PHP Program to Calculate the Permutation nPr

PHP Program to print all permutations of a given string

Last Updated : 10 Dec, 2021

A permutation also called an "arrangement number" or "order," is a rearrangement of the elements of an ordered list S into a one-to-one

A permutation also called an "arrangement number" or "order," is a rearrangement of the elements of an ordered list S into a one-to-one correspondence with S itself. A string of length n has n! permutation.

Source: Mathword(http://mathworld.wolfram.com/Permutation.html)

Below are the permutations of string ABC.
ABC ACB BAC BCA CBA CAB

Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.

Here is a solution that is used as a basis in backtracking.

NewPermutation

PHP

<?php 
// PHP program to print all 
// permutations of a given string. 

/* Permutation function @param 
   str string to calculate permutation 
   for @param l starting index @param 
   r end index */
function permute($str, $l, $r) 
{ 
    if ($l == $r) 
        echo $str. "\n"; 
    else
    { 
        for ($i = $l; $i <= $r; $i++) 
        { 
            $str = swap($str, $l, $i); 
            permute($str, $l + 1, $r); 
            $str = swap($str, $l, $i); 
        } 
    } 
} 

/* Swap Characters at position @param 
   a string value @param i position 1 
   @param j position 2 @return swapped 
   string */
function swap($a, $i, $j) 
{ 
    $temp; 
    $charArray = str_split($a); 
    $temp = $charArray[$i] ; 
    $charArray[$i] = $charArray[$j]; 
    $charArray[$j] = $temp; 
    return implode($charArray); 
} 

// Driver Code 
$str = "ABC"; 
$n = strlen($str); 
permute($str, 0, $n - 1); 

// This code is contributed by mits. 
?>

Output:

ABC
ACB
BAC
BCA
CBA
CAB

Algorithm Paradigm: Backtracking

Time Complexity: O(n*n!) Note that there are n! permutations and it requires O(n) time to print a permutation.

Auxiliary Space: O(r - l)

Note: The above solution prints duplicate permutations if there are repeating characters in the input string. Please see the below link for a solution that prints only distinct permutations even if there are duplicates in input.
Print all distinct permutations of a given string with duplicates.
Permutations of a given string using STL

PHP Program to Calculate the Permutation nPr

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