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Generate all binary strings without consecutive 1’s

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Given an integer, K. Generate all binary strings of size k without consecutive 1’s.

Examples: 

Input : K = 3  
Output : 000 , 001 , 010 , 100 , 101
Input : K = 4
Output :0000 0001 0010 0100 0101 1000 1001 1010

Idea behind that is IF string ends with ‘1’ then we put only ‘0’ at the end. IF string ends with ‘0’ then we put both ‘0’ and ‘1’ at the end of string for generating new string.

Below is algorithm  

K : size of string 
First We Generate All string starts with '0'
initialize n = 1 .
GenerateALLString ( K , Str , n )
a. IF n == K
PRINT str.
b. IF previous character is '1' :: str[n-1] == '1'
put str[n] = '0'
GenerateAllString ( K , str , n+1 )
c. IF previous character is '0' :: str[n-1] == '0'
First We Put zero at end and call function
PUT str[n] = '0'
GenerateAllString ( K , str , n+1 )
PUT str[n] = '1'
GenerateAllString ( K , str , n+1 )
Second Generate all binary string starts with '1'
DO THE SAME PROCESS

Below is the recursive implementation: 

C++

// C++ program to Generate
// all binary string without
// consecutive 1's of size K
#include<bits/stdc++.h>
using namespace std ;
 
// A utility function generate all string without
// consecutive 1'sof size K
void generateAllStringsUtil(int K, char str[], int n)
{
     
    // Print binary string without consecutive 1's
    if (n  == K)
    {
         
        // Terminate binary string
        str[n] = '\0' ;
        cout << str << " ";
        return ;
    }
 
    // If previous character is '1' then we put
    // only 0 at end of string
    //example str = "01" then new string be "010"
    if (str[n-1] == '1')
    {
        str[n] = '0';
        generateAllStringsUtil (K , str , n+1);
    }
 
    // If previous character is '0' than we put
    // both '1' and '0' at end of string
    // example str = "00" then
    // new string "001" and "000"
    if (str[n-1] == '0')
    {
        str[n] = '0';
        generateAllStringsUtil(K, str, n+1);
        str[n] = '1';
        generateAllStringsUtil(K, str, n+1) ;
    }
}
 
// Function generate all binary string without
// consecutive 1's
void generateAllStrings(int K )
{
    // Base case
    if (K <= 0)
        return ;
 
    // One by one stores every
    // binary string of length K
    char str[K];
 
    // Generate all Binary string
    // starts with '0'
    str[0] = '0' ;
    generateAllStringsUtil ( K , str , 1 ) ;
 
    // Generate all Binary string
    // starts with '1'
    str[0] = '1' ;
    generateAllStringsUtil ( K , str , 1 );
}
 
// Driver program to test above function
int main()
{
    int K = 3;
    generateAllStrings (K) ;
    return 0;
}

                    

Java

// Java program to Generate all binary string without
// consecutive 1's of size K
import java.util.*;
import java.lang.*;
 
public class BinaryS {
 
    // Array conversion to String--
    public static String toString(char[] a) {
        String string = new String(a);
        return string;
    }
 
    static void generate(int k, char[] ch, int n) {
       
        // Base Condition when we
        // reached at the end of Array**
        if (n == k) {
           
            // Printing the Generated String**
            // Return to the previous case*
            System.out.print(toString(ch)+" ");
            return;
 
        }
       
        // If the first Character is
        //Zero then adding**
        if (ch[n - 1] == '0') {
            ch[n] = '0';
            generate(k, ch, n + 1);
            ch[n] = '1';
            generate(k, ch, n + 1);
        }
       
        // If the Character is One
        // then add Zero to next**
        if (ch[n - 1] == '1') {
 
            ch[n] = '0';
           
            // Calling Recursively for the
            // next value of Array
            generate(k, ch, n + 1);
 
        }
    }
 
    static void fun(int k) {
 
        if (k <= 0) {
            return;
        }
 
        char[] ch = new char[k];
       
        // Initializing first character to Zero
        ch[0] = '0';
       
        // Generating Strings starting with Zero--
        generate(k, ch, 1);
 
        // Initialized first Character to one--
        ch[0] = '1';
        generate(k, ch, 1);
 
    }
 
    public static void main(String args[]) {
 
        int k = 3;
       
