As the title suggests, I'd like to select the first row of each set of rows grouped with a GROUP BY .

Specifically, if I've got a purchases table that looks like this:

SELECT * FROM purchases;

My Output:

id | customer | total
---+----------+------
 1 | Joe      | 5
 2 | Sally    | 3
 3 | Joe      | 2
 4 | Sally    | 1

I'd like to query for the id of the largest purchase ( total ) made by each customer . Something like this:

SELECT FIRST(id), customer, FIRST(total)
FROM  purchases
GROUP BY customer
ORDER BY total DESC;

Expected Output:

FIRST(id) | customer | FIRST(total)
----------+----------+-------------
        1 | Joe      | 5
        2 | Sally    | 3

On Oracle 9.2+ (not 8i+ as originally stated), SQL Server 2005+, PostgreSQL 8.4+, DB2, Firebird 3.0+, Teradata, Sybase, Vertica:

WITH summary AS (
    SELECT p.id, 
           p.customer, 
           p.total, 
           ROW_NUMBER() OVER(PARTITION BY p.customer 
                                 ORDER BY p.total DESC) AS rk
      FROM PURCHASES p)
SELECT s.*
  FROM summary s
 WHERE s.rk = 1

Supported by any database:

But you need to add logic to break ties:

  SELECT MIN(x.id),  -- change to MAX if you want the highest
         x.customer, 
         x.total
    FROM PURCHASES x
    JOIN (SELECT p.customer,
                 MAX(total) AS max_total
            FROM PURCHASES p
        GROUP BY p.customer) y ON y.customer = x.customer
                              AND y.max_total = x.total
GROUP BY x.customer, x.total

In PostgreSQL this is typically simpler and faster (more performance optimization below):

SELECT DISTINCT ON (customer)
       id, customer, total
FROM   purchases
ORDER  BY customer, total DESC, id;

Or shorter (if not as clear) with ordinal numbers of output columns:

SELECT DISTINCT ON (2)
       id, customer, total
FROM   purchases
ORDER  BY 2, 3 DESC, 1;

If total can be NULL (won't hurt either way, but you'll want to match existing indexes):

...
ORDER  BY customer, total DESC NULLS LAST, id;

Major points

Index

The perfect index for the above query would be a multi-column index spanning all three columns in matching sequence and with matching sort order:

CREATE INDEX purchases_3c_idx ON purchases (customer, total DESC, id);

May be too specialized for real world applications. But use it if read performance is crucial. If you have DESC NULLS LAST in the query, use the same in the index so Postgres knows sort order matches.

Effectiveness / Performance optimization

You have to weigh cost and benefit before you create a tailored index for every query. The potential of above index largely depends on data distribution .

The index is used because it delivers pre-sorted data, and in Postgres 9.2 or later the query can also benefit from an index only scan if the index is smaller than the underlying table. The index has to be scanned in its entirety, though.

Benchmark

I had a simple benchmark here for Postgres 9.1, which was outdated by 2016. So I ran a new one with a better, reproducible setup for Postgres 9.4 and 9.5 and added the detailed results in another answer .

Benchmark

Testing the most interesting candidates with Postgres 9.4 and 9.5 with a halfway realistic table of 200k rows in purchases and 10k distinct customer_id (avg. 20 rows per customer).

For Postgres 9.5 I ran a 2nd test with effectively 86446 distinct customers. See below (avg. 2.3 rows per customer).

Setup

Main table

CREATE TABLE purchases (
  id          serial
, customer_id int  -- REFERENCES customer
, total       int  -- could be amount of money in Cent
, some_column text -- to make the row bigger, more realistic
);

I use a serial (PK constraint added below) and an integer customer_id since that's a more typical setup. Also added some_column to make up for typically more columns.

Dummy data, PK, index - a typical table also has some dead tuples:

INSERT INTO purchases (customer_id, total, some_column)    -- insert 200k rows
SELECT (random() * 10000)::int             AS customer_id  -- 10k customers
     , (random() * random() * 100000)::int AS total     
     , 'note: ' || repeat('x', (random()^2 * random() * random() * 500)::int)
FROM   generate_series(1,200000) g;

ALTER TABLE purchases ADD CONSTRAINT purchases_id_pkey PRIMARY KEY (id);

DELETE FROM purchases WHERE random() > 0.9; -- some dead rows

INSERT INTO purchases (customer_id, total, some_column)
SELECT (random() * 10000)::int             AS customer_id  -- 10k customers
     , (random() * random() * 100000)::int AS total     
     , 'note: ' || repeat('x', (random()^2 * random() * random() * 500)::int)
FROM   generate_series(1,20000) g;  -- add 20k to make it ~ 200k

CREATE INDEX purchases_3c_idx ON purchases (customer_id, total DESC, id);

VACUUM ANALYZE purchases;

customer table - for superior query

CREATE TABLE customer AS
SELECT customer_id, 'customer_' || customer_id AS customer
FROM   purchases
GROUP  BY 1
ORDER  BY 1;

ALTER TABLE customer ADD CONSTRAINT customer_customer_id_pkey PRIMARY KEY (customer_id);

VACUUM ANALYZE customer;

In my second test for 9.5 I used the same setup, but with random() * 100000 to generate customer_id to get only few rows per customer_id .

