Permutations - all possible sets of numbers - php

Question

I have numbers, from 0 to 8. I would like in result, all possible sets of those numbers, each set should use all numbers, each number can occur only once in a set.
I would like to see solution made in PHP that could print out result. Or, at least, I would like some refreshment in theory of combinatorics, as I have long forgotten it. What is the formula to calculate how many permutations will there be?
Example sets:
0-1-2-3-4-5-6-7-8
0-1-2-3-4-5-6-8-7
0-1-2-3-4-5-8-6-7
0-1-2-3-4-8-5-6-7
0-1-2-3-8-4-5-6-7
0-1-2-8-3-4-5-6-7
and so on...

Answer 1

You're looking for the permutations formula:
nPk = n!/(n-k)!
In your case, you have 9 entries and you want to choose all of them, that's 9P9 = 9! = 362880
You can find a PHP algorithm to permutate in recipe 4.26 of O'Reilly's "PHP Cookbook".
pc_permute(array(0, 1, 2, 3, 4, 5, 7, 8));
Copied in from O'Reilly:
function pc_permute($items, $perms = array( )) {
if (empty($items)) {
print join(' ', $perms) . "\n";
} else {
for ($i = count($items) - 1; $i >= 0; --$i) {
$newitems = $items;
$newperms = $perms;
list($foo) = array_splice($newitems, $i, 1);
array_unshift($newperms, $foo);
pc_permute($newitems, $newperms);
}
}
}

Answer 2

Since PHP 5.5 you can use Generators. Generators save a lot of memory and are way faster (more than half compared to pc_permute()). So if you have any chance of having PHP 5.5 installed, you definitely want Generators.
This snipped is ported from Python: https://stackoverflow.com/a/104436/3745311
function permutations(array $elements)
{
if (count($elements) <= 1) {
yield $elements;
} else {
foreach (permutations(array_slice($elements, 1)) as $permutation) {
foreach (range(0, count($elements) - 1) as $i) {
yield array_merge(
array_slice($permutation, 0, $i),
[$elements[0]],
array_slice($permutation, $i)
);
}
}
}
}
Sample usage:
$list = ['a', 'b', 'c'];
foreach (permutations($list) as $permutation) {
echo implode(',', $permutation) . PHP_EOL;
}
Output:
a,b,c
b,a,c
b,c,a
a,c,b
c,a,b
c,b,a

Answer 3

Since this question often comes up in Google Search results, here's a modified version of the accepted answer that returns all combinations in an array and passes them as a return value of the function.
function pc_permute($items, $perms = array( )) {
if (empty($items)) {
$return = array($perms);
} else {
$return = array();
for ($i = count($items) - 1; $i >= 0; --$i) {
$newitems = $items;
$newperms = $perms;
list($foo) = array_splice($newitems, $i, 1);
array_unshift($newperms, $foo);
$return = array_merge($return, pc_permute($newitems, $newperms));
}
}
return $return;
}
To use:
$value = array('1', '2', '3');
print_r(pc_permute($value));

Answer 4

I've something that You may like
function combination_number($k,$n){
$n = intval($n);
$k = intval($k);
if ($k > $n){
return 0;
} elseif ($n == $k) {
return 1;
} else {
if ($k >= $n - $k){
$l = $k+1;
for ($i = $l+1 ; $i <= $n ; $i++)
$l *= $i;
$m = 1;
for ($i = 2 ; $i <= $n-$k ; $i++)
$m *= $i;
} else {
$l = ($n-$k) + 1;
for ($i = $l+1 ; $i <= $n ; $i++)
$l *= $i;
$m = 1;
for ($i = 2 ; $i <= $k ; $i++)
$m *= $i;
}
}
return $l/$m;
}
function array_combination($le, $set){
$lk = combination_number($le, count($set));
$ret = array_fill(0, $lk, array_fill(0, $le, '') );
$temp = array();
for ($i = 0 ; $i < $le ; $i++)
$temp[$i] = $i;
$ret[0] = $temp;
for ($i = 1 ; $i < $lk ; $i++){
if ($temp[$le-1] != count($set)-1){
$temp[$le-1]++;
} else {
$od = -1;
for ($j = $le-2 ; $j >= 0 ; $j--)
if ($temp[$j]+1 != $temp[$j+1]){
$od = $j;
break;
}
if ($od == -1)
break;
$temp[$od]++;
for ($j = $od+1 ; $j < $le ; $j++)
$temp[$j] = $temp[$od]+$j-$od;
}
$ret[$i] = $temp;
}
for ($i = 0 ; $i < $lk ; $i++)
for ($j = 0 ; $j < $le ; $j++)
$ret[$i][$j] = $set[$ret[$i][$j]];
return $ret;
}
Here is how to use it:
To get the number of combinations:
combination_number(3,10); // returns number of combinations of ten-elements set.
To get all possible combinations:
$mySet = array("A","B","C","D","E","F");
array_combination(3, $mySet); // returns all possible combinations of 3 elements of six-elements set.
Hope You make use of that.

