PHP full permutation algorithm implementation program code

PHP full permutation algorithm implementation program code_PHP tutorial

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Release： 2016-07-13 10:09:52

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PHP full permutation algorithm implementation program code

Randomly select m (m≤n) elements from n different elements and arrange them in a certain order, which is called from n Take an arrangement of m elements from different elements. When m=n, all permutations are called full permutations.

Introduction

For example, the total arrangement of the three elements 1, 2, and 3 is:

　1,2,3

　1,3,2

　2,1,3

　2,3,1

　3,1,2

　3,2,1

A total of 3*2*1=6 types 3!

2 formulas

The total number of permutations f(n)=n! (definition 0!=1)

Recursive algorithm

　1,2,3

　1,3,2

　2,1,3

　2,3,1

　3,2,1

　3,1,2

This is because the algorithm only considers how to output the full arrangement, but does not consider whether there is a problem with transposition. So I came up with a solution, which is to modify the transposition function

For example, if 1 2 3 is transposed, it should not be directly 3 2 1, so that 3 and 1 can be transposed directly; instead, 3 should be arranged at the front and back, and 1 2 should be in sequence

Basic Algorithm

The following introduces four types of total permutation algorithms:

　(A) Dictionary order

　(B) Increasing carry number method

　(D) Ortho substitution method

Implementing the full permutation algorithm

The code is as follows

header("content-type:text/html;charset=utf-8");/**
* @param array $a The collection of elements to be arranged, which will change dynamically
* @param array $b stores the current arrangement
* @param array $M The set of elements to be arranged, equivalent to a constant, always the initial set of elements to be arranged
*/
function wholerange($a,$b,$M){
$range=array();
if(count($a) > 1){
$d=$b;
foreach($a as $value){
$b[]=$value;
$c=array_diff($M,$b);
if(count($c) > 0){
$range[]=wholerange($c,$b,$M);
}
$b=$d;
}
}elseif(count($a) == 1){
foreach($a as $value){
$b[]=$value;
}
$onerange="";
foreach($b as $value){
$onerange.=$value;
}
$range[]=$onerange;
}
return $range;
}
/**
* Recursive output array
*
* @param array $arr Array to be output
* @return int Returns the number of array elements*/
function recursionarray($arr){
$i=0;
foreach($arr as $value){
if(is_array($value)){
$i+=recursionarray($value);
}else{
echo $value."
";
$i++;
}
}
return $i;
}
$a=array('A','B','C','D');
$b=array();
$range=wholerange($a,$b,$a);
$count=recursionarray($range);
echo "There are total ".$count."arrangements";
?>