SQL Challenge/Puzzle: How to merge nested ranges?

Question

• This challenge is based on a real life use-case involving IP ranges.
• The solution I came with is based on the stack trace challenge I've presented previously. Each range start is treated as a PUSH operation and each range end + 1 is treated as a POP operation.

---

The Challenge

We have a data set of ranges where each range has a starting point, ending point and a value.

create table ranges
(
    range_start     int         not null
   ,range_end       int         not null
   ,range_val       char(1)     not null
)
;

A range can contain another range or follow another range, but cannot be equal to another range or intersect with another range.

These are valid relations between ranges:

(1)           (2)           (3)           (4)
---------     ---------     ---------     -------- -----------
---                 ---        ---

These relations are not valid:

(5)                (6)
-------        --------       
-------              --------

Our initial ranges, when presented graphically, might look something like this (The letter represents range_val):

AAAAAAAA  BBCCCCCCC
 DDE   F   GGGGG
   H       IIII
             J

The goal is to take the initial set of ranges and create a new set under the following rule:

A contained range will override the corresponding sub-range of the the containing range.

The requested result, when presented graphically, might look something like this

ADDHAAAF  BIIJIGCCC

Requirements

• The solution should be a single SQL query (sub-queries are fine).
• The use of T-SQL, PL/SQL etc. is not allowed.
• The use of UDF (User Defined Functions) is not allowed.

Data Sample

AAAAAAAAAAAAAAAAAAAAAAAAAAAA  BBBB    CCCCCCCCCCCCCCCCCCCCCCCCC
DDDE  FFFFFFFF    GGGGGGGGG               HHHHHHHH    IIIIIII
JJ      KKKLLL       MM NN                              OOOOO
            P                                              QQ

insert into ranges (range_start,range_end,range_val) values (1  ,28 ,'A');
insert into ranges (range_start,range_end,range_val) values (31 ,34 ,'B');
insert into ranges (range_start,range_end,range_val) values (39 ,63 ,'C');
insert into ranges (range_start,range_end,range_val) values (1  ,3  ,'D');
insert into ranges (range_start,range_end,range_val) values (4  ,4  ,'E');
insert into ranges (range_start,range_end,range_val) values (7  ,14 ,'F');
insert into ranges (range_start,range_end,range_val) values (19 ,27 ,'G');
insert into ranges (range_start,range_end,range_val) values (43 ,50 ,'H');
insert into ranges (range_start,range_end,range_val) values (55 ,61 ,'I');
insert into ranges (range_start,range_end,range_val) values (1  ,2  ,'J');
insert into ranges (range_start,range_end,range_val) values (9  ,11 ,'K');
insert into ranges (range_start,range_end,range_val) values (12 ,14 ,'L');
insert into ranges (range_start,range_end,range_val) values (22 ,23 ,'M');
insert into ranges (range_start,range_end,range_val) values (25 ,26 ,'N');
insert into ranges (range_start,range_end,range_val) values (57 ,61 ,'O');
insert into ranges (range_start,range_end,range_val) values (13 ,13 ,'P');
insert into ranges (range_start,range_end,range_val) values (60 ,61 ,'Q');

Requested Results

(Nulls are presented here as empty spaces)

JJDEAAFFKKKLPLAAAAGGGMMGNNGA  BBBB    CCCCHHHHHHHHCCCCIIOOOQQCC

range_start range_end range_val
----------- --------- ---------
1           2          J
3           3          D
4           4          E
5           6          A
7           8          F
9           11         K
12          12         L
13          13         P
14          14         L
15          18         A
19          21         G
22          23         M
24          24         G
25          26         N
27          27         G
28          28         A
29          30         
31          34         B
35          38         
39          42         C
43          50         H
51          54         C
55          56         I
57          59         O
60          61         Q
62          63         C

Optional addition final row:

64

Answer 1

Oracle solution:

with l as ( select level lvl from dual connect by level < 66 ),
     r as ( select range_start r1, range_end r2, range_val v, 
                    range_end - range_start + 1 cnt 
              from ranges ),
     t1 as (select distinct lvl, 
                   nvl(max(v) keep (dense_rank first order by cnt) 
                              over (partition by lvl), '*' ) m
              from l left join r on lvl between r1 and r2 ),
     t2 as (select lvl, m, case when lag(m) over (order by lvl) <> m then 0 else 1 end mrk 
              from t1),
     t3 as (select lvl, m, lvl - sum(mrk) over (order by lvl) grp from t2)
select min(lvl) r1, max(lvl) r2, nullif(min(m), '*') val
  from t3 group by grp order by r1

Output is as requested. My English is far from good, so it's hard to explain, but let's try:

• l - number generator,
• r - data from ranges with counted distance,
• t1 - finds value with minimal distance for each lvl,
• t2 - adds markers telling if range starts,
• t3 - adds column which we will next use for grouping data.