SQL Server 2014

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CREATE TABLE Table_Entity (
  id int,
  Level_1 Varchar(10),
  Level_2 Varchar(10),
  Level_3 Varchar(10),
  Level_4 Varchar(10)
);

INSERT INTO Table_Entity(id, Level_1, Level_2, Level_3, Level_4) VALUES 
 (1,'A1', null, null, null)
,(2, null, 'B1', null, null)
,(3, null, null, 'C1', null)
,(4, null, 'B2', null, null)
,(5, 'A2', null, null, null)
,(6, null, 'B3', null, null)
,(7, null, null, 'C2', null)
,(8, null, null, 'C3', null)
,(9, null, null, null, 'D1')
,(10, 'A3', null, null, null)
;

select * from table_Entity;

CREATE TABLE Table_Entity_OUTPUT (
  id int, 
  Level_1 Varchar(10),
  Level_2 Varchar(10),
  Level_3 Varchar(10),
  Level_4 Varchar(10)
);

INSERT INTO Table_Entity_OUTPUT(id, Level_1, Level_2, Level_3, Level_4) VALUES (1, 'A1', null, null, null);
INSERT INTO Table_Entity_OUTPUT(id, Level_1, Level_2, Level_3, Level_4) VALUES (2, 'A1', 'B1', null, null);
INSERT INTO Table_Entity_OUTPUT(id, Level_1, Level_2, Level_3, Level_4) VALUES (3, 'A1', 'B1', 'C1', null);
INSERT INTO Table_Entity_OUTPUT(id, Level_1, Level_2, Level_3, Level_4) VALUES (4, 'A1', 'B2', null, null);
INSERT INTO Table_Entity_OUTPUT(id, Level_1, Level_2, Level_3, Level_4) VALUES (5, 'A2', null, null, null);
INSERT INTO Table_Entity_OUTPUT(id, Level_1, Level_2, Level_3, Level_4) VALUES (6, 'A2', 'B3', null, null);
INSERT INTO Table_Entity_OUTPUT(id, Level_1, Level_2, Level_3, Level_4) VALUES (7, 'A2', 'B3', 'C2', null);
INSERT INTO Table_Entity_OUTPUT(id, Level_1, Level_2, Level_3, Level_4) VALUES (8, 'A2', 'B3', 'C3', null);
INSERT INTO Table_Entity_OUTPUT(id, Level_1, Level_2, Level_3, Level_4) VALUES (9, 'A2', 'B3', 'C3', 'D1');
INSERT INTO Table_Entity_OUTPUT(id, Level_1, Level_2, Level_3, Level_4) VALUES (10, 'A3', null, null, null);

id	Level_1	Level_2	Level_3	Level_4
1	A1	null	null	null
2	null	B1	null	null
3	null	null	C1	null
4	null	B2	null	null
5	A2	null	null	null
6	null	B3	null	null
7	null	null	C2	null
8	null	null	C3	null
9	null	null	null	D1
10	A3	null	null	null

with  t0 as(
select *
  ,row_number()over(order by id) rn
from Table_Entity
)
,t1 as(
select *
  ,max(case when Level_1 is null then 0 else rn end)over(order by id) L1_p
  ,max(case when Level_2 is null then 0 else rn end)over(order by id) L2_p
  ,max(case when Level_3 is null then 0 else rn end)over(order by id) L3_p
  ,max(case when Level_4 is null then 0 else rn end)over(order by id) L4_p
from  ( select *,row_number()over(order by id) rn   from Table_Entity )t0
)
,t2 as(
select *
  ,L1_p L1_px
  ,case when L2_p<L1_p then L1_p 
   else L2_p 
   end L2_px
  ,case when L3_p<L2_p then L2_p 
        when L3_p<L1_p then L1_p 
   else L3_p end L3_px
  ,case when L4_p<L3_p then L3_p 
        when L4_p<L2_p then L2_p 
        when L4_p<L1_p then L1_p
   else L4_p end L4_px
from t1
)
,t3 as (
select id,Level_1,Level_2,Level_3,Level_4
  ,lag(Level_1,rn-L1_px)over(order by id) L1_h
  ,lag(Level_2,rn-L2_px)over(order by id) L2_h
  ,lag(Level_3,rn-L3_px)over(order by id) L3_h
  ,lag(Level_4,rn-L4_px)over(order by id) L4_h
  ,L1_px,L2_px,L3_px,L4_px ,rn ,L1_p,L2_p,L3_p,L4_p
from t2
)
select * from t3;

id	Level_1	Level_2	Level_3	Level_4	L1_h	L2_h	L3_h	L4_h	L1_px	L2_px	L3_px	L4_px	rn	L1_p	L2_p	L3_p	L4_p
1	A1	null	null	null	A1	null	null	null	1	1	1	1	1	1	0	0	0
2	null	B1	null	null	A1	B1	null	null	1	2	2	2	2	1	2	0	0
3	null	null	C1	null	A1	B1	C1	null	1	2	3	3	3	1	2	3	0
4	null	B2	null	null	A1	B2	null	null	1	4	4	3	4	1	4	3	0
5	A2	null	null	null	A2	null	null	null	5	5	4	3	5	5	4	3	0
6	null	B3	null	null	A2	B3	null	null	5	6	6	3	6	5	6	3	0
7	null	null	C2	null	A2	B3	C2	null	5	6	7	7	7	5	6	7	0
8	null	null	C3	null	A2	B3	C3	null	5	6	8	8	8	5	6	8	0
9	null	null	null	D1	A2	B3	C3	D1	5	6	8	9	9	5	6	8	9
10	A3	null	null	null	A3	null	null	null	10	10	10	10	10	10	6	8	9