生成所有二进制排列，以便在所有排列中的每个点之前有大于0的1或等于1

生成给定长度的所有排列，以使每个排列在排列的所有前缀中都具有大于0的1。

例子：

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 

像排列生成问题一样，递归是解决此问题的最简单方法。我们从一个空字符串开始，将1附加到该字符串上并重复执行。重复执行时，如果在任何时候找到更多1，我们将附加0并再进行一次递归调用。

下面是实现：

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*/

输出：

1111  1110  1101  1100  1011  1010