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Distinct Numbers obtained by generating all permutations of a Binary String

Last Updated : 23 Jul, 2025
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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:

Below is the implementation of the above approach:

C++ 
#include <iostream>
#include <algorithm>
#include <set>

using namespace std;

// Function to convert binary
// string to equivalent decimal
int binToDec(string n) {
  string num(n);
  int dec_value = 0;

  // Initializing base
  // value to 1, i.e 2 ^ 0
  int base1 = 1;

  int len1 = num.length();

  for (int i = len1 - 1; i >= 0; i--) {

    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
void printDecimal(string permute) {

  // Set to store distinct
  // decimal representations
  set<int> allDecimals;

  sort(permute.begin(), permute.end());

  // Iterate over all permutations
  do {
    // Convert the current binary
    // representation to decimal
    int result = binToDec(permute);

    // Add the current decimal
    // value into the set
    allDecimals.insert(result);
  } while (next_permutation(permute.begin(), permute.end()));

  // Print the distinct decimals   
  for (auto i : allDecimals)
    cout << i << " ";
  cout << endl;
}

// Utility function to print all
// distinct decimal representations
// of all permutations of string
void totalPermutations(string string)
{
  
  // Function call to print all distinct
  // decimal values represented by all
  // permutations of the given string
  printDecimal(string);
}

// Given binary  string
string binarystring = "1010";

int main() {
  totalPermutations(binarystring);
  return 0;
}

// This code is contributed by phasing17.
Java 
import java.util.*;

public class Main {
    // Function to convert binary string to equivalent decimal
    static int binToDec(String n) {
        String num = new String(n);
        int dec_value = 0;

        // Initializing base value to 1, i.e 2 ^ 0
        int base1 = 1;

        int len1 = num.length();

        for (int i = len1 - 1; i >= 0; i--) {
            if (num.charAt(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
    static void printDecimal(String permute) {
        // Set to store distinct decimal representations
        Set<Integer> allDecimals = new HashSet<Integer>();

        char[] charArray = permute.toCharArray();
        Arrays.sort(charArray);

        // Iterate over all permutations
        do {
            // Convert the current binary representation to decimal
            int result = binToDec(new String(charArray));

            // Add the current decimal value into the set
            allDecimals.add(result);
        } while (nextPermutation(charArray));

        // Print the distinct decimals
        for (int i : allDecimals) {
            System.out.print(i + " ");
        }
        System.out.println();
    }

    // Utility function to print all distinct decimal representations of all permutations of string
    static void totalPermutations(String str) {
        // Function call to print all distinct decimal values represented by all permutations of the given string
        printDecimal(str);
    }

    // Given binary string
    static String binarystring = "1010";

    public static void main(String[] args) {
        totalPermutations(binarystring);
    }

    // Function to get the next permutation of a character array
    static boolean nextPermutation(char[] arr) {
        int i = arr.length - 2;
        while (i >= 0 && arr[i] >= arr[i + 1]) {
            i--;
        }

        if (i < 0) {
            return false;
        }

        int j = arr.length - 1;
        while (arr[j] <= arr[i]) {
            j--;
        }

        swap(arr, i, j);
        reverse(arr, i + 1, arr.length - 1);

        return true;
    }

    // Function to swap two elements in a character array
    static void swap(char[] arr, int i, int j) {
        char temp = arr[i];
        arr[i] = arr[j];
        arr[j] = temp;
    }

    // Function to reverse a portion of a character array
    static void reverse(char[] arr, int i, int j) {
        while (i < j) {
            swap(arr, i, j);
            i++;
            j--;
        }
    }
}
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)
C# 
using System;
using System.Collections.Generic;
using System.Linq;

namespace BinaryPermutations {
class Program {
    static void Main(string[] args)
    {
        string binaryString = "1010";
        TotalPermutations(binaryString);
    }

    static int BinToDec(string n)
    {
        string num = n;
        int dec_value = 0;
        int base1 = 1;
        int len1 = num.Length;

        for (int i = len1 - 1; i >= 0; i--) {
            if (num[i] == '1') {
                dec_value += base1;
            }
            base1 = base1 * 2;
        }

        return dec_value;
    }

    static void PrintDecimal(string permute)
    {
        HashSet<int> allDecimals = new HashSet<int>();
        char[] permuteChars = permute.ToCharArray();
        Array.Sort(permuteChars);

        do {
            int result = BinToDec(new string(permuteChars));
            allDecimals.Add(result);
        } while (NextPermutation(permuteChars));

        foreach(int i in allDecimals)
        {
            Console.Write(i + " ");
        }

        Console.WriteLine();
    }

    static void TotalPermutations(string str)
    {
        PrintDecimal(str);
    }

    static bool NextPermutation(char[] array)
    {
        // Find non-increasing suffix
        int i = array.Length - 1;
        while (i > 0 && array[i - 1] >= array[i]) {
            i--;
        }

        if (i <= 0) {
            return false;
        }

        // Find successor to pivot
        int j = array.Length - 1;
        while (array[j] <= array[i - 1]) {
            j--;
        }

        char temp = array[i - 1];
        array[i - 1] = array[j];
        array[j] = temp;

        // Reverse suffix
        j = array.Length - 1;
        while (i < j) {
            temp = array[i];
            array[i] = array[j];
            array[j] = temp;
            i++;
            j--;
        }

        return true;
    }
}
}
// This code is provided by user_dtewbxkn77n
JavaScript 
// JavaScript implementation of above approach

// Function to convert binary
// string to equivalent decimal
function binToDec(n) {
    let num = n;
    let dec_value = 0;

    // Initializing base
    // value to 1, i.e 2 ^ 0
    let base1 = 1;

    let len1 = num.length;

    for (let i = len1 - 1; i >= 0; i--) {
        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
function printDecimal(permute) {
    // Set to store distinct
    // decimal representations
    let allDecimals = new Set();

    // Iterate over all permutations
    permute.forEach((i) => {
        // Initialize an empty string
        let s = "";

        // Traverse the list
        for (let j of i) {
            // Add each element
            // to the string
            s += j;
        }

        // Convert the current binary
        // representation to decimal
        let result = binToDec(s);

        // Add the current decimal
        // value into the set
        allDecimals.add(result);
    });
    
    allDecimals = Array.from(allDecimals)
    allDecimals.sort(function(a, b) 
    {
        return a - b;
    })
    // Print the distinct decimals
    console.log(allDecimals);
}

// Utility function to print all
// distinct decimal representations
// of all permutations of string
function totalPermutations(string) {
    // Initialize an empty list
    let lis = string.split("");

    // Generate all permutations
    let permutelist = permute(lis);

    // Pass the list of permutations
    // to the printDecimal function
    printDecimal(permutelist);
}

// Helper function to generate all permutations
function permute(arr) {
    let result = [];
    if (arr.length === 1) {
        return [arr];
    }
    for (let i = 0; i < arr.length; i++) {
        let current = arr[i];
        let remaining = [...arr.slice(0, i), ...arr.slice(i + 1)];
        let subpermutes = permute(remaining);
        for (let j = 0; j < subpermutes.length; j++) {
            result.push([current, ...subpermutes[j]]);
        }
    }
    return result;
}

// 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!)


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Analysis of Algorithms

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