Answer 5

I've ported the Python itertools code listed here (using generators). The advantage over the solutions posted so far is that it allows you to specify r (permutation size).
function permutations($pool, $r = null) {
$n = count($pool);
if ($r == null) {
$r = $n;
}
if ($r > $n) {
return;
}
$indices = range(0, $n - 1);
$cycles = range($n, $n - $r + 1, -1); // count down
yield array_slice($pool, 0, $r);
if ($n <= 0) {
return;
}
while (true) {
$exit_early = false;
for ($i = $r;$i--;$i >= 0) {
$cycles[$i]-= 1;
if ($cycles[$i] == 0) {
// Push whatever is at index $i to the end, move everything back
if ($i < count($indices)) {
$removed = array_splice($indices, $i, 1);
array_push($indices, $removed[0]);
}
$cycles[$i] = $n - $i;
} else {
$j = $cycles[$i];
// Swap indices $i & -$j.
$i_val = $indices[$i];
$neg_j_val = $indices[count($indices) - $j];
$indices[$i] = $neg_j_val;
$indices[count($indices) - $j] = $i_val;
$result = [];
$counter = 0;
foreach ($indices as $indx) {
array_push($result, $pool[$indx]);
$counter++;
if ($counter == $r) break;
}
yield $result;
$exit_early = true;
break;
}
}
if (!$exit_early) {
break; // Outer while loop
}
}
}
It works for me, but no promises!
Example usage:
$result = iterator_to_array(permutations([1, 2, 3, 4], 3));
foreach ($result as $row) {
print implode(", ", $row) . "\n";
}

Answer 6

This is my version of class. This class builds and returns permutated array as result
class Permutation {
private $result;
public function getResult() {
return $this->result;
}
public function permute($source, $permutated=array()) {
if (empty($permutated)){
$this->result = array();
}
if (empty($source)){
$this->result[] = $permutated;
} else {
for($i=0; $i<count($source); $i++){
$new_permutated = $permutated;
$new_permutated[] = $source[$i];
$new_source = array_merge(array_slice($source,0,$i),array_slice($source,$i+1));
$this->permute($new_source, $new_permutated);
}
}
return $this;
}
}
$arr = array(1,2,3,4,5);
$p = new Permutation();
print_r($p->permute($arr)->getResult());
The last three lines to test my class.

Answer 7

This is a simple recursive function that prints all permutations (written in pseudocode)
function rec(n, k) {
if (k == n) {
for i = 0 to n-1
print(perm[i], ' ');
print('\n');
}
else {
for i = 0 to n-1 {
if (not used[i]) {
used[i] = true;
perm[k] = i;
rec(n, k+1);
used[i] = false;
}
}
}
}
And it is called like this:
rec(9, 0);

Answer 8

Lexicographical order. There is no recursion. Almost no limits for array length.
There is no sort. It's running rather fast. It's easy to understand.
Minus: it gives a notice, but you can add a condition to start compare with the second element or error_reporting(0).
$a = array(
1,
2,
3,
4,
5
);
$b = array_reverse($a);
print_r($a);
//here need "br"
while ($a != $b)
{
foreach(array_reverse($a, true) as $k => $v)
{
if ($v < $a[$k + 1])
{
foreach(array_reverse($a, true) as $ka => $val)
{
if ($val > $v) break;
}
$ch = $a[$k];
$a[$k] = $a[$ka];
$a[$ka] = $ch;
$c = array_slice($a, 0, $k + 1);
print_r($a = array_merge($c, array_reverse(array_slice($a, $k + 1))));
//here need "br"
break;
}
}
}

Answer 9

You're basically talking about permutations where both n and k are 9 so you'll have 9! different permutations; see this: http://en.wikipedia.org/wiki/Permutation.

Answer 10

Here is my proposal, hope a little bit clearer than accepted answer.
function permutate($elements, $perm = array(), &$permArray = array())
{
if(empty($elements))
{
array_push($permArray,$perm); return;
}
for($i=0;$i<=count($elements)-1;$i++)
{
array_push($perm,$elements[$i]);
$tmp = $elements; array_splice($tmp,$i,1);
permutate($tmp,$perm,$permArray);
array_pop($perm);
}
return $permArray;
}
and usage:
$p = permutate(array('a','b','c'));
foreach($p as $perm)
print join(",",$perm)."|\n";

