# Generate all binary strings without consecutive 1’s

Given a 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] = '1' 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 recursive C++ implementation.

`// 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 "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 ` `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; ` `} ` |

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Output:

000 001 010 100 101

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

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