Weighted sum of a column vector and a derived bit vector

Question

We have a table of bid prices and sizes of two buyers. Bid price p with size s means that the buyer is open to buy s number of product at price p<

Answer 1

Below is for BigQuery Standard SQL an dis generic enough to not depend on number of buyers as well as naming for price and size fields. The only expectation is for all prices go first and then all respective sizes as it is in your example. Also i assume all numbers are integers (as in example in question) but this can be adjust to deal with FLOATs

#standardSQL
WITH t_ext AS (
  SELECT * EXCEPT(arr), 
    ARRAY(SELECT CAST(val AS INT64) FROM UNNEST(arr) val WITH OFFSET WHERE OFFSET < 4) AS prices,
    ARRAY(SELECT CAST(val AS INT64) FROM UNNEST(arr) val WITH OFFSET WHERE OFFSET >= 4) AS sizes,
    (SELECT MAX(CAST(val AS INT64)) FROM UNNEST(arr) val WITH OFFSET WHERE OFFSET < 4) AS bestPrice
  FROM (
    SELECT *, REGEXP_EXTRACT_ALL(TO_JSON_STRING(T), r':(\d+)') AS arr
    FROM `project.dataset.table` t
  )
)
SELECT * EXCEPT(prices, sizes), 
  (SELECT SUM(size)
    FROM UNNEST(prices) price WITH OFFSET
    JOIN UNNEST(sizes) size WITH OFFSET
    USING(OFFSET) 
    WHERE price = bestPrice
  ) AS bS
FROM t_ext  

The only what you need to change in above query is number of buyers - in below expressions (in those below - 4 can be replaced with ARRAY_LENGTH(arr) / 2

WHERE OFFSET < 4
WHERE OFFSET >= 4
WHERE OFFSET < 4

For example, for below dummy data (4 buyers)

#standardSQL
WITH `project.dataset.table` AS (
  SELECT 1 pA, 2 pB, 3 pC, 4 pD, 1 sA, 1 sB, 1 sC, 5 sD UNION ALL
  SELECT 1, 4, 2, 4, 1, 6, 1, 5 UNION ALL
  SELECT 4, 4, 2, 1, 7, 1, 1, 1
), t_ext AS (
  SELECT * EXCEPT(arr), 
    ARRAY(SELECT CAST(val AS INT64) FROM UNNEST(arr) val WITH OFFSET WHERE OFFSET < 4) AS prices,
    ARRAY(SELECT CAST(val AS INT64) FROM UNNEST(arr) val WITH OFFSET WHERE OFFSET >= 4) AS sizes,
    (SELECT MAX(CAST(val AS INT64)) FROM UNNEST(arr) val WITH OFFSET WHERE OFFSET < 4) AS bestPrice
  FROM (
    SELECT *, REGEXP_EXTRACT_ALL(TO_JSON_STRING(T), r':(\d+)') AS arr
    FROM `project.dataset.table` t
  )
)
SELECT * EXCEPT(prices, sizes), 
  (SELECT SUM(size)
    FROM UNNEST(prices) price WITH OFFSET
    JOIN UNNEST(sizes) size WITH OFFSET
    USING(OFFSET) 
    WHERE price = bestPrice
  ) AS bS
FROM t_ext

result is

Row pA  pB  pC  pD  sA  sB  sC  sD  bestPrice   bS   
1   1   2   3   4   1   1   1   5   4           5    
2   1   4   2   4   1   6   1   5   4           11   
3   4   4   2   1   7   1   1   1   4           8