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# php – Permutations – all possible sets of numbers

Questions:

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…

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);
}
}
}
``````

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
``````

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));
``````

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.

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.

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";
}
``````

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);
``````

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;
}
}
}
``````

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.

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";
``````

Try this…

``````//function to generate and print all N! permutations of \$str. (N = strlen(\$str))

function permute(\$str,\$i,\$n) {
if (\$i == \$n)
print "\$str\n";
else {
for (\$j = \$i; \$j < \$n; \$j++) {
swap(\$str,\$i,\$j);
permute(\$str, \$i+1, \$n);
swap(\$str,\$i,\$j); // backtrack.
}
}
}

// function to swap the char at pos \$i and \$j of \$str.

function swap(&\$str,\$i,\$j) {
\$temp = \$str[\$i];
\$str[\$i] = \$str[\$j];
\$str[\$j] = \$temp;
}
\$str = "0123";
permute(\$str,0,strlen(\$str)); // call the function.
``````

``````//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>';
}
``````

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
)

)
``````