Answer 11

//function call
print_r(combinations([1,2,3,4,5,6,7,8,9,10,11,12,13]));
/**
* #param $mainArray
* #param int $size - optional
* #param array $combinations - optional
* #return mixed
*/
function combinations($mainArray, $size = 3, $combinations = [])
{
if (empty($combinations)) {
$combinations = $mainArray;
}
if ($size == 1) {
return str_replace('-','',$combinations);;
}
$newCombination = array();
foreach ($mainArray as $key => $val){
foreach ($combinations as $char) {
if(in_array($val, explode('-', $char))){
continue;
}
$newCombination[] = $val . '-' . $char;
}
}
return combinations($mainArray, $size - 1, $newCombination);
}
//========================= Next solution ==================================
function sampling($chars, $size, $combinations = array()) {
# if it's the first iteration, the first set
# of combinations is the same as the set of characters
if (empty($combinations)) {
$combinations = $chars;
}
# we're done if we're at size 1
if ($size == 1) {
return $combinations;
}
# initialise array to put new values in
$new_combinations = array();
# loop through existing combinations and character set to create strings
foreach ($combinations as $combination) {
foreach ($chars as $char) {
$new_combinations[] = $combination .'-'. $char ;
}
}
# call same function again for the next iteration
return $this->sampling($chars, $size - 1, $new_combinations);
}
function array_has_dupes($array) {
return count($array) !== count(array_unique($array));
}
function total() {
// Generate ticket price
$arrfinal = array();
// combinations
$chars = array(1,2,3,4,5,6,7,8,9,10,11,12,13); // for 10 digits
$combinations = $this->sampling($chars, 3);
//print_r($combinations); //exit;
foreach($combinations as $key => $val)
{
$arr = explode('-', $val);//str_split($val);
if(!$this->array_has_dupes($arr)){
$arrfinal[] = str_replace('-', '', $val);
}
}
echo '<pre>'; print_r($arrfinal); echo '</pre>';
}

Answer 12

Simple solution using recursion
function filterElement($element){
if(is_array($element[0])){
return $element[0];
}
# base case
return $element;
}
function permutation($input, $path){
// base case 1
if(count($input) == 0){
return [$path];
}
$output = [];
foreach($input as $index => $num){ # 1, 2,3, 4
$copyPath = $path; # copy the path - []
$copyPath[] = $num; # append the number [1]
# remove the current number
$inputLocal = $input;
unset($inputLocal[$index]); # [2, 3, 4]
$permute = permutation($inputLocal, $copyPath); # call [2, 3, 4], [1]
# for all element find add to output
foreach($permute as $ele){
# filter ouput
$output[] = filterElement($ele);
}
}
return $output;
}
print_r(permutation([1,2,3,4], []));
output
Array
(
[0] => Array
(
[0] => 1
[1] => 2
[2] => 3
[3] => 4
)
[1] => Array
(
[0] => 1
[1] => 2
[2] => 4
[3] => 3
)
[2] => Array
(
[0] => 1
[1] => 3
[2] => 2
[3] => 4
)
[3] => Array
(
[0] => 1
[1] => 3
[2] => 4
[3] => 2
)
[4] => Array
(
[0] => 1
[1] => 4
[2] => 2
[3] => 3
)
[5] => Array
(
[0] => 1
[1] => 4
[2] => 3
[3] => 2
)
[6] => Array
(
[0] => 2
[1] => 1
[2] => 3
[3] => 4
)
[7] => Array
(
[0] => 2
[1] => 1
[2] => 4
[3] => 3
)
[8] => Array
(
[0] => 2
[1] => 3
[2] => 1
[3] => 4
)
[9] => Array
(
[0] => 2
[1] => 3
[2] => 4
[3] => 1
)
[10] => Array
(
[0] => 2
[1] => 4
[2] => 1
[3] => 3
)
[11] => Array
(
[0] => 2
[1] => 4
[2] => 3
[3] => 1
)
[12] => Array
(
[0] => 3
[1] => 1
[2] => 2
[3] => 4
)
[13] => Array
(
[0] => 3
[1] => 1
[2] => 4
[3] => 2
)
[14] => Array
(
[0] => 3
[1] => 2
[2] => 1
[3] => 4
)
[15] => Array
(
[0] => 3
[1] => 2
[2] => 4
[3] => 1
)
[16] => Array
(
[0] => 3
[1] => 4
[2] => 1
[3] => 2
)
[17] => Array
(
[0] => 3
[1] => 4
[2] => 2
[3] => 1
)
[18] => Array
(
[0] => 4
[1] => 1
[2] => 2
[3] => 3
)
[19] => Array
(
[0] => 4
[1] => 1
[2] => 3
[3] => 2
)
[20] => Array
(
[0] => 4
[1] => 2
[2] => 1
[3] => 3
)
[21] => Array
(
[0] => 4
[1] => 2
[2] => 3
[3] => 1
)
[22] => Array
(
[0] => 4
[1] => 3
[2] => 1
[3] => 2
)
[23] => Array
(
[0] => 4
[1] => 3
[2] => 2
[3] => 1
)
)