The “Satellites” software is aimed to compute time intervals when the maximum number of satellites is available.

INSTALLING

To compile the project the cmake, gcc-multilib and g++-multilib are required. To install them in Ubuntu use

$ sudo apt-get install cmake gcc-multilib g++-multilib

To compile the project, go to the directory where you want the project to be installed and run the commands

$ cmake <path-to-the-root-of-the-project>
$ make

USING THE PROGRAM

After compiling the project an executable file satellites.ui will be created in the installation directory. Run satellites.ui with a path to the data file containing time intervals as a parameter.

$ satellites.ui <path-to-intervals>

SOURCE CODE STRUCTURE

The project consists of five modules.

1) googletest is a C++ test framework ( see https://github.com/google/googletest )
2) satellites.compilation computes times intervals with the maximum number of available satellites.
3) satellites.misc parses a file with time intervals.
4) satellites.test uses googletest framework to test the satellites.computation and satellites.misc modules.
5) satellites.ui provides a user interface.

APPROACH

1) Parse a file into a list of time slots [begin,end]

2) Add 1ms to the end time of each time slot to exclude the last millisecond. [begin, end)

3) Put all intervals on a timeline

|----------------------------------------------------------------->
0         [      [         )        )                            t,ms

We use a std::multimap<unsigned,int> timeMap variable to store the timeline. The first parameter (key) of the map is a time stamp at which an event occurs. The second parameter (value) describes the event. If a satellite appears at a timestamp, then the value is 1, if a satellite disappeared, then the value is -1. (If there n satellites appear, then the values is n, if n satellites disappear then the value is -n). We use multimap instead of map, because there might be more than one events occur at a time stamp.

4) Iterate over the timeline and accumulate the values (take care of the cases when being > end in [begin,end)). Accumulation gives a number of satellites available at a time stamp.

5) The depth within the brackets is the number of satellites available. Find the maximum depth of the brackets.

6) Find time slots when with the maximum depth. (Take care, that there could be time intervals when [begin,end), begin > end. (This is possible if the time is recorded in another time zone)).

7) Print the time slots and maxSatellites value.

ALTERNATIVE SOLUTIONS

Inserting a pair into the timeMap takes O(log n) time. Inserting n elements into the map takes O(n log n) time. When the number of satellites gets rather big, this might become an issue.
Since we don’t take into account the date and the precision is milliseconds, we can use an array of 86 400 000 + 1 integers to store the timeline, where an index corresponds to a timestamp and value is the number of satellites at the time stamp. (Additional (+1) ms we need, because we add 1 millisecond to each time interval). Putting time stamps on a timeline would require O(n) time. 
The issue of using an array of 86400000 elements is that it requires additionally ~330MB of memory (using int32_t items). Besides, iterating over this array will take longer (~1s on I-Core I5 2.5GHz) than iterating over a map of a small number of satellites (> 1ms on I-Core I5 2.5GHz). 
Knowing that the number of satellites is rather small and assuming it will not get extremely large (millions) in the nearest future we decide to use a multimap instead of an array.

FUTURE IMPROVEMENTS

- Make support for the 60th (leap) second.
- Make support for other time formats.
- Implement a ‘--help’ key to the application.