Print distinct sorted permutations with duplicates allowed in input

Difficulty Level : Medium
Last Updated : 18 Oct, 2020

Write a program to print all distinct permutations of a given string in sorted order. Note that the input string may contain duplicate characters.
In mathematics, the notion of permutation relates to the act of arranging all the members of a set into some sequence or order, or if the set is already ordered, rearranging (reordering) its elements, a process called permuting.
Source – Wikipedia
Examples:

Input : BAC
Output : ABC ACB BAC BCA CAB CBA
Input : AAB
Output : AAB ABA BAA
Input : DBCA
Output: ABCD ABDC ACBD ACDB ADBC ADCB BACD BADC BCAD BCDA BDAC BDCA CABD CADB CBAD CBDA CDAB CDBA DABC DACB DBAC DBCA DCAB DCBA

Concept Used: The number of Strings generated by a string of distinct characters of length ‘n’ is equal to ‘n!’. Sorting any given string and generating the lexicographically next bigger string until we reach the largest lexicographically string from those characters.

Different permutations of word “geeks”
Length of string = 5
Character ‘e’ repeats 2 times.
Result = 5!/2! = 60.

Steps:

Example: Consider a string “ABCD”.
Step 1: Sort the string.
Step 2: Obtain the total number of permutations which can be formed from that string.
Step 3: Print the sorted string and then loop for the number of (permutations-1) times as 1st string is already printed.
Step 4: Find the next greater string,.
Here is the implementation of this problem –

C++

// C++ program to print all permutations 
// of a string in sorted order.
#include <bits/stdc++.h>
using namespace std;
 
// Calculating factorial of a number
int factorial(int n) 
{
    int f = 1;
    for (int i = 1; i <= n; i++) 
        f = f * i;
    return f;
}
 
// Method to find total number of permutations
int calculateTotal(string temp, int n) 
{
    int f = factorial(n);
 
    // Building Map to store frequencies of
    // all characters.
    map<char, int> hm;
    for (int i = 0; i < temp.length(); i++) 
    {
        hm[temp[i]]++;
    }
 
    // Traversing map and
    // finding duplicate elements.
    for (auto e : hm) 
    {
        int x = e.second;
        if (x > 1) 
        {
            int temp5 = factorial(x);
            f /= temp5;
        }
        return f;
    }
}
 
static void nextPermutation(string &temp;) 
{
     
    // Start traversing from the end and
    // find position 'i-1' of the first character
    // which is greater than its successor.
    int i;
    for (i = temp.length() - 1; i > 0; i--)
        if (temp[i] > temp[i - 1]) break;
 
    // Finding smallest character after 'i-1' and
    // greater than temp[i-1]
    int min = i;
    int j, x = temp[i - 1];
    for (j = i + 1; j < temp.length(); j++)
        if ((temp[j] < temp[min]) and 
            (temp[j] > x)) 
            min = j;
 
    // Swapping the above found characters.
    swap(temp[i - 1], temp[min]);
 
    // Sort all digits from position next to 'i-1'
    // to end of the string.
    sort(temp.begin() + i, temp.end());
 
    // Print the String
    cout << temp << endl;
}
 
void printAllPermutations(string s)
{
     
    // Sorting String
    string temp(s);
    sort(temp.begin(), temp.end());
 
    // Print first permutation
    cout << temp << endl;
 
    // Finding the total permutations
    int total = calculateTotal(temp, temp.length());
    for (int i = 1; i < total; i++) 
    {
        nextPermutation(temp);
    }
}
 
// Driver Code
int main() 
{
    string s = "AAB";
    printAllPermutations(s);
}
 
// This code is contributed by
// sanjeev2552

Java

// Java program to print all permutations of a string
// in sorted order.
import java.io.*;
import java.util.*;
 
class Solution {
 
  // Calculating factorial of a number
  static int factorial(int n) {
    int f = 1;
    for (int i = 1; i <= n; i++)
      f = f * i;
    return f;
  }
 
  // Method to print the array
  static void print(char[] temp) {
    for (int i = 0; i < temp.length; i++)
      System.out.print(temp[i]);
    System.out.println();
  }
 
  // Method to find total number of permutations
  static int calculateTotal(char[] temp, int n) {
    int f = factorial(n);
 
    // Building HashMap to store frequencies of 
    // all characters.
    HashMap<Character, Integer> hm = 
                     new HashMap<Character, Integer>();
    for (int i = 0; i < temp.length; i++) {
      if (hm.containsKey(temp[i]))
        hm.put(temp[i], hm.get(temp[i]) + 1);
      else
        hm.put(temp[i], 1);
    }
 
    // Traversing hashmap and finding duplicate elements.
    for (Map.Entry e : hm.entrySet()) {
      Integer x = (Integer)e.getValue();
      if (x > 1) {
        int temp5 = factorial(x);
        f = f / temp5;
      }
    }
    return f;
  }
 
  static void nextPermutation(char[] temp) {
 
    // Start traversing from the end and
    // find position 'i-1' of the first character 
    // which is greater than its  successor. 
    int i;
    for (i = temp.length - 1; i > 0; i--)
      if (temp[i] > temp[i - 1])
        break;
 
    // Finding smallest character after 'i-1' and
    // greater than temp[i-1]
    int min = i;
    int j, x = temp[i - 1];
    for (j = i + 1; j < temp.length; j++)
      if ((temp[j] < temp[min]) && (temp[j] > x))
        min = j;
 
    // Swapping the above found characters.
    char temp_to_swap;
    temp_to_swap = temp[i - 1];
    temp[i - 1] = temp[min];
    temp[min] = temp_to_swap;
 
