# Generate all binary strings without consecutive 1’s

• Difficulty Level : Medium
• Last Updated : 28 Jun, 2022

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``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'` `;``    ``generateAllStringsUtil ( K , str , 1 ) ;` `    ``// Generate all Binary string``    ``// starts with '1'``    ``str = ``'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'``;` `    ``// Generating Strings starting with Zero--``    ``generate(k, ch, 1);` `    ``// Initialized first Character to one--``    ``ch = ``'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

 ``

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 ``using` `namespace` `std;` `void` `All_Binary_Strings(``bool` `arr[],``int` `num,``int` `r)``{``    ``if``(r==num)``    ``{``        ``for``(``int` `i=0;i

## 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;``        ``All_Binary_Strings(a, num, 1);``        ``a = 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

 ``

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 ``using` `namespace` `std;` `void` `All_Binary_Strings(string str,``int` `num)``{``    ``int` `len=str.length();``    ``if``(len==num)``    ``{``        ``cout<

## 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

 ``

Time Complexity: O(2^n)

Auxiliary Space: O(n)

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