Randomise array of numbers with disqualifying conditions - php

Question

I wish to create an array with random sequences that correspond to my conditions.
The sequence should be composed of 8 different numbers from 1-8.
I should not have more than 2 successive numbers in the first 4 or last 4 numbers. Ex: 1,2,3 is not good nor 5,3,4 because they are successive if sorted (3,4,5).
This is a good example: 1,4,5,7, | 8,6,3,2
This is NOT a good example: 1,3,2,6, | 5,7,8,4 because 1,3,2 are successive numbers if sorted (1,2,3) in the first 4 digits
I made this:
$sequences = array();
while(count($sequences) < 100){
//Random 8 numbers sequence from 1-8
$sequence = array();
while(count($sequence) < 8){
$rand = rand(1,8);
if(!in_array($rand, $sequence)){
array_push($sequence, $rand);
}
}
//Insert if numbers are not successive.
//Struggling here
if(?????){
array_push($sequences, $sequence);
}
}
print_r($sequences);
It's working for the generation part of it but I can't figure how to insert sequences that do not contain successive numbers. Any thoughts?

Answer 1

You can represent the two groups of digits as a 1 or 0 and pick which elements go in each set by picking one of the 8 bit binary strings with four 1s and 0s and no sequences of 3 consecutive 1s or 0s. Each of these binary strings representes by one of the following integers:
43 45 51 53 54 75 77 83 85 86 89 90 101 102 105 106 108
147 149 150 153 154 165 166 169 170 172 178 180 201 202 204 210 212
The second half are all symmetric with the first half, so we can just pick a number from the first half and then do some processing to pick the whole set:
$combinations = array(43,45,51,53,54,75,77,83,85,86,89,90,101,102,105,106,108);
// Pick a random combination
$combination = $combinations[array_rand($combinations)];
if (mt_rand() & 1)
$combination = 255 - $combination;
$combination = str_split(str_pad(decbin($combination), 8, '0', STR_PAD_LEFT));
// Get the first four values
$first = array_keys(array_filter($combination, function($x){ return $x == '0'; }));
shuffle($first); // Permute them
// Get the last four values
$last = array_keys(array_filter($combination, function($x){ return $x == '1'; }));
shuffle($last); // Permute them
$result = array_map(function($x){ return $x + 1; }, array_merge($first, $last));
This will a random sequence with your constraints uniformly at random and should be quite efficient. Some sample outputs:
[6, 2, 3, 8, 1, 4, 5, 7]
[1, 6, 2, 4, 3, 5, 8, 7]
[6, 3, 1, 8, 2, 4, 5, 7]
[5, 8, 4, 2, 7, 1, 6, 3]
[5, 2, 8, 1, 3, 6, 7, 4]
[8, 6, 2, 4, 7, 1, 3, 5]
[7, 1, 5, 4, 8, 3, 2, 6]
[5, 1, 3, 6, 2, 7, 8, 4]
[1, 7, 2, 5, 3, 8, 4, 6]
[5, 6, 3, 8, 2, 7, 4, 1]

Answer 2

This is probably an ineffective way (in terms of resources) and could be more considered as a hack, but;
$sequence = array(1,2,4,5,8,9,5,7);
usort($sequence, function($a, $b) {
//if $a + 1 = $b, then $b + 1;
return ($a + 1) == $b ? $b = $b + 1 : 1;
});
print_r($sequence);
This would return;
Array ( [0] => 5 [1] => 8 [2] => 2 [3] => 1 [4] => 4 [5] => 9 [6] => 5 [7] => 7 )

Answer 3

It's not really a beautiful code, I could shorten it but still, it's working.
$sequence = array();
$sequences = array();
$loops = 0;
while($loops < 10000){
$loops++;
//Get a sequence
while(count($sequence) < 8){
$rand = rand(1,8);
if(!in_array($rand, $sequence)){
array_push($sequence, $rand);
}
}
//Checks if sequence meet requirements
//This part could be summarized in a function
$first = array($sequence[0], $sequence[1], $sequence[2],$sequence[3]);
$last = array($sequence[4], $sequence[5], $sequence[6],$sequence[7]);
sort($first);
sort($last);
if($first[1] != $first[0]+1 || $first[1] !=$first[2]-1){
if($first[2] != $first[1]+1 || $first[2] !=$first[3]-1){
if($last[1] != $last[0]+1 || $last[1] !=$last[2]-1){
if($last[2] != $last[1]+1 || $last[2] !=$last[3]-1){
$sequence = array_merge($first, $last);
if(!in_array($sequence, $sequences)){
array_push($sequences, $sequence);
}
}
}
}
}
$sequence = array();
}
print_r($sequences);