查找数字属于哪个间隔

Question

I have a large set of intervals (start, end) that are continguous and non overlapping. Given a number, I want to find out which interval it belongs to.

I am currently coding up a binary search based solution - I wanted to know if this would be possible using standard library data structs such as TreeMap or a TreeSet.

Answer 1

If I understand your needs correctly, you have a List of ranges like (1,5), (6,10),(11,18) and so on. When given an input like 4, you want to return the range which contains this input.

Here is a version in Scala:

scala> val input = List((1,5), (6,10),(11,18))
input: List[(Int, Int)] = List((1,5), (6,10), (11,18))

scala> input.filter(elem => 4 <= elem._2 && 4 >= elem._1)
res1: List[(Int, Int)] = List((1,5))

You can expand on this by extracting this into a method and pass the input parameter.

You could replace the type of collection that you want depending on the use case. Have a look here at the collections performance characteristics:

http://docs.scala-lang.org/overviews/collections/performance-characteristics.html

If you want to use a TreeSet, you could do the following:

scala> val in = TreeSet((1,5),(6,10),(11,15))
in: scala.collection.immutable.TreeSet[(Int, Int)] = TreeSet((1,5), (6,10))

scala> in.filter(elem => 4 <= elem._2 && 4 >= elem._1)
res2: scala.collection.immutable.TreeSet[(Int, Int)] = TreeSet((1,5))

Answer 2

Yes, it's possible to do using standard Java's or Scala's TreeMap (which is RB tree underneath).

Code:

import scala.collection.immutable.TreeMap

val ranges = TreeMap((1, 5), (8, 10), (11, 18))

def contains(intervals: TreeMap[Int, Int])(el: Int) =
  intervals.to(el).lastOption.exists(_._2 >= el)

(-1 to 20).foreach { i =>
  println(s"$i ${contains(ranges)(i)}")
}

Prints:

-1 false
0 false
1 true
2 true
3 true
4 true
5 true
6 false
7 false
8 true
9 true
10 true
11 true
12 true
13 true
14 true
15 true
16 true
17 true
18 true
19 false
20 false

The idea is to use to method, that returns a projection of the map with keys smaller or equal to the given element. If your map contains the interval that intersects given point, then this interval will be the largest key in the projection. So the only thing left is to check that the value (right boundary) of that interval is larger than the element in question.

Both to and lastOption methods work in O(log n) for RB tree.

This implementation assumes that ranges are inclusive, but it should be easy to modify this code for exclusive ranges.