# Print all permutations with repetition of characters

Given a string of length n, print all permutation of the given string. Repetition of characters is allowed. Print these permutations in lexicographically sorted order
Examples:

```Input: AB
Ouput: All permutations of AB with repetition are:
AA
AB
BA
BB

Input: ABC
Output: All permutations of ABC with repetition are:
AAA
AAB
AAC
ABA
...
...
CCB
CCC
```

For an input string of size n, there will be n^n permutations with repetition allowed. The idea is to fix the first character at first index and recursively call for other subsequent indexes. Once all permutations starting with the first character are printed, fix the second character at first index. Continue these steps till last character. Thanks to PsychoCoder for providing following C implementation.

## C++

 `// C++ program to print all permutations  ` `// with repetition of characters  ` `#include ` `#include ` `using` `namespace` `std; ` ` `  ` `  `/* Following function is used by ` `the library qsort() function  ` `to sort an array of chars */` `int` `compare (``const` `void` `* a, ``const` `void` `* b);  ` ` `  `/* The main function that recursively ` `prints all repeated permutations of ` `the given string. It uses data[] to store all  ` `permutations one by one */` `void` `allLexicographicRecur (``char` `*str, ``char``* data,  ` `                            ``int` `last, ``int` `index)  ` `{  ` `    ``int` `i, len = ``strlen``(str);  ` ` `  `    ``// One by one fix all characters at ` `    ``// the given index and recur for  ` `    ``// the/ subsequent indexes  ` `    ``for` `( i = 0; i < len; i++ )  ` `    ``{  ` `        ``// Fix the ith character at index  ` `        ``// and if this is not the last  ` `        ``// index then recursively call  ` `        ``// for higher indexes  ` `        ``data[index] = str[i] ;  ` ` `  `        ``// If this is the last index then ` `        ``// print the string stored in  ` `        ``// data[]  ` `        ``if` `(index == last)  ` `            ``cout << data << endl;  ` `        ``else` `// Recur for higher indexes  ` `            ``allLexicographicRecur (str, data, last, index+1);  ` `    ``}  ` `}  ` ` `  `/* This function sorts input string, ` `allocate memory for data (needed  ` `for allLexicographicRecur()) and  ` `calls allLexicographicRecur() for  ` `printing all permutations */` `void` `allLexicographic(``char` `*str)  ` `{  ` `    ``int` `len = ``strlen` `(str) ;  ` ` `  `    ``// Create a temp array that will  ` `    ``// be used by allLexicographicRecur()  ` `    ``char` `*data = (``char` `*) ``malloc` `(``sizeof``(``char``) * (len + 1)) ;  ` `    ``data[len] = ``'\0'``;  ` ` `  `    ``// Sort the input string so that ` `    ``// we get all output strings in  ` `    ``// lexicographically sorted order  ` `    ``qsort``(str, len, ``sizeof``(``char``), compare);  ` ` `  `    ``// Now print all permutaions  ` `    ``allLexicographicRecur (str, data, len-1, 0);  ` ` `  `    ``// Free data to avoid memory leak  ` `    ``free``(data);  ` `}  ` ` `  `// Needed for library function qsort()  ` `int` `compare (``const` `void` `* a, ``const` `void` `* b)  ` `{  ` `    ``return` `( *(``char` `*)a - *(``char` `*)b );  ` `}  ` ` `  `// Driver code  ` `int` `main()  ` `{  ` `    ``char` `str[] = ``"ABC"``;  ` `    ``cout << ``"All permutations with repetition of "``<<  ` `                                ``str <<``" are: "``<

## C

 `// C program to print all permutations with repetition ` `// of characters ` `#include ` `#include ` `#include ` ` `  `/* Following function is used by the library qsort() function ` `  ``to sort an array of chars */` `int` `compare (``const` `void` `* a, ``const` `void` `* b); ` ` `  `/* The main function that recursively prints all repeated  ` `   ``permutations of  the given string. It uses data[] to store all ` `   ``permutations one by one */` `void` `allLexicographicRecur (``char` `*str, ``char``* data, ``int` `last, ``int` `index) ` `{ ` `    ``int` `i, len = ``strlen``(str); ` ` `  `    ``// One by one fix all characters at the given index and recur for  ` `    ``// the/ subsequent indexes ` `    ``for` `( i=0; i

