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 // 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
