Generate all binary permutations such that there are more or equal 1’s than 0’s before every point in all permutations

Generate all permutations of given length such that every permutation has more or equal 1’s than 0’s in all prefixes of the permutation.

Examples:

Input: len = 4
Output: 1111 1110 1101 1100 1011 1010
Note that a permutation like 0101 can not be in output because
there are more 0's from index 0 to 2 in this permutation.

Input: len = 3
Output: 111 110 101

Input: len = 2
Output: 11 10

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Like permutation generation problems, recursion is the simplest approach to solve this. We start with an empty string, attach 1 to it and recur. While recurring, if we find more 1’s at any point, we append a 0 and make one more recursive call.

Below is the implementation:

C++

 // C++ program to generate all permutations of 1's and 0's such that // every permutation has more 1's than 0's at all indexes. #include #include using namespace std;    // ones & zeroes --> counts of 1's and 0's in current string 'str' // len ---> desired length of every permutation void generate(int ones, int zeroes, string str, int len) {     // If length of current string becomes same as desired length     if (len == str.length())     {         cout << str << "  ";         return;     }        // Append a 1 and recur     generate(ones+1, zeroes, str+"1", len);        // If there are more 1's, append a 0 as well, and recur     if (ones > zeroes)         generate(ones, zeroes+1, str+"0", len); }    // Driver program to test above function int main() {     string str = "";     generate(0, 0, str, 4);     return 0; }

Java

 // Java program to generate all permutations of 1's and 0's such that  // every permutation has more 1's than 0's at all indexes.    class GFG {    // ones & zeroes --> counts of 1's and 0's in current string 'str'  // len ---> desired length of every permutation      static void generate(int ones, int zeroes, String str, int len) {         // If length of current string becomes same as desired length          if (len == str.length()) {             System.out.print(str + " ");             return;         }            // Append a 1 and recur          generate(ones + 1, zeroes, str + "1", len);            // If there are more 1's, append a 0 as well, and recur          if (ones > zeroes) {             generate(ones, zeroes + 1, str + "0", len);         }     }    // Driver program to test above function      public static void main(String[] args) {         String str = "";         generate(0, 0, str, 4);     } }    /* This Java code is contributed by PrinciRaj1992*/

Python3

 # Python 3 program to generate all permutations of 1's and 0's such that # every permutation has more 1's than 0's at all indexes.    # ones & zeroes --> counts of 1's and 0's in current string 'str' # len ---> desired length of every permutation def generate(ones, zeroes, str, len1):     # If length of current string becomes same as desired length     if (len1 == len(str)):         print(str,end =" ")         return            # Append a 1 and recur     generate(ones+1, zeroes, str+"1", len1)        # If there are more 1's, append a 0 as well, and recur     if (ones > zeroes):         generate(ones, zeroes+1, str+"0", len1)    # Driver program to test above function if __name__ == '__main__':     str = ""     generate(0, 0, str, 4)    # This code is contributed by # Surendra_Gangwar

C#

 // C# program to generate all permutations of 1's and 0's such that  // every permutation has more 1's than 0's at all indexes.     using System;                           public class GFG {     // ones & zeroes --> counts of 1's and 0's in current string 'str'  // len ---> desired length of every permutation      static void generate(int ones, int zeroes, String str, int len) {         // If length of current string becomes same as desired length          if (len == str.Length) {             Console.Write(str + " ");             return;         }             // Append a 1 and recur          generate(ones + 1, zeroes, str + "1", len);             // If there are more 1's, append a 0 as well, and recur          if (ones > zeroes) {             generate(ones, zeroes + 1, str + "0", len);         }     }     // Driver program to test above function      public static void Main() {         String str = "";         generate(0, 0, str, 4);     } }     /* This Java code is contributed by 29AjayKumar*/

Output:

1111  1110  1101  1100  1011  1010

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