为所有潜在组合创建动态for循环PHP函数

Question

The code below will create an array for all possible combination that can occur when you have four different variables. The variables always need to equal 1. The for loops I have created work and I understand how to make this work for more variables, but can I make this dynamic? I need to have a function that has how many variables there are as a parameter. If there are three variables create the three forloops. If there are 10... create the 10 corresponding for loops to determine all possible combinations.

$anarray2 = array();
for( $a = 1; $a <= 97; $a++ ) {
  for( $b = 1; $a + $b <=98 ; $b++ ) {
    for( $c = 1; $a + $b + $c <= 99; $c++ ) {
      $d = 100 - ( $a + $b + $c );
      $var_1 = $a / 100;
      $var_2 = $b / 100;
      $var_3 = $c / 100;
      $var_4 = $d / 100;
      $anarray2[] = array( $var_1, $var_2, $var_3, $var_4 );
    }
  }
}
print_array( $anarray2 );

Answer 1

You're effectively looking to share out I identical items to N people in all of the different possible ways.

If there is one person (N==1), then there is only one way to do this - give that person all I items.

If there is more than one person (N>1), then we can consider how many items can be assigned to the first person, and then what the possible assignments are for the remaining N-1 people in each case.

This leads to a nice recursive solution. Firstly we solve the problem for N=1:

function assign($I, $N) {
    $anarray = array();

    if ($N == 1) {
        $anarray[] = array($I);
    } else {
        // Coming up...
    }

return $anarray;
}

Now we solve the problem for N=k (some constant) in terms of N=k-1 - that is, we solve the problem using the solution to a smaller problem. This will reach all the way back to the solution when N=1.

function assign($I, $N) {
    $anarray = array();

    if ($N == 1) {
        $anarray[] = array($I);
    } else {
        for ($i = $I; $i < $I; $i++) {
            foreach (assign($I - $i, $N - 1) as $subproblem) {
                $anarray[] = array_merge(array($i), $subproblem);
            }
        }
    }

    return $anarray;
}    

Something like that should do the job.