PHP Program to print all permutations of a given string
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
Here is a solution that is used as a basis in backtracking.
<?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
