Generate all binary strings without consecutive 1’s

Given an integer K. Task is Print All binary string of size K (Given number).

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>

Output

000 001 010 100 101 

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>

Output

00 01 10 

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;
}

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.

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>

Output

0000 0001 0010 0100 0101 1000 1001 1010 

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

This article is contributed by Nishant Singh . If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.