        //Calling function fun with argument k
        fun(k);
       
        //This code is Contributed by Praveen Tiwari
    }
}

                    

Python3

# Python3 program to Generate all binary string
# without consecutive 1's of size K
 
# A utility function generate all string without
# consecutive 1'sof size K
def generateAllStringsUtil(K, str, n):
     
    # print binary string without consecutive 1's
    if (n == K):
         
        # terminate binary string
        print(*str[:n], sep = "", end = " ")
        return
     
    # if previous character is '1' then we put
    # only 0 at end of string
    # example str = "01" then new string be "000"
    if (str[n-1] == '1'):
        str[n] = '0'
        generateAllStringsUtil (K, str, n + 1)
         
    # if previous character is '0' than we put
    # both '1' and '0' at end of string
    # example str = "00" then new string "001" and "000"
    if (str[n-1] == '0'):
        str[n] = '0'
        generateAllStringsUtil(K, str, n + 1)
        str[n] = '1'
        generateAllStringsUtil(K, str, n + 1)
         
# function generate all binary string without
# consecutive 1's
def generateAllStrings(K):
     
    # Base case
    if (K <= 0):
        return
     
    # One by one stores every
    # binary string of length K
    str = [0] * K
     
    # Generate all Binary string starts with '0'
    str[0] = '0'
    generateAllStringsUtil (K, str, 1)
     
    # Generate all Binary string starts with '1'
    str[0] = '1'
    generateAllStringsUtil (K, str, 1)
 
# Driver code
K = 3
generateAllStrings (K)
 
# This code is contributed by SHUBHAMSINGH10

                    

C#

// C# program to Generate
// all binary string without
// consecutive 1's of size K
using System;
class GFG {
 
  // Array conversion to String--
  static string toString(char[] a) {
    string String = new string(a);
    return String;
  }
 
  static void generate(int k, char[] ch, int n) {
 
    // Base Condition when we
    // reached at the end of Array**
    if (n == k) {
 
      // Printing the Generated String**
      // Return to the previous case*
      Console.Write(toString(ch)+" ");
      return;
 
    }
 
    // If the first Character is
    //Zero then adding**
    if (ch[n - 1] == '0') {
      ch[n] = '0';
      generate(k, ch, n + 1);
      ch[n] = '1';
      generate(k, ch, n + 1);
    }
 
    // If the Character is One
    // then add Zero to next**
    if (ch[n - 1] == '1') {
 
      ch[n] = '0';
 
      // Calling Recursively for the
      // next value of Array
      generate(k, ch, n + 1);
 
    }
  }
 
  static void fun(int k)
  {
    if (k <= 0)
    {
      return;
    }
    char[] ch = new char[k];
 
    // Initializing first character to Zero
    ch[0] = '0';
 
    // Generating Strings starting with Zero--
    generate(k, ch, 1);
 
    // Initialized first Character to one--
    ch[0] = '1';
    generate(k, ch, 1);
 
  }
 
  // Driver code
  static void Main()
  {
    int k = 3;
 
    //Calling function fun with argument k
    fun(k);
  }
}
 
// This code is contributed by divyeshrabadiya07.

                    

Javascript

<script>
// Javascript implementation
 
// A utility function generate all string without
// consecutive 1'sof size K
function generateAllStringsUtil(K, str, n)
{
      
    // Print binary string without consecutive 1's
    if (n  == K)
    {
          
        // Terminate binary string
        str[n] = '\0' ;
        document.write(str.join("") + " ");
        return ;
    }
  
    // If previous character is '1' then we put
    // only 0 at end of string
    //example str = "01" then new string be "010"
    if (str[n-1] == '1')
    {
        str[n] = '0';
        generateAllStringsUtil (K , str , n+1);
    }
  
    // If previous character is '0' than we put
    // both '1' and '0' at end of string
    // example str = "00" then
    // new string "001" and "000"
    if (str[n-1] == '0')
    {
        str[n] = '0';
        generateAllStringsUtil(K, str, n+1);
        str[n] = '1';
        generateAllStringsUtil(K, str, n+1) ;
    }
}
  
// Function generate all binary string without
// consecutive 1's
function generateAllStrings(K )
{
    // Base case
    if (K <= 0)
        return ;
  
    // One by one stores every
    // binary string of length K
    var str = new Array(K);
  
