PHP algorithm big arrays issue with memory - php

Question

I am working on some algorithm in PHP dealing with binary values or strings containing 0s and 1s. I am calculating the list for n-numbers, from starting list 0f {0,1} for n=1;
Anyway, arrays a[] and b[] are becoming big after for n > 20, reaching memory issue. So my question is how this algorithm can be optimized to use less memory? Should i store binary strings in a different format in memory except string format or do I need to restructure the algorithm itself? Any idea?
while ($n < 1 || $n > 65)
fscanf(STDIN, "%d\n", $n);
$listn = array("0","1");
$doublearray[] = $listn;
for ($i=1; $i<$n;$i++) {
foreach ($listn as $member) {
$a[] = "0" . $member;
}
$reflectedlistn = array_reverse($listn);
foreach ($reflectedlistn as $member) {
$b[] = "1" . $member;
}
$listn = array_merge($a, $b);
$doublearray[] = $listn;
$a = array();
$b = array();
}
$arr = array_slice($doublearray[$n-1], -$n);
echo "\n";
foreach ($arr as $item) {
echo $item . "\n";
}

Answer 1

You could optimize your algorithm by storing numbers.
while ($n < 1 || $n > 65)
fscanf(STDIN, "%d\n", $n);
$listn = array(0, 1); // use numbers
$doublearray[] = $listn;
for ($i = 1; $i < $n; $i++) {
foreach ($listn as $member) {
$a[] = 0 + $member; //actually do nothing
}
$reflectedlistn = array_reverse($listn);
foreach ($reflectedlistn as $member) {
$b[] = (1 << $i) + $member; // add 1 to the begining
}
$listn = array_merge($a, $b);
$doublearray[] = $listn;
$a = array();
$b = array();
}
$arr = array_slice($doublearray[$n - 1], -$n);
echo "\n";
foreach ($arr as $item) {
echo decbin($item) . "\n"; // convert dec into bin string representation
}
It saves near 15% of memory.
Then remove useless array $a.
$listn = array(0, 1); // use numbers
$doublearray[] = $listn;
for ($i = 1; $i < $n; $i++) {
$reflectedlistn = array_reverse($listn);
foreach ($reflectedlistn as $member) {
$b[] = (1 << $i) + $member; // add 1 to the begining
}
$listn = array_merge($listn, $b);
$doublearray[] = $listn;
$a = array();
$b = array();
}
$arr = array_slice($doublearray[$n - 1], -$n);
echo "\n";
foreach ($arr as $item) {
echo decbin($item) . "\n"; // convert dec into bin string representation
}
more 20% of memory.
But it won't help, because this algorithm creates arrays with 2^n elements. And arrays are Very Huge in PHP.
So, is there any point to optimize it? Or better create new one? Please, describe what are you want to achieve to get better solution.