Print all permutations with repetition of characters (original) (raw)

Last Updated : 13 Sep, 2022

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

Examples:

Input: AB
Output:
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 the following C implementation.

C++ `

// C++ program to print all permutations // with repetition of characters #include <bits/stdc++.h> #include<string.h> 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 permutations 
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: "<<endl ; allLexicographic(str); return 0; }

// This code is contributed by rathbhupendra

C

// C program to print all permutations with repetition // of characters #include<stdio.h> #include<stdlib.h> #include<string.h>

/* Following function is used by the library qsort() function to sort an array of chars */ int compare (const void * a, const void * b);

// 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)
        printf("%s\n", data);
    else // Recur for higher indexes
        allLexicographicRecur (str, data, last, index+1);
}

}

// 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 permutations
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 program to test above functions int main() { char str[] = "ABC"; printf("All permutations with repetition of %s are: \n", str); allLexicographic(str); return 0; }

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 permutations
    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

Python3

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 range(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 permutations
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

C#

// C# program to print all permutations // with repetition of characters using System;

public 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[i];

        // If this is the last index then print 
        // the string stored in data[]
        if (index == last)
            Console.WriteLine(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
    Array.Sort(temp);
    str = new String(temp);

    // Now print all permutations
    allLexicographicRecur(str, data, length - 1, 0);
}

// Driver Code
public static void Main(String[] args) 
{
    String str = "ABC";
    Console.Write("All permutations with " + 
               "repetition of {0} are: \n", str);
    allLexicographic(str);
}

}

// This code is contributed by PrinciRaj1992

JavaScript

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

Time Complexity: O(n^n)
Auxiliary Space: O(n)

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()).