    // Generate all Binary string
    // starts with '0'
    str[0] = '0' ;
    generateAllStringsUtil ( K , str , 1 ) ;
  
    // Generate all Binary string
    // starts with '1'
    str[0] = '1' ;
    generateAllStringsUtil ( K , str , 1 );
}
 
/* Driver code */
var K = 3;
generateAllStrings(K);
 
// This is code is contributed
// by shivani
</script>

                    

PHP

<?php
 
// A utility function to generate all strings without
// consecutive 1's of size K
function generateAllStringsUtil($K, &$str, $n) {
    // Print binary string without consecutive 1's
    if ($n == $K) {
        // Terminate binary string
        echo implode("", array_slice($str, 0, $n)) . " ";
        return;
    }
 
    // If previous character is '1', then put only '0' at the end of the string
    if ($str[$n-1] == '1') {
        $str[$n] = '0';
        generateAllStringsUtil($K, $str, $n + 1);
    }
 
    // If previous character is '0', put both '1' and '0' at the end of the string
    if ($str[$n-1] == '0') {
        $str[$n] = '0';
        generateAllStringsUtil($K, $str, $n + 1);
        $str[$n] = '1';
        generateAllStringsUtil($K, $str, $n + 1);
    }
}
 
// Function to generate all binary strings without consecutive 1's
function generateAllStrings($K) {
    // Base case
    if ($K <= 0) {
        return;
    }
 
    // One by one store every binary string of length K
    $str = array_fill(0, $K, 0);
 
    // Generate all binary strings starting with '0'
    $str[0] = '0';
    generateAllStringsUtil($K, $str, 1);
 
    // Generate all binary strings starting with '1'
    $str[0] = '1';
    generateAllStringsUtil($K, $str, 1);
}
 
// Driver program to test the above function
$K = 3;
generateAllStrings($K);
 
?>

                    

Output
000 001 010 100 101 

Time complexity: O(2^K) where K is the size of the binary string. This is due to the fact that the algorithm recursively generates all possible binary strings of length K.
Auxiliary space: O(K), since we are using a string array of size K to store the binary string.

This problem is solved by using a recursion tree having two possibilities 0 or 1 just like selecting elements in a subsequence.

So we can also implement above approach using boolean array as well.

C++14

#include <bits/stdc++.h>
using namespace std;
 
void All_Binary_Strings(bool arr[],int num,int r)
{
    if(r==num)
    {
        for(int i=0;i<num;i++)
        cout<<arr[i];
        cout<<" ";
        return;
    }
    else if(arr[r-1])
    {
        arr[r]=0;
        All_Binary_Strings(arr,num,r+1);
    }
    else
    {
         arr[r]=0;
        All_Binary_Strings(arr,num,r+1);
         arr[r]=1;
        All_Binary_Strings(arr,num,r+1);
    }
}
 
void print(bool a[],int& num)
{
    a[0]=0;
    All_Binary_Strings(a,num,1);
    a[0]=1;
    All_Binary_Strings(a,num,1);
}
 
//driver's code
int main()
{
    int n=2;
    bool a[n];
    print(a,n);
    return 0;
}

                    

Java

/*package whatever //do not write package name here */
 
import java.io.*;
 
class GFG {
    static void All_Binary_Strings(int arr[],int num,int r)
{
    if(r == num)
    {
        for(int i = 0; i < num; i++)
            System.out.print(arr[i]);
            System.out.print(" ");
         
        return;
    }
    else if(arr[r-1] == 1)
    {
        arr[r] = 0;
        All_Binary_Strings(arr,num,r+1);
    }
    else
    {
        arr[r] = 0;
        All_Binary_Strings(arr,num,r+1);
        arr[r] = 1;
        All_Binary_Strings(arr,num,r+1);
    }
}
 
static void print(int a[],int num)
{
    a[0] = 0;
    All_Binary_Strings(a,num,1);
    a[0] = 1;
    All_Binary_Strings(a,num,1);
}
 
// Driver code
public static void main(String args[])
{
    int n = 2;
    int a[] = new int[n];
    print(a,n);
}
}
 
// This code is contributed by shinjanpatra.

