python algorithm: how to efficiently find if two integer sets are intersected?

Question

Given a set [2004, 2008], what is the fastest way to find if this set is intersected with other sets?

Actually I am dealing a problem with database, the table has 2 columns, one is the lower bound, the other one is the higher bound. The task is to find all the intersected rows with the given 2 tuple(like [2004,2008]).

I am using mongodb, is this intrinsically supported(I mean have keywords to do it). I have large user base, so I want this task to be completed as fast as possible.

EDIT: To stat more clear, a database table contains following rows:

20 30
10 50
60 90
...

Given the input (25 40) range, I want to return the rows which represent a range, have intersection with the given range.

so return is: (20 30),(10 50)

Answer 1

I don't know MongoDB at all, but you're basically looking for

SELECT * from the_table where not (lower_bound > 2008 or upper_bound < 2004) .

Answer 2

Try this, assuming low and high are your bound fields:

db.ranges.find({'low': {'$lt': self.high}, 'high': {'$gt': self.low}})

Substitute $lte and $gte if you want your query to be inclusive rather than exclusive.

Answer 3

MongoDB does not support intersection. Perform intersection on the Python level using the intersection() API of sets.

Answer 4

Since you're dealing with lower bounds and upper bounds, you can just check bounds.

def intersects(this, others):
    upper, lower = this
    return [[u, l] for u, l in others 
            if (l < upper < u) or (l < lower < u)]

I don't know MongoDB but if you could implement that logic in the database, I can't help but think that it would be faster.

Answer 5

You could use a mongodb query with a Javascript expression (assuming lowerbounds and upperbounds are the limits of the set being intersected):

f = function() { return this.lower <= upperbounds && this.upper >= lowerbounds; }
db.ranges.find(f);

This should handle all cases including when [this.lower, this.upper] is a superset or proper subset of [lowerbounad, upperbounds].