Loop in lines of true table - php

Question

I have a problem about loop in line of true table. I need get all lines where only there are 3 positions with value equal 1, Look sample:
For a table with 4 elements exists 16 possibilities but I need just 4 of their. So I need to get the 4 positions without pass in all others positions:
[00002] 0-0-0-1
[00003] 0-0-1-0
[00004] 0-0-1-1
[00005] 0-1-0-0
[00006] 0-1-0-1
[00007] 0-1-1-0
[00008] 0-1-1-1 I want this
[00009] 1-0-0-0
[00010] 1-0-0-1
[00011] 1-0-1-0
[00012] 1-0-1-1 I want this
[00013] 1-1-0-0
[00014] 1-1-0-1 I want this
[00015] 1-1-1-0 I want this
[00016] 1-1-1-1
Look for 4 elements it's easy make a loop but you imagine a table with millions elements. Following is a code for ilustre my first thought:
$t1 = time();
echo "\n\n";
echo "################ Started in :" . date('d/m/Y H:i:s', $t1);
echo "\n\n";
$votesCount = 4;
$possibilities = pow(2, $votesCount);
for ($i = 0; $i < $possibilities; $i++) {
$binare = str_pad(decbin($i), $votesCount, 0, STR_PAD_LEFT);
$arrayBinare = str_split($binare);
$posVote = str_pad($i + 1, 5, 0, STR_PAD_LEFT);
$c = "[" . $posVote . '] ' . implode('-', $arrayBinare);
if (array_sum($arrayBinare) == 3) {
echo "<b>$c</b> I want this<br>";
continue;
}
echo "$c <br>";
}
$t2 = time();
echo "\n";
echo "################ Finished in:" . date('d/m/Y H:i:s', $t2);
echo "\n";
echo "################ Duraction: " . ($t2 - $t1) . ' seconds';
echo "\n";

Answer 1

A recursive solution looks like this:
function Enumerate(len, rem)
if rem = 0 then return [0]^len
if len < rem then return {}
if len = rem then return {[1]^rem}
return ({[0]} & Enumerate(len - 1, rem))
union
({[1]} & Enumerate(len - 1, rem - 1))
The notation [1]^rem means the vector of length rem containing only 1; the operator & returns all vectors obtained by concatenating vectors from the RHS to vectors in the LHS. This short-circuits when it detects that solutions can't be obtained or when there is only one possible solution, but you could remove this to print all permutations and just check them. Example execution:
Enumerate(4, 3) = {[0,1,1,1],[1,0,1,1],[1,1,0,1],[1,1,1,0]}
4 < 3? no
4 = 3? no
[0] & Enumerate(3, 3) = [0] & [1,1,1] = [0,1,1,1]
3 = 0? no
3 < 3? no
3 = 3? yes, return [1,1,1]
[1] & Enumerate(3, 2) = [1] & ([0,1,1],[1,0,1],[1,1,0]| = {[1,0,1,1],[1,1,0,1],[1,1,1,0]}
2 = 0? no
3 < 2? no
3 = 3? no
[0] & Enumerate(2, 2) = [0] & [1,1] = [0,1,1]
2 = 0? no
2 < 2? no
2 = 2? yes, return [1,1]
[1] & Enumerate(2, 1) = [1] & {[0,1],[1,0]) = {[1,0,1],[1,1,0]}
1 = 0? no
2 < 1? no
2 = 1? no
[0] & Enumerate(1, 1) = [0] & [1] = [0,1]
1 = 0? no
1 < 1? no
1 = 1? yes, return [1]
[1] & Enumerate(1, 0) = [1] & [0] = [1,0]
0 = 0? yes, return [0]
If you want this to be iterative rather than recursive, add a stack data structure and manage the stack explicitly in a while loop while the stack's not empty.
If you want the position of each solution in the ordered space of all solutions - simply interpret the vector as the sequence of digits of a len-digit binary number and add one. So, [0,1,1,1] becomes (0111)b = (7)d + 1 = (8)d = 8.

Answer 2

With millions of rows, you definitely want to move the selection logic on the database side, or you'll have to make insane amounts of calculations on the PHP side, leading to potential performance & memory issues.
Assuming you have 4 vote columns storing 1 or 0:
SELECT *
FROM votes
WHERE (vote1 + vote2 + vote3 + vote4) = 3
And if you are storing booleans, you can cast it as an integer : WHERE CAST(vote1 AS SIGNED INTEGER) + ...