                    

Python3

def All_Binary_Strings(arr,num,r):
 
    if(r == num):
 
        for i in range(num):
            print(arr[i],end="")
        print(end=" ")
        return
     
    elif(arr[r-1]):
 
        arr[r] = 0
        All_Binary_Strings(arr, num, r + 1)
 
    else:
     
        arr[r] = 0
        All_Binary_Strings(arr,num,r+1)
        arr[r] = 1
        All_Binary_Strings(arr,num,r+1)
 
 
def Print(a,num):
    a[0] = 0
    All_Binary_Strings(a,num,1)
    a[0] = 1
    All_Binary_Strings(a,num,1)
 
 
# driver's code
 
n = 2
a = [False for i in range(n)]
Print(a,n)
 
# This code is contributed by shinjanpatra

                    

C#

// C# program to Generate
// all binary string without
using System;
 
public static class GFG {
 
    public static void All_Binary_Strings(int[] arr,
                                          int num, int r)
    {
        if (r == num) {
            for (int i = 0; i < num; i++) {
                Console.Write(arr[i]);
            }
            Console.Write(" ");
            return;
        }
        else if (arr[r - 1] == 1) {
            arr[r] = 0;
            All_Binary_Strings(arr, num, r + 1);
        }
        else {
            arr[r] = 0;
            All_Binary_Strings(arr, num, r + 1);
            arr[r] = 1;
            All_Binary_Strings(arr, num, r + 1);
        }
    }
 
    public static void print(int[] a, ref int num)
    {
        a[0] = 0;
        All_Binary_Strings(a, num, 1);
        a[0] = 1;
        All_Binary_Strings(a, num, 1);
    }
 
    // driver's code
    public static void Main()
    {
        int n = 2;
        int[] a = new int[n];
        print(a, ref n);
    }
}
 
// This code is contributed by Aarti_Rathi

                    

Javascript

<script>
 
function All_Binary_Strings(arr,num,r)
{
    if(r == num)
    {
        for(let i = 0; i < num; i++)
        document.write(arr[i]);
        document.write(" ");
        return;
    }
    else if(arr[r-1])
    {
        arr[r] = 0;
        All_Binary_Strings(arr, num, r + 1);
    }
    else
    {
         arr[r] = 0;
        All_Binary_Strings(arr,num,r+1);
         arr[r] = 1;
        All_Binary_Strings(arr,num,r+1);
    }
}
 
function print(a,num)
{
    a[0] = 0;
    All_Binary_Strings(a,num,1);
    a[0] = 1;
    All_Binary_Strings(a,num,1);
}
 
// driver's code
 
let n=2;
let a = new Array(n).fill(false);
print(a,n);
 
// This code is contributed by shinjanpatra
</script>

                    

PHP

<?php
 
function allBinaryStrings($arr, $num, $r) {
    if ($r == $num) {
        for ($i = 0; $i < $num; $i++) {
            echo $arr[$i];
        }
        echo " ";
        return;
    } else if ($arr[$r-1] == 1) {
        $arr[$r] = 0;
        allBinaryStrings($arr, $num, $r+1);
    } else {
        $arr[$r] = 0;
        allBinaryStrings($arr, $num, $r+1);
        $arr[$r] = 1;
        allBinaryStrings($arr, $num, $r+1);
    }
}
 
function printBinaryStrings($num) {
    $arr = array_fill(0, $num, 0);
    $arr[0] = 0;
    allBinaryStrings($arr, $num, 1);
    $arr[0] = 1;
    allBinaryStrings($arr, $num, 1);
}
 
// Driver code
$n = 2;
printBinaryStrings($n);
 
?>

                    

Output
00 01 10 

Time Complexity: O(2^n),as we can see that we are calling the recursive function two times for every recursion level. Hence, the time complexity is 2^n.
Space Complexity: O(n) since we are using a boolean array of size n.

The above approach can also be solved using string. It does not have any effect on complexity but string handling, printing and operating is easy.

