You have two lists with meetings scheduling (start time, end time). Meetings in single list don't intersect. Find all intersecting meetings across the two lists.

Is my complexity \$O(N*M)\$? If I use binary search I might get \$O(N*logM)\$. Can you think of a better algorithm?

For simplicity, I didn't use DateTime. I just assumed meetings are in round hours.

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApplication2
{

    public class IntersectingMeetings
    {
        public IntersectingMeetings()
        {
            MeetingList meetingList1 = new MeetingList();
            MeetingList meetingList2 = new MeetingList();
            meetingList1.AddMeeting(2,3);
            meetingList1.AddMeeting(1,2);
           
            meetingList1.AddMeeting(4,6);

            meetingList2.AddMeeting(2,3);
            meetingList2.AddMeeting(3,4);
            meetingList2.AddMeeting(5,6);
            List<Meeting> intersectionsList = FindInterSections(meetingList1, meetingList2);
        }

        private List<Meeting> FindInterSections(MeetingList meetingList1,MeetingList meetingList2)
        {
            meetingList1.list.Sort();
            meetingList2.list.Sort();
            List<Meeting> intersectingList = new List<Meeting>();
            foreach (var item in meetingList1.list)
            {
                foreach (var other in meetingList2.list)
                {
                    if ((item.StartTime >= other.StartTime && item.EndTime <= other.EndTime) ||
                        (other.StartTime >=item.StartTime && other.EndTime <=item.EndTime))
                    {
                        intersectingList.Add(item);
                        intersectingList.Add(other);
                    }
                }
            }
            return intersectingList; 
        }
    }

    
    public class MeetingList
    {
        public List<Meeting> list;
        public MeetingList()
        {
            list = new List<Meeting>();
        }
        public void AddMeeting(int start, int end)
        {
            list.Add(new Meeting(start,end));
        }
    }

    public class Meeting : IComparable<Meeting>
    {
        public int StartTime { set; get; }
        public int EndTime { set; get; }

        public Meeting(int start, int end)
        {
            StartTime = start;
            EndTime = end;
        }

        public int CompareTo(Meeting other)
        {
            if (StartTime > other.StartTime)
            {
                return 1;
            }
            else if (StartTime < other.StartTime)
            {
                return -1;
            }
            return 0;
        }
    }
}