. I've included a complete example with tests.

#include <stdlib.h>
#include <assert.h>
#include <limits.h>
#include <map>

struct RangeContainer {
  typedef std::map<int,int> RangeMap;
  typedef std::pair<int,int> Range;

  void insert(const Range &range)
  {
    range_map.insert(range);
  }

  Range find(const Range &x) const
  {
    RangeMap::const_iterator iter = range_map.upper_bound(x.second);
    if (iter==range_map.begin()) {
      return invalidRange();
    }
    --iter;
    Range y = *iter;
    if (y.first<x.first && x.second<y.second) {
      return y;
    }

    return invalidRange();
  }

  static Range invalidRange()
  {
    return Range(INT_MAX,INT_MIN);
  }

  RangeMap range_map;
};


static void test1()
{
  RangeContainer c;
  typedef RangeContainer::Range Range;
  c.insert(Range(1,10));
  c.insert(Range(20,30));
  assert(c.find(Range(-5,-4))==c.invalidRange());
  assert(c.find(Range(1,10))==c.invalidRange());
  assert(c.find(Range(2,9))==Range(1,10));
  assert(c.find(Range(2,10))==c.invalidRange());
  assert(c.find(Range(11,19))==c.invalidRange());
  assert(c.find(Range(21,29))==Range(20,30));
  assert(c.find(Range(20,29))==c.invalidRange());
  assert(c.find(Range(21,30))==c.invalidRange());
  assert(c.find(Range(35,40))==c.invalidRange());
}

int main(int argc,char **argv)
{
  test1();
  return EXIT_SUCCESS;
}

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