interval (1,20]
subintervals (1,3],(5,10],(11,12],(15,17]
A (sort of) balanced tree would look like:
    (5,10]
  (1,3]  (15,17]
       (11,12]
 

##</code><code>##

If you consider the number 4 with the above tree
4<=5 so you traverse down the left side.
4>1 && 4>3 so you take the right child
the right child is null so 4 is not covered.
Considering 12.
12>10 so go down right branch
12<=15 so go down left branch
12>11 and 12<=12 so 12 is covered.<