如何检查两个或更多个时间段在c ++中是否相互重叠？

Question

I am using std::pair to get start time and end time of each time periods and I put all those time periods in an array (say classes[no_of_time_periods]). Code for it:

int getClassTimes(int N)
{
   int subsets, startTime, endTime;
   std::pair<int,int> classes[N];
   for(int i=0;i<N;i++)
   {
       printf("Please Enter Class %d Start Time and End Time:",(i+1));
       scanf("%d",&startTime);
       scanf("%d",&endTime);
       classes[i] = std::make_pair(startTime,endTime);
   }
   subsets = compute(classes,N);
   return subsets;
}

I know I can check if two time periods overlap or not using following condition:

if(!(classes[i].first<classes[j].second && classes[i].second>classes[j].first))

But I want to check for more than two time periods. Example:

Input:
No_Of_Time_Periods = 5
Time_Period 1      = 1 to 3
Time_Period 2      = 3 to 5
Time_Period 3      = 5 to 7
Time_Period 4      = 2 to 4
Time_Period 5      = 4 to 6

Calculation(Number of subsets of non-overlapping Time Periods):
**Note: If end time of one class is start time of other, they are non-overlapping.
Ex((1 to 3) and (3 to 5) are non-overlapping.)**

(1 to 3)(3 to 5)
(1 to 3)(3 to 5)(5 to 7)
(1 to 3)(4 to 6)
(1 to 3)(5 to 7)
(2 to 4)(4 to 6)
(2 to 4)(5 to 7)
(3 to 5)(5 to 7)

Output:
Total Number of subsets of non-overlapping classes:7

I found the logic and I wrote the code.But while submitting in Online Judge(SPOJ), it says "Time Limit Exceeded".So, Obviously my code was not well optimized. How to achieve this using c++ with better performance? Any Help would be appreciated. Thanks in advance!

Answer 1

This is so confusing! The overlap test should be like so:

if ((classes[i].second < classes[j].first) || (classes[i].first > classes[j].second))
  printf("no overlap");

if (!((classes[i].second < classes[j].first) || (classes[i].first > classes[j].second)))
  printf("overlap");

assuming classes[n].first is always less than classes[n].second

Answer 2

check out interval trees. You will get logarithmic complexity: http://en.wikipedia.org/wiki/Interval_tree