C++14

#include <bits/stdc++.h>
using namespace std;
 
void All_Binary_Strings(string str,int num)
{
    int len=str.length();
    if(len==num)
    {
        cout<<str<<" ";
        return;
    }
    else if(str[len-1]=='1')
        All_Binary_Strings(str+'0',num);
    else
    {
        All_Binary_Strings(str+'0',num);
        All_Binary_Strings(str+'1',num);
    }
}
 
void print(int& num)
{
    string word;
    word.push_back('0');
    All_Binary_Strings(word,num);
    word[0]='1';
    All_Binary_Strings(word,num);
}
 
//driver's code
int main()
{
    int n=4;
    print(n);
    return 0;
}

                    

Java

import java.util.*;
 
public class GFG {
 
    static void All_Binary_Strings(String str, int num)
    {
        int len = str.length();
        if (len == num) {
            System.out.print(str + " ");
            return;
        }
        else if (str.charAt(len - 1) == '1')
            All_Binary_Strings(str + '0', num);
        else {
            All_Binary_Strings(str + '0', num);
            All_Binary_Strings(str + '1', num);
        }
    }
 
    static void print(int num)
    {
        String word = "";
        word += '0';
        All_Binary_Strings(word, num);
        word = "1";
        All_Binary_Strings(word, num);
    }
 
    // driver's code
    public static void main(String[] args)
    {
        int n = 4;
        print(n);
    }
}
 
// This code is contributed by Karandeep1234

                    

Python3

def All_Binary_Strings(str,num):
 
    Len = len(str)
    if(Len == num):
        print(str,end = " ")
        return
 
    elif(str[Len - 1]=='1'):
        All_Binary_Strings(str+'0',num)
    else:
        All_Binary_Strings(str+'0',num)
        All_Binary_Strings(str+'1',num)
 
def Print(num):
 
    word = ""
    word += '0'
    All_Binary_Strings(word,num)
    word = '1'
    All_Binary_Strings(word,num)
 
# Driver's code
n = 4
Print(n)
 
# This code is contributed by shinjanpatra.

                    

C#

using System;
using System.Collections;
using System.Collections.Generic;
 
public class GFG {
 
  static void All_Binary_Strings(String str, int num)
  {
    int len = str.Length;
    if (len == num) {
      Console.Write(str + " ");
      return;
    }
    else if (str[len - 1] == '1')
      All_Binary_Strings(str + '0', num);
    else {
      All_Binary_Strings(str + '0', num);
      All_Binary_Strings(str + '1', num);
    }
  }
 
  static void print(int num)
  {
    string word = "";
    word += '0';
    All_Binary_Strings(word, num);
    word = "1";
    All_Binary_Strings(word, num);
  }
 
  // driver's code
  public static void Main(string[] args)
  {
    int n = 4;
    print(n);
  }
}
 
// This code is contributed by Karandeep1234

                    

Javascript

<script>
 
function All_Binary_Strings(str,num)
{
    let len = str.length;
    if(len == num)
    {
        document.write(str," ");
        return;
    }
    else if(str[len - 1]=='1')
        All_Binary_Strings(str+'0',num);
    else
    {
        All_Binary_Strings(str+'0',num);
        All_Binary_Strings(str+'1',num);
    }
}
 
function print(num)
{
    let word = "";
    word += '0';
    All_Binary_Strings(word,num);
    word = '1';
    All_Binary_Strings(word,num);
}
 
// driver's code
 
let n = 4;
print(n);
 
// This code is contributed by shinjanpatra.
</script>

                    

PHP

<?php
 
function allBinaryStrings($str, $num) {
    $len = strlen($str);
     
    if ($len == $num) {
        echo $str . " ";
        return;
    } elseif ($str[$len - 1] == '1') {
        allBinaryStrings($str . '0', $num);
    } else {
        allBinaryStrings($str . '0', $num);
        allBinaryStrings($str . '1', $num);
    }
}
 
function printBinaryStrings($num) {
    $word = '0';
    allBinaryStrings($word, $num);
 
    $word = '1';
    allBinaryStrings($word, $num);
}
 
// Driver code
$n = 4;
printBinaryStrings($n);
 
?>

                    

Output
0000 0001 0010 0100 0101 1000 1001 1010 

Time Complexity: O(2^n)
Auxiliary Space: O(n)

Another easy recursion method to Generate Binary Strings Without Consecutive 1’s.

