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

  • Difficulty Level : Hard
  • Last Updated : 26 May, 2021

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

Examples: 

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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 

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 <iostream>
#include <cstring>
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*/

Javascript




<script>
      // JavaScript 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
      function generate(ones, zeroes, str, len) {
          // If length of current string becomes same as desired length
        if (len === str.length) {
            document.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
      var str = "";
      generate(0, 0, str, 4);
</script>

Output: 

1111  1110  1101  1100  1011  1010

This article was contributed by Sachin. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
 




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