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.

My complexity is O(NM)? If I will use binary search i might get O(NlogM)...
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;
        }
    }
}

UPDATE: there is a better Solution then mine An efficient approach is to first sort the intervals according to starting time. Once we have the sorted intervals, we can combine all intervals in a linear traversal. The idea is, in sorted array of intervals, if interval[i] doesn’t overlap with interval[i-1], then interval[i+1] cannot overlap with interval[i-1] because starting time of interval[i+1] must be greater than or equal to interval[i]. Following is the detailed step by step algorithm.

1. Sort the intervals based on increasing order of starting time.
2. Push the first interval on to a stack.
3. For each interval do the following ……..a. If the current interval does not overlap with the stack top, push it. ……..b. If the current interval overlaps with stack top and ending time of current interval is more than that of stack top, update stack top with the ending time of current interval.
4. At the end stack contains the merged intervals.

http://www.geeksforgeeks.org/merging-intervals/