Object sizes for table purchases

Generated with this query.

               what                | bytes/ct | bytes_pretty | bytes_per_row
-----------------------------------+----------+--------------+---------------
 core_relation_size                | 20496384 | 20 MB        |           102
 visibility_map                    |        0 | 0 bytes      |             0
 free_space_map                    |    24576 | 24 kB        |             0
 table_size_incl_toast             | 20529152 | 20 MB        |           102
 indexes_size                      | 10977280 | 10 MB        |            54
 total_size_incl_toast_and_indexes | 31506432 | 30 MB        |           157
 live_rows_in_text_representation  | 13729802 | 13 MB        |            68
 ------------------------------    |          |              |
 row_count                         |   200045 |              |
 live_tuples                       |   200045 |              |
 dead_tuples                       |    19955 |              |

Queries

1. row_number() in CTE, (see other answer)

WITH cte AS (
   SELECT id, customer_id, total
        , row_number() OVER(PARTITION BY customer_id ORDER BY total DESC) AS rn
   FROM   purchases
   )
SELECT id, customer_id, total
FROM   cte
WHERE  rn = 1;

2. row_number() in subquery (my optimization)

SELECT id, customer_id, total
FROM   (
   SELECT id, customer_id, total
        , row_number() OVER(PARTITION BY customer_id ORDER BY total DESC) AS rn
   FROM   purchases
   ) sub
WHERE  rn = 1;

3. DISTINCT ON (see other answer)

SELECT DISTINCT ON (customer_id)
       id, customer_id, total
FROM   purchases
ORDER  BY customer_id, total DESC, id;

4. rCTE with LATERAL subquery (see here)

WITH RECURSIVE cte AS (
   (  -- parentheses required
   SELECT id, customer_id, total
   FROM   purchases
   ORDER  BY customer_id, total DESC
   LIMIT  1
   )
   UNION ALL
   SELECT u.*
   FROM   cte c
   ,      LATERAL (
      SELECT id, customer_id, total
      FROM   purchases
      WHERE  customer_id > c.customer_id  -- lateral reference
      ORDER  BY customer_id, total DESC
      LIMIT  1
      ) u
   )
SELECT id, customer_id, total
FROM   cte
ORDER  BY customer_id;

5. customer table with LATERAL (see here)

SELECT l.*
FROM   customer c
,      LATERAL (
   SELECT id, customer_id, total
   FROM   purchases
   WHERE  customer_id = c.customer_id  -- lateral reference
   ORDER  BY total DESC
   LIMIT  1
   ) l;

6. array_agg() with ORDER BY (see other answer)

SELECT (array_agg(id ORDER BY total DESC))[1] AS id
     , customer_id
     , max(total) AS total
FROM   purchases
GROUP  BY customer_id;

Results

Execution time for above queries with EXPLAIN ANALYZE (and all options off), best of 5 runs.

All queries used an Index Only Scan on purchases2_3c_idx (among other steps). Some of them just for the smaller size of the index, others more effectively.

A. Postgres 9.4 with 200k rows and ~ 20 per customer_id

1. 273.274 ms  
2. 194.572 ms  
3. 111.067 ms  
4.  92.922 ms  
5.  37.679 ms  -- winner
6. 189.495 ms

B. The same with Postgres 9.5

1. 288.006 ms
2. 223.032 ms  
3. 107.074 ms  
4.  78.032 ms  
5.  33.944 ms  -- winner
6. 211.540 ms  

C. Same as B., but with ~ 2.3 rows per customer_id

1. 381.573 ms
2. 311.976 ms
3. 124.074 ms  -- winner
4. 710.631 ms
5. 311.976 ms
6. 421.679 ms

Original (outdated) benchmark from 2011

I ran three tests with PostgreSQL 9.1 on a real life table of 65579 rows and single-column btree indexes on each of the three columns involved and took the best execution time of 5 runs.
Comparing @OMGPonies' first query ( A ) to the above DISTINCT ON solution ( B ):

A: 567.218 ms
B: 386.673 ms

A: 249.136 ms
B:  55.111 ms

A:   0.143 ms
B:   0.072 ms

Same test repeated with the index described in the other answer

CREATE INDEX purchases_3c_idx ON purchases (customer, total DESC, id);

1A: 277.953 ms  
1B: 193.547 ms

2A: 249.796 ms -- special index not used  
2B:  28.679 ms

3A:   0.120 ms  
3B:   0.048 ms

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