## Java

 `// Java program to print all permutations  ` `// with repetition of characters ` `import` `java.util.Arrays; ` ` `  `class` `GFG  ` `{ ` ` `  `    ``// The main function that recursively prints  ` `    ``// all repeated permutations of the given string.  ` `    ``// It uses data[] to store all permutations one by one ` `    ``static` `void` `allLexicographicRecur(String str, ``char``[] data, ` `                                      ``int` `last, ``int` `index)  ` `    ``{ ` `        ``int` `length = str.length(); ` ` `  `        ``// One by one fix all characters at the given index  ` `        ``// and recur for the subsequent indexes ` `        ``for` `(``int` `i = ``0``; i < length; i++)  ` `        ``{ ` ` `  `            ``// Fix the ith character at index and if  ` `            ``// this is not the last index then  ` `            ``// recursively call for higher indexes ` `            ``data[index] = str.charAt(i); ` ` `  `            ``// If this is the last index then print  ` `            ``// the string stored in data[] ` `            ``if` `(index == last) ` `                ``System.out.println(``new` `String(data)); ` `            ``else` `                ``allLexicographicRecur(str, data, last,  ` `                                           ``index + ``1``); ` `        ``} ` `    ``} ` ` `  `    ``// This function sorts input string, allocate memory  ` `    ``// for data(needed for allLexicographicRecur()) and calls ` `    ``// allLexicographicRecur() for printing all permutations ` `    ``static` `void` `allLexicographic(String str)  ` `    ``{ ` `        ``int` `length = str.length(); ` ` `  `        ``// Create a temp array that will be used by ` `        ``// allLexicographicRecur() ` `        ``char``[] data = ``new` `char``[length + ``1``]; ` `        ``char``[] temp = str.toCharArray(); ` ` `  `        ``// Sort the input string so that we get all  ` `        ``// output strings in lexicographically sorted order ` `        ``Arrays.sort(temp); ` `        ``str = ``new` `String(temp); ` ` `  `        ``// Now print all permutaions ` `        ``allLexicographicRecur(str, data, length - ``1``, ``0``); ` `    ``} ` ` `  `    ``// Driver Code ` `    ``public` `static` `void` `main(String[] args)  ` `    ``{ ` `        ``String str = ``"ABC"``; ` `        ``System.out.printf(``"All permutations with "` `+  ` `                   ``"repetition of %s are: \n"``, str); ` `        ``allLexicographic(str); ` `    ``} ` `} ` ` `  `// This code is contributed by ` `// sanjeev2552 `

## Python

 `# Python program to print all permutations with repetition ` `# of characters ` ` `  `def` `toString(``List``): ` `    ``return` `''.join(``List``) ` ` `  `# The main function that recursively prints all repeated ` `# permutations of the given string. It uses data[] to store ` `# all permutations one by one ` `def` `allLexicographicRecur (string, data, last, index): ` `    ``length ``=` `len``(string) ` ` `  `    ``# One by one fix all characters at the given index and ` `    ``# recur for the subsequent indexes ` `    ``for` `i ``in` `xrange``(length): ` ` `  `        ``# Fix the ith character at index and if this is not ` `        ``# the last index then recursively call for higher ` `        ``# indexes ` `        ``data[index] ``=` `string[i] ` ` `  `        ``# If this is the last index then print the string ` `        ``# stored in data[] ` `        ``if` `index``=``=``last: ` `            ``print` `toString(data) ` `        ``else``: ` `            ``allLexicographicRecur(string, data, last, index``+``1``) ` ` `  `# This function sorts input string, allocate memory for data ` `# (needed for allLexicographicRecur()) and calls ` `# allLexicographicRecur() for printing all permutations ` `def` `allLexicographic(string): ` `    ``length ``=` `len``(string) ` ` `  `    ``# Create a temp array that will be used by ` `    ``# allLexicographicRecur() ` `    ``data ``=` `[""] ``*` `(length``+``1``) ` ` `  `    ``# Sort the input string so that we get all output strings in ` `    ``# lexicographically sorted order ` `    ``string ``=` `sorted``(string) ` ` `  `    ``# Now print all permutaions ` `    ``allLexicographicRecur(string, data, length``-``1``, ``0``) ` ` `  `# Driver program to test the above functions ` `string ``=` `"ABC"` `print` `"All permutations with repetition of "` `+` `string ``+` `" are:"` `allLexicographic(string) ` ` `  `# This code is contributed to Bhavya Jain `

Output:

```All permutations with repetition of ABC are:
AAA
AAB
AAC
ABA
ABB
ABC
ACA
ACB
ACC
BAA
BAB
BAC
BBA
BBB
BBC
BCA
BCB
BCC
CAA
CAB
CAC
CBA
CBB
CBC
CCA
CCB
CCC
```

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Following is recursion tree for input string “AB”. The purpose of recursion tree is to help in understanding the above implementation as it shows values of different variables.

```                              data=""
/         \
/           \
index=0           index=0
i=0               i=1
data="A"           data="B"
/   \              /    \
/      \            /      \
index=1  index=1    index=1    index=1
i=0      i=1        i=0        i=1
data="AA"  data="AB"  data="BA"  data="BB"
```

In the above implementation, it is assumed that all characters of the input string are different. The implementation can be easily modified to handle the repeated characters. We have to add a preprocessing step to find unique characters (before calling allLexicographicRecur()).