Postgres 13

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CREATE TABLE reviews (
  id          int
, review_date date
, app_id      int -- REFERENCES apps.id
);

INSERT INTO reviews VALUES
  ( 1, '2020-08-01', 1)
, ( 2, '2020-08-02', 1)
, ( 3, '2020-08-03', 1)
, ( 4, '2020-08-04', 1)
, ( 5, '2020-08-05', 1)
, ( 6, '2020-08-06', 1)
, ( 7, '2020-08-07', 1)
, ( 8, '2020-08-07', 1)
, ( 9, '2020-08-07', 1)
, (10, '2020-08-07', 1)
, (21, '2020-08-03', 2)
, (22, '2020-08-03', 2)
, (23, '2020-08-03', 2)
, (24, '2020-08-03', 2)
, (25, '2020-08-03', 2)
, (26, '2020-08-05', 2)
, (31, '2020-08-02', 3)
, (32, '2020-08-02', 3)
, (33, '2020-08-02', 3)
, (34, '2020-08-02', 3)
, (35, '2020-08-02', 3)
, (36, '2020-08-03', 3)
;
22 rows affected

-- earliest review & current total count per app
SELECT app_id, min(review_date) AS earliest_review, count(*)::int AS total_ct
FROM   reviews
GROUP  BY 1;


app_id
earliest_review
total_ct


3
2020-08-02
6

2
2020-08-03
6

1
2020-08-01
10


-- Series of days from earliest to latest review
SELECT generate_series(min(review_date)
                     , max(review_date)
                     , '1 day')::date
FROM   reviews;


generate_series


2020-08-01

2020-08-02

2020-08-03

2020-08-04

2020-08-05

2020-08-06

2020-08-07


-- complete solution
-- WITH TIES requires Postgres 13 or later
WITH cte AS (
   SELECT app_id, min(review_date) AS earliest_review, count(*)::int AS total_ct
   FROM   reviews
   GROUP  BY 1
   )
SELECT *
FROM  (
   SELECT generate_series(min(review_date)
                        , max(review_date)
                        , '1 day')::date
   FROM   reviews
   ) d(review_window_start)
LEFT  JOIN LATERAL (
   SELECT total_ct, array_agg(app_id) AS apps
   FROM  (
      SELECT app_id, total_ct
      FROM   cte c
      WHERE  c.earliest_review >= d.review_window_start
      ORDER  BY total_ct DESC
      FETCH  FIRST 1 ROWS WITH TIES
      ) sub
   GROUP  BY 1
   ) a ON true;


review_window_start
total_ct
apps


2020-08-01
10
{1}

2020-08-02
6
{3,2}

2020-08-03
6
{2}

2020-08-04
null
null

2020-08-05
null
null

2020-08-06
null
null

2020-08-07
null
null


-- the same for Postgres 12 or older
WITH cte AS (
   SELECT app_id, min(review_date) AS earliest_review, count(*)::int AS total_ct
   FROM   reviews
   GROUP  BY 1
   )
SELECT *
FROM  (
   SELECT generate_series(min(review_date)
                        , max(review_date)
                        , '1 day')::date
   FROM   reviews
   ) d(review_window_start)
LEFT  JOIN LATERAL (
   SELECT total_ct, array_agg(app_id) AS apps
   FROM  (
      SELECT total_ct, app_id
          ,  rank() OVER (ORDER BY total_ct DESC) AS rnk
      FROM   cte c
      WHERE  c.earliest_review >= d.review_window_start
      ) sub
   WHERE  rnk = 1
   GROUP  BY 1
   ) a ON true;


review_window_start
total_ct
apps


2020-08-01
10
{1}

2020-08-02
6
{3,2}

2020-08-03
6
{2}

2020-08-04
null
null

2020-08-05
null
null

2020-08-06
null
null

2020-08-07
null
null
review_window_start	total_ct	apps
2020-08-01	10	{1}
2020-08-02	6	{3,2}
2020-08-03	6	{2}
2020-08-04	null	null
2020-08-05	null	null
2020-08-06	null	null
2020-08-07	null	null