How to make a permutation without the repetitions?

Question

My goal is to test the solution of a game I created. Like a sudoku, you play with a grid. The grid makes you find a secret combination. The way I create the grid makes it impossible to make sure there is only one possible solution, and if there is more than one the grid is false. So I have to test the grid with all possible combinations. The fastest way to create all combinations is to generate all the possible presences of each possible number of the combination : for example [1,1,1 | 1,2,0 | 3,0,0] if lenght of the combination is 3 and three possible values. With that info I need to use permutation.

Here is the script I wrote :

function recursion($grd_chfr, $pt_chfr, $tab, &$tab_all) {
    if($grd_chfr == 0) {
        $tab_all[] = $tab;
        return;
    }
    for($n = $pt_chfr; $n <= $grd_chfr; $n++) {
        $b = $tab;
        $b[] =  $n;
        recursion($grd_chfr - $n, $n, $b, $tab_all);
    }
}

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)
                );
            }
        }
    }
}

$somme = 7;
$depart = 1;
$entrees = 7;
$tab_all = [];

$time_start = microtime(true);

// I use a recursive function to get every manner to spread values, to fill the combination whose length is $somme
recursion($somme, $depart, [], $tab_all);

$new_tab_all = [];
$count_gen = 0;

//  if the number of possible values to use ($entrees) is higher or smaller than the length of the combination I adjust by adding zeros or by deleting distributions
foreach($tab_all as $tab){
    if(count($tab) < $entrees){
        $count = count($tab);
        for($x = $depart; $x <= $entrees - $count; $x++){
            $tab[] = 0;
        }
        //  I create all possible permutation for each distribution, and that's where there is too much duplicatas
        foreach(permutations($tab) as $combi){
            if(!in_array($combi, $new_tab_all)) {
                $new_tab_all[] = $combi;
            }
        }
    }
    elseif(count($tab) == $entrees){
        $new_tab_all[] = $tab;
    }
}


$time_stop = microtime(true);
echo round(($time_stop - $time_start), 2)."s d'écoulées, ".count($new_tab_all)." solutions (".$count_gen." générées).</br></br>";

I need a script to get every possible unique permutation of a combination. For example, having the array [1,1,2,3], I would like a script returning [[1,1,3,2], [1,3,1,2], [3,1,1,2], [2,1,3,1], [2,3,1,1], [1,3,2,1], [1,1,2,3], ...] an never having twice the same combination.

To make permutations, I use a script but it generates a lot of repetitions with combinations like [1,1,1,1,2,3]. I found it there : Permutations - all possible sets of numbers

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)
                );
            }
        }
    }
}

I also found a script which I think is what I need, but it is scripted in python, and I need it in php. I found it there : permutations with unique values

class unique_element:
    def __init__(self,value,occurrences):
        self.value = value
        self.occurrences = occurrences

def perm_unique(elements):
    eset=set(elements)
    listunique = [unique_element(i,elements.count(i)) for i in eset]
    u=len(elements)
    return perm_unique_helper(listunique,[0]*u,u-1)

def perm_unique_helper(listunique,result_list,d):
    if d < 0:
        yield tuple(result_list)
    else:
        for i in listunique:
            if i.occurrences > 0:
                result_list[d]=i.value
                i.occurrences-=1
                for g in  perm_unique_helper(listunique,result_list,d-1):
                    yield g
                i.occurrences+=1




a = list(perm_unique([1,1,2]))
print(a)

I don't know how to translate the second code in php, or how to modify the first code to exclude repetitions.

Answer 1

• You start with an original collection, lets say [a, b, a]
• now you need to parse the collection
• for each unique element of the collection, you create a list started by the current element and followed by the permutation of the collection minus the current element (repetition allowed here) like this: pseudo code of the permutation recursive algorithm