Distinct Numbers obtained by generating all permutations of a Binary String

Given a binary string S, the task is to print all distinct decimal numbers that can be obtained by generating all permutations of the binary string.

Examples:

Input: S = “110”
Output: {3, 5, 6}
Explanation:
All possible permutations are {“110”, “101”, “110”, “101”, “011”, “011”}.
Equivalent decimal numbers of these binary strings are {6, 5, 6, 5, 3, 3} respectively.
Therefore, the distinct decimal numbers obtained are {3, 5, 6}.

Input: S = “1010”
Output: {3, 5, 6, 9, 10, 12}

Approach: The problem can be solved using a Set. Follow the steps below to solve the problem:

• Convert the given string to a list of characters.
• Permute this list using built-in python function itertools. permutations().
• Initialize an empty string s.
• Traverse the list of permutations and perform the following steps for each permutation:
  • Iterate over the characters and add them to the string.
  • Convert this binary string to equivalent decimal.
  • Insert the current decimal value obtained into a set.
• Finally, print the numbers present in the set.

Below is the implementation of the above approach:

Python3

# Python3 program for the above approach

from itertools import permutations

# Function to convert binary
# string to equivalent decimal
def binToDec(n):

    num = n
    dec_value = 0

    # Initializing base
    # value to 1, i.e 2 ^ 0
    base1 = 1

    len1 = len(num)

    for i in range(len1 - 1, -1, -1):

        if (num[i] == '1'):
            dec_value += base1

        base1 = base1 * 2

    # Return the resultant
    # decimal number
    return dec_value

# Function to print all distinct
# decimals represented by the
# all permutations of the string
def printDecimal(permute):

    # Set to store distinct
    # decimal representations
    allDecimals = set()

    # Iterate over all permutations
    for i in permute:

        # Initialize an empty string
        s = ""

        # Traverse the list
        for j in i:

            # Add each element
            # to the string
            s += j

        # Convert the current binary
        # representation to decimal
        result = binToDec(s)

        # Add the current decimal
        # value into the set
        allDecimals.add(result)

    # Print the distinct decimals
    print(allDecimals)

# Utility function to print all
# distinct decimal representations
# of all permutations of string
def totalPermutations(string):

    # Convert string to list
    lis = list(string)

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

    printDecimal(permutelist)


# Given binary  string
binarystring = '1010'

# Function call to print all distinct
# decimal values represented by all
# permutations of the given string
totalPermutations(binarystring)

Output:

{3, 5, 6, 9, 10, 12}

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