C++

#include <iostream>
#include <vector>
using namespace std;
 
vector<string> generate_binary_strings(int n) {
  if (n == 0) {
    return {""};
  }
  if (n == 1) {
    return {"0", "1"};
  }
  vector<string> result;
  for (string s : generate_binary_strings(n - 1)) {
    result.push_back(s + "0");
    if (s[s.length() - 1] != '1') {
      result.push_back(s + "1");
    }
  }
  return result;
}
 
int main() {
  vector<string> binary_strings = generate_binary_strings(4);
  for (string s : binary_strings) {
    cout << s << " ";
  }
  return 0;
}
 
// This code is contributed by Susobhan Akhuli

                    

Java

// Java code for the above approach
import java.util.ArrayList;
 
public class Main {
  public static ArrayList<String> generateBinaryStrings(int n) {
    if (n == 0) {
      ArrayList<String> emptyList = new ArrayList<String>();
      emptyList.add("");
      return emptyList;
    }
    if (n == 1) {
      ArrayList<String> list = new ArrayList<String>();
      list.add("0");
      list.add("1");
      return list;
    }
    ArrayList<String> result = new ArrayList<String>();
    ArrayList<String> prevList = generateBinaryStrings(n - 1);
    for (String s : prevList) {
      result.add(s + "0");
      if (s.charAt(s.length() - 1) != '1') {
        result.add(s + "1");
      }
    }
    return result;
  }
 
  public static void main(String[] args) {
    ArrayList<String> binaryStrings = generateBinaryStrings(4);
    for (String s : binaryStrings) {
      System.out.print(s + " ");
    }
  }
}
 
// This code is contributed adityashatmfh

                    

Python3

def generate_binary_strings(n: int):
    if n == 0:
        return [""]
    if n == 1:
        return ["0", "1"]
    result = []
    for s in generate_binary_strings(n-1):
        result.append(s + "0")
        if s[-1] != "1":
            result.append(s + "1")
    return result
 
# Example usage
arr = generate_binary_strings(4)
for i in arr:
      print(i,end=' ')
 
# This code is contributed by Susobhan Akhuli

                    

C#

using System;
using System.Collections.Generic;
 
public class Gfg
{
  static List<string> GenerateBinaryStrings(int n)
  {
    if (n == 0)
    {
      return new List<string>() { "" };
    }
 
    if (n == 1)
    {
      return new List<string>() { "0", "1" };
    }
 
    var result = new List<string>();
    foreach (string s in GenerateBinaryStrings(n - 1))
    {
      result.Add(s + "0");
 
      if (s[s.Length - 1] != '1')
      {
        result.Add(s + "1");
      }
    }
 
    return result;
  }
 
  static void Main(string[] args)
  {
    List<string> binaryStrings = GenerateBinaryStrings(4);
 
    foreach (string s in binaryStrings)
    {
      Console.Write(s + " ");
    }
 
    Console.ReadLine();
  }
}

                    

Javascript

// Javascript implementation of above approach
    function generate_binary_strings(n) {
        if (n == 0) {
              return [""];
        }
        if (n == 1) {
              return ["0", "1"];
        }
        let result = [];
        var temp = generate_binary_strings(n - 1);
        for (let i = 0; i < temp.length;i++) {
            let s = temp[i];
            result.push(s + "0");
            if (s[s.length - 1] != '1') {
              result.push(s + "1");
            }
        }
        return result;
    }
 
    // main function
    let binary_strings = generate_binary_strings(4);
    for (let i = 0;i<binary_strings.length;i++)
    console.log(binary_strings[i]+" ");
     
// This code is contributed by Abhijeet Kumar(abhijeet19403)

                    

PHP

<?php
 
function generateBinaryStrings($n) {
    if ($n == 0) {
        return [""];
    }
    if ($n == 1) {
        return ["0", "1"];
    }
    $result = [];
    $subStrings = generateBinaryStrings($n - 1);
    foreach ($subStrings as $s) {
        $result[] = $s . "0";
        if ($s[strlen($s) - 1] != "1") {
            $result[] = $s . "1";
        }
    }
    return $result;
}
 
// Example usage
$arr = generateBinaryStrings(4);
foreach ($arr as $i) {
    echo $i . ' ';
}
 
?>

                    

Output
0000 0001 0010 0100 0101 1000 1001 1010 

Time Complexity: O(2n), where n is the length of the binary strings to be generated.
Auxiliary Space: O(2n) because at any point in time, the function stores all the binary strings generated so far in the result list, and as the number of strings generated is 2n, the space required to store them is also 2n.




Last Updated : 08 Dec, 2023
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