optimizing a huge but simple mysql query of sums

Question

how would one go about finding solutions to all possible combinations of a,b,c,d,e,f where

a+b+c+d+e+f = x

given a,b,c,d,e,f are integers between 0-999 and x is a fixed integer

and the solution

a,b,c,d,e,f < y

(where each comma is a thousand separator)

ex. the huge number 304,153,525,784,175,764 is a solution to x=2705

since: 304+153+525+784+175+764 = 2705

here's a query i am trying for x=2705 and y=304153525784175764

SELECT 
    a.id,
    b.id,
    c.id,
    d.id,
    e.id,
    f.id,
    a.id+b.id+c.id+d.id+e.id+f.id AS sum
    a.id*1000*1000*1000*1000*1000+
    b.id*1000*1000*1000*1000+
    c.id*1000*1000*1000+
    d.id*1000*1000+
    e.id*1000+
    f.id AS solution
FROM a JOIN b JOIN c JOIN d JOIN e JOIN f
WHERE sum = 2705
AND solution <= 304153525784175764
ORDER BY solution DESC

how can one simplify this query which is currently far too big

is there perhaps a simpler way to get the solutions?

Answer 1

If a=000, then the problem degenerates to finding b..f such that b+c+d+e+f =2705. There will be an awfully large number of solutions (with 3-digit values). My point is that the resultset is too big; so no query can be 'reasonably sized'.

Anyway, I would approach it from a programming language, then think about moving to SQL:

for a in (000..304)   -- this is the main use for "y"
    for b in (000..999)
        if a + b > 2705 then break
        for c in (000..999)
            if a + b + c > 2705 then break
            for d in (000..999)
                if a + b + c + d > 2705 then break
                for e in (max(000, 2705-1000-(a+b+c+d))..999)
                    if a + b + c + d + e > 2705 then break
                    f = 2705 - (a + b + c + d + e);
                    if f between 000 and 999 then
                        print a,b,c,d,e,f

(Perhaps I would handle 304 separately. Or maybe stop b at 153 only when a==304.)

I cringe to think how long this would take to run in a well-optimized compiler. And cringe even more at the size of the temp tables needed to do the task in SQL.