Distinct permutations of a number

Given an integer N, the task is to print all distinct permutations of the number N.

Examples:

Input: N = 133
Output: 133 313 331
Explanation:
There are a total of 6 permutations, which are [133, 313, 331, 133, 313, 331].
Out of all these permutations, distinct permutations are [133, 313, 331].

Input: N = 7668
Output: 7668 7686 7866 6768 6786 6678 6687 6876 6867 8766 8676 8667

Approach: Follow the steps below to solve the problem:

• Initialize an empty string to store the equivalent string representation of N.
• Initialize a Map to convert each character of the string to an integer and store it as a list.
• Permute this list using built-in python functions itertools. permutations().
• Initialize another list, say newList.
• Traverse the permutations of the list and if the permutation(list) is not in newList then append this list to newList.
• Initialize an empty string, s = “” and another empty list say permuteList.
• Traverse the list newlist and for each list, perform the following operations:
  • Traverse the list and add each element to the string s.
  • After traversing, convert the string to an integer.
  • Append this integer to permuteList.
• Print the values of permuteList as the possible distinct permutations.

Below is the implementation of the above approach:

Python3

# Python3 program for the above approach

from itertools import permutations

# Utility function to print
# all distinct permutations
def uniquePermutationsUtil(permute):

    p = []

    # Traverse the list permute[]
    for i in permute:

        # Convert this permutation to list
        permutelist = list(i)

        # Append this list to p
        p.append(permutelist)

    # Stores unique permutations
    newlist = []

    # Traverse list p[]
    for i in p:

        # If permutation is
        # not in newlist
        if i not in newlist:
            newlist.append(i)

    # Initialize empty list
    permutelist = []

    # Traverse the list newlist[]
    for i in newlist:

        # Initialize empty string
        s = ""

        # Traversing in element list
        for j in i:

            # Convert each
            # element to string
            s = s + str(j)

        # Convert string to integer
        s = int(s)

        # Append the unique
        # permutation to permutelist
        permutelist.append(s)

    # Print all distinct permutations
    print(*permutelist)

# Function to print all
# distinct permutations
def uniquePermutations(N):

    # Stores equivalent string
    # representation of N
    num = str(N)

    # Convert each character to
    # integer and store in the list
    lis = list(map(int, num))

    # Built in method to store all
    # permutations of the list
    permute = permutations(lis)

    # Print unique permutations
    uniquePermutationsUtil(permute)

# Driver Code

# Given value of N
N = 7668

# Function call to find all
# distinct permutations of N
uniquePermutations(N)

Output:

7668 7686 7866 6768 6786 6678 6687 6876 6867 8766 8676 8667

Time Complexity: O(N * N!)
Auxiliary Space: O(N * N!)