Question

I have a bunch of (date)intervals which might overlap. The intervals come from different sources. I want to ‘flatten’ this ‘timeline’ and then find all intervals where no interval was.

If you look at: http://www.dgp.toronto.edu/people/JamesStewart/378notes/22intervals/
to the “A more complex example” section. I thus want to find the intervals where no composer was alive.

How do I do that? and how would you implement such a thing in PHP?
Does PHP also have some easy functions for building the tree?

many thx!

edit
My input is a number of arrays (2, 3 or 4) with each containing start and stop dates like so:

 $myarray1[0]['start']['date'] = 'somedate'
 $myarray1[0]['stop']['date'] = 'somedate'
 $myarray1[1]['start']['date'] = 'somedate'
 $myarray1[1]['stop']['date'] = 'somedate'
 $myarray1[2]['start']['date'] = 'somedate'
 $myarray1[2]['stop']['date'] = 'somedate'

the same goes for myarray2, myarray3 and so

Answer 1

Basic algorithm

For each composer, create two objects. One is a birth object with the composer’s name and the year of birth. The other is a death object, again with the composer’s name and the year of death.

Now sort these objects together.

Keep an int, initialised to 0 for num_composers_alive.

Iterate through the ordered list of objects. Every time you encounter a birth object, increment num_composers_alive. Every time you encounter a death object, decrement num_composers_alive.

While incrementing or decrementing, every time you hit a death and decrement, check if num_composers_alive went to 0. If so, you just entered a period when no composer was alive. Output that number or store it somewhere. Every time you hit a birth and increment, check if num_composers_alive is now 1. If so, you just ended a period when no composer was alive. Output that number or store it somewhere.

Implementation

This is going to depend on the form of your input and output. I don’t believe PHP has a native concept of trees, but I might be wrong on that. Try implementing the above, and open a separate question if you get stuck.

To be honest, I’m not sure why you need trees to solve the above problem anyway, but maybe it’s for something else.