    // Sort all digits from position next to 'i-1'
    // to end of the string.
    Arrays.sort(temp, i, temp.length);
 
    // Print the String
    print(temp);
  }
 
  static void printAllPermutations(String s) {
 
    // Sorting String
    char temp[] = s.toCharArray();
    Arrays.sort(temp);
 
    // Print first permutation
    print(temp);
 
    // Finding the total permutations
    int total = calculateTotal(temp, temp.length);
    for (int i = 1; i < total; i++)
      nextPermutation(temp);
  }
 
  // Driver Code
  public static void main(String[] args) {
    String s = "AAB";
    printAllPermutations(s);
  }
}

Python3

# Python3 program to print 
# all permutations of a 
# string in sorted order.
from collections import defaultdict
 
# Calculating factorial 
# of a number
def factorial(n):
 
    f = 1
     
    for i in range (1, n + 1):
        f = f * i
    return f
 
# Method to find total 
# number of permutations
def calculateTotal(temp, n):
 
    f = factorial(n)
 
    # Building Map to store 
    # frequencies of all 
    # characters.
    hm = defaultdict (int)
     
    for i in range (len(temp)):
        hm[temp[i]] += 1
    
    # Traversing map and
    # finding duplicate elements.
    for e in hm:
        x = hm[e]
        if (x > 1):
            temp5 = factorial(x)
            f //= temp5
        return f
 
def nextPermutation(temp):
     
    # Start traversing from 
    # the end and find position 
    # 'i-1' of the first character
    # which is greater than its successor
    for i in range (len(temp) - 1, 0, -1):
        if (temp[i] > temp[i - 1]):
            break
 
    # Finding smallest character 
    # after 'i-1' and greater 
    # than temp[i-1]
    min = i
    x = temp[i - 1]
    for j in range (i + 1, len(temp)):
        if ((temp[j] < temp[min]) and
            (temp[j] > x)):
            min = j
 
    # Swapping the above 
    # found characters.
    temp[i - 1], temp[min] = (temp[min], 
                              temp[i - 1])
 
    # Sort all digits from 
    # position next to 'i-1'
    # to end of the string
    temp[i:].sort()
 
    # Print the String
    print (''.join(temp))
 
def printAllPermutations(s):
     
    # Sorting String
    temp = list(s)
    temp.sort()
 
    # Print first permutation
    print (''.join( temp))
 
    # Finding the total permutations
    total = calculateTotal(temp, 
                           len(temp))
    for i in range (1, total):
        nextPermutation(temp)
 
# Driver Code
if __name__ == "__main__":
 
    s = "AAB"
    printAllPermutations(s)
 
# This code is contributed by Chitranayal

C#

// C# program to print all permutations 
// of a string in sorted order.
using System;
using System.Collections.Generic;
 
class GFG
{
 
// Calculating factorial of a number
static int factorial(int n) 
{
    int f = 1;
    for (int i = 1; i <= n; i++)
    f = f * i;
    return f;
}
 
// Method to print the array
static void print(char[] temp)
{
    for (int i = 0; i < temp.Length; i++)
    Console.Write(temp[i]);
    Console.WriteLine();
}
 
// Method to find total number of permutations
static int calculateTotal(char[] temp, int n)
{
    int f = factorial(n);
 
    // Building Dictionary to store frequencies  
    // of all characters.
    Dictionary<char, 
               int> hm = new Dictionary<char,
                                        int>();
    for (int i = 0; i < temp.Length; i++) 
    {
        if (hm.ContainsKey(temp[i]))
            hm[temp[i]] = hm[temp[i]] + 1;
        else
            hm.Add(temp[i], 1);
    }
 
    // Traversing hashmap and 
    // finding duplicate elements.
    foreach(KeyValuePair<char, int> e in hm)
    {
        int x = e.Value;
        if (x > 1)
        {
            int temp5 = factorial(x);
            f = f / temp5;
        }
    }
    return f;
}
 
static void nextPermutation(char[] temp) 
{
 
    // Start traversing from the end and
    // find position 'i-1' of the first character 
    // which is greater than its successor. 
    int i;
    for (i = temp.Length - 1; i > 0; i--)
    if (temp[i] > temp[i - 1])
        break;
 
    // Finding smallest character after 'i-1' 
    // and greater than temp[i-1]
    int min = i;
    int j, x = temp[i - 1];
    for (j = i + 1; j < temp.Length; j++)
    if ((temp[j] < temp[min]) && (temp[j] > x))
        min = j;
 
    // Swapping the above found characters.
    char temp_to_swap;
    temp_to_swap = temp[i - 1];
    temp[i - 1] = temp[min];
    temp[min] = temp_to_swap;
 
    // Sort all digits from position next to 'i-1'
    // to end of the string.
    Array.Sort(temp, i, temp.Length-i);
 
    // Print the String
    print(temp);
}
 
static void printAllPermutations(String s)
{
 
    // Sorting String
    char []temp = s.ToCharArray();
    Array.Sort(temp);
 
    // Print first permutation
    print(temp);
 
    // Finding the total permutations
    int total = calculateTotal(temp, temp.Length);
    for (int i = 1; i < total; i++)
    nextPermutation(temp);
}
 
// Driver Code
public static void Main(String[] args) 
{
    String s = "AAB";
    printAllPermutations(s);
}
}
 
// This code is contributed by Rajput-Ji

Output:

AAB
ABA
BAA

Time Complexity: O(n*m) where n is the size of the array and m is the number of permutations possible.
Auxiliary Space: O(n).

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