A range intersection algorithm better than O(n)?

Question

Range intersection is a simple, but non-trivial problem.

Its has been answered twice already:

• Find number range intersection
• Comparing date ra

Answer 1

Edit: It sounds like this solution is more or less an Interval Tree. A more complete implementation of an Interval Tree can be found here.

class TreeNode
{
public:
    long pivot;
    List leaves;  //Any ranges that intersect the pivot
    TreeNode left;        //Tree nodes that fall to the left of the pivot
    TreeNode right;       //Tree nodes that fall to the right of the pivot
};

Prep O(n log n):

1. Create the list of ranges
2. Pick the pivot points (possibly by using a sorted list of the end dates.) ??
3. Build your tree.

Search:

1. Use binary search to find the first pivot that is >= TestRange.End

2. Traverse the tree until the pivot > TestRange.Start

   2a. Add the leaves to your result.

---

Example:

Ranges:

• 0 - 2
• 1 - 2
• 2 - 3
• 1 - 4
• 2 - 4
• 0 - 5
• 4 - 5
• 2 - 6
• 3 - 7

Tree:

                             4
               --------------+------------------
               3             |                 7
               |            1-4                |
               |            2-4                |
               |            0-5                |
               |            4-5                |
      ---------+------                 --------+--------
      2        |    null              6        |       null
 -----+----   2-3                 ----+----   3-7
null  |  null                   null  |  null    
     0-2                             2-6
     1-2