declare @AlphaList table (AlphaKey char);

insert into @AlphaList(AlphaKey) values ('A');
insert into @AlphaList(AlphaKey) values ('A');
insert into @AlphaList(AlphaKey) values ('B');
insert into @AlphaList(AlphaKey) values ('B');
insert into @AlphaList(AlphaKey) values ('C');
insert into @AlphaList(AlphaKey) values ('D');
insert into @AlphaList(AlphaKey) values ('D');
insert into @AlphaList(AlphaKey) values ('E');

select 
 RANK() over (order by AlphaKey) as Rank
, dense_RANK() over (order by AlphaKey) as [Rank by density]
, ROW_NUMBER() over (order by AlphaKey) as RowNumber
, AlphaKey
from @AlphaList;

Rank	Rank by density	RowNumber	AlphaKey
1	1	1	A
1	1	2	A
3	2	3	B
3	2	4	B
5	3	5	C
6	4	6	D
6	4	7	D
8	5	8	E

--===========================================================================
--      Create a multi-million row test table.  This is not a measured
--      part of the test.
--===========================================================================
--===== Conditionally drop the test table to make reruns easier
     IF OBJECT_ID('TempDB..#AlphaList','U') IS NOT NULL
        DROP TABLE #AlphaList
;
--===== Create and populate a multi-million row test table on the fly
 SELECT TOP 5000000
        AlphaListID = IDENTITY(INT,1,1),
        AlphaKey    = CHAR(ABS(CHECKSUM(NEWID()))%26+65) --A thru Z randomly
   INTO #AlphaList
   FROM Master.sys.All_Columns t1
  CROSS JOIN Master.sys.All_Columns t2
;
--===== Create the expected indexes
  ALTER TABLE #AlphaList
    ADD PRIMARY KEY CLUSTERED (AlphaListID)
;
 CREATE NONCLUSTERED INDEX IX_#AlphaList_AlphaKey
     ON #AlphaList (AlphaKey)
;
--===========================================================================
--      Test 3 different methods with CPU and Duration measurements.
--===========================================================================
--===== "Clear the guns"
  PRINT REPLICATE('=',80);
  PRINT '========== Traditional RowNumber Method ==========';
   DBCC FREEPROCCACHE;
   DBCC DROPCLEANBUFFERS;
    SET STATISTICS TIME ON;

--===== Test the code
select AlphaKey
from (
        select row_number() over(partition by AlphaKey order by AlphaKey) rownum, 
        AlphaKey 
        from #AlphaList 
) al
where rownum = 1        
order by AlphaKey
;
    SET STATISTICS TIME OFF;

--===== "Clear the guns"
  PRINT REPLICATE('=',80);
  PRINT '========== Simple Distinct ==========';
   DBCC FREEPROCCACHE;
   DBCC DROPCLEANBUFFERS;
    SET STATISTICS TIME ON;

--===== Test the code
SELECT DISTINCT AlphaKey
   FROM #AlphaList
ORDER BY AlphaKey
;
    SET STATISTICS TIME OFF;

--===== "Clear the guns"
  PRINT REPLICATE('=',80);
  PRINT '========== New Rank Method from Article ==========';
   DBCC FREEPROCCACHE;
   DBCC DROPCLEANBUFFERS;
    SET STATISTICS TIME ON;

--===== Test the code
with AlphaRank(Rank, RowNumber, AlphaKey) as (
select 
  RANK() over (order by AlphaKey) as Rank
, ROW_NUMBER() over (order by AlphaKey) as RowNumber
, AlphaKey
from #AlphaList
)
select AlphaKey
from AlphaRank
where Rank=RowNumber
;
    SET STATISTICS TIME OFF;

(5000000 row(s) affected)
================================================================================
========== Traditional RowNumber Method ==========
DBCC execution completed. If DBCC printed error messages, contact your system administrator.
DBCC execution completed. If DBCC printed error messages, contact your system administrator.

(26 row(s) affected)

SQL Server Execution Times:
   CPU time = 2875 ms,  elapsed time = 3005 ms.
================================================================================
========== Simple Distinct ==========
DBCC execution completed. If DBCC printed error messages, contact your system administrator.
DBCC execution completed. If DBCC printed error messages, contact your system administrator.

(26 row(s) affected)

SQL Server Execution Times:
   CPU time = 2985 ms,  elapsed time = 3043 ms.
================================================================================
========== New Rank Method from Article ==========
DBCC execution completed. If DBCC printed error messages, contact your system administrator.
DBCC execution completed. If DBCC printed error messages, contact your system administrator.

(26 row(s) affected)

SQL Server Execution Times:
   CPU time = 7953 ms,  elapsed time = 8037 ms.