PHP permutation recursive and permutation combination instance code detailed

1. Arranging recursion

If p represents the full arrangement of n elements, and Pi means that n elements do not contain the full permutation of element I, (i) pi indicates the arrangement of the prefix I in front of the permutation pi, then the full arrangement of n elements is recursively defined as:
① if n=1, then the permutation p has only one element i;
② if n>1, then the entire arrangement p is composed of the permutation (i) pi;
By definition, you can see that if you have generated the permutation pi for (k-1) elements, then the arrangement of the K elements can be generated by adding element I to each pi.

Code:

function rank ($base, $temp =null) {    $len = strlen ($base);    if ($len <= 1)    {        echo $temp. $base. ' <br/> ';    }    else    {for        ($i =0; $i < $len; + + $i)        {            rank (substr ($base, 0, $i). substr ($base, $i +1, $len-$i-1), $temp. $base [$i]);}}    Rank (' 123 ');

However, after several tests of the results of the operation, it was found that there was a problem: if the same element exists, then the whole permutation is repeated.
For example, there are only three cases of the full arrangement of ' 122 ': ' 122 ', ' 212 ', ' 221 ';
Slightly modified, add a judge to repeat the flag, resolved the problem (code below):

function Fsrank ($base, $temp =null) {    static $ret = Array ();    $len = strlen ($base);    if ($len <= 1)    {        //echo $temp. $base. ' <br/> ';        $ret [] = $temp. $base;    }    else    {for        ($i =0; $i < $len; + + $i)        {            $had _flag = false;            for ($j =0; $j < $i; + + $j)            {                if ($base [$i] = = $base [$j])                {                    $had _flag = true;                    break;                }            }            if ($had _flag)            {                continue;            }            Fsrank (substr ($base, 0, $i). substr ($base, $i +1, $len-$i-1), $temp. $base [$i]);        }    return $ret;} print ' <pre> ';p rint_r (Fsrank (' 122 '));p rint ' </pre> ';

2. Permutation combination Instances

<?php/** * Math problem to solve: Calculate C (a,1) * C (b, 1) * ... * combination of C (n, 1), where C (n, 1) represents an arbitrary element from n elements * * Examples of practical problems to solve: A grade has m classes, the number of each class Different, now to draw from each class A person to form a group, * by the group to represent the grade to participate in the school's activities, please give all possible combinations *//* ################################### start Calculate ################################### *//** * Array Description: The array is a two-dimensional array, the first-dimensional index represents the class number, the second-dimensional index represents the student number */$CombinList =                    Array (1 = = Array ("Student10", "Student11"), 2 = = Array ("Student20", "Student21", "Student22"), 3 = = Array ("Student30"), 4 = = Array ("STUDENT40", "Student41", "Student42", "Stud Ent43 ") */* calculate C (a,1) * C (b, 1) * ... * C (n, 1) value */$CombineCount = 1;foreach ($CombinList as $Key + $Value) {$Combin Ecount *= count ($Value);}     $RepeatTime = $CombineCount, foreach ($CombinList as $ClassNo + $StudentList) {//$StudentList the maximum number of repetitions that occur vertically after splitting a component into a combination    $RepeatTime = $RepeatTime/count ($StudentList);    $StartPosition = 1; Start looping for students in each class foreach ($StudentList as $Student) {$TempStartPosition = $StartPosition;        $SpaceCount = $CombineCount/count ($StudentList)/$RepeatTime;               for ($J = 1; $J <= $SpaceCount; $J + +) {for ($I = 0; $I < $RepeatTime; $I + +) {            $Result [$TempStartPosition + $I] [$ClassNo] = $Student;        } $TempStartPosition + = $RepeatTime * COUNT ($StudentList);    } $StartPosition + = $RepeatTime; }}/* print result */echo "<pre>";p Rint_r ($Result);? >