Print N-bit binary numbers having more 1’s than 0’s in all prefixes

Given a positive integer n, print all n-bit binary numbers having more 1’s than 0’s for any prefix of the number.

Examples:

Input : n = 2
Output : 11 10

Input : n = 4
Output : 1111 1110 1101 1100 1011 1010

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

A simple but not efficient solution will be to generate all N-bit binary numbers and print those numbers that satisfy the conditions. The time complexity of this solution is exponential.

An efficient solution is to generate only those N-bit numbers that satisfy the given conditions. We use recursion. At each point in the recursion, we append 0 and 1 to the partially formed number and recur with one less digit.

C++

// CPP program to print all N-bit binary 
#include <bits/stdc++.h> 
using namespace std; 
  
/* function to generate n  digit numbers*/
void printRec(string number, int extraOnes,  
                       int remainingPlaces) 
{ 
    /* if number generated */
    if (0 == remainingPlaces) { 
        cout << number << " "; 
        return; 
    } 
  
    /* Append 1 at the current number and reduce  
       the remaining places by one */
    printRec(number + "1", extraOnes + 1,  
                           remainingPlaces - 1); 
  
    /* If more ones than zeros, append 0 to the  
       current number and reduce the remaining  
       places by one*/
    if (0 < extraOnes)  
        printRec(number + "0", extraOnes - 1,  
                            remainingPlaces - 1);     
} 
  
void printNums(int n) 
{ 
    string str = ""; 
    printRec(str, 0, n); 
} 
  
/*driver function*/
int main() 
{ 
    int n = 4; 
    printNums(n); 
    return 0; 
} 

Java

// java program to print all N-bit binary 
import java.io.*; 
  
class GFG  
{ 
    // function to generate n digit numbers 
    static void printRec(String number, int extraOnes,  
                                   int remainingPlaces) 
    { 
        // if number generated  
        if (0 == remainingPlaces)  
        { 
            System.out.print( number +" "); 
            return; 
        } 
      
        // Append 1 at the current number and   
        // reduce the remaining places by one  
        printRec(number + "1", extraOnes + 1,  
                            remainingPlaces - 1); 
      
        // If more ones than zeros, append 0 to the  
        // current number and reduce the remaining  
        // places by one 
        if (0 < extraOnes)  
            printRec(number + "0", extraOnes - 1,  
                            remainingPlaces - 1);  
    } 
      
    static void printNums(int n) 
    { 
        String str = ""; 
        printRec(str, 0, n); 
    } 
      
    // Driver function 
    public static void main (String[] args)  
    { 
        int n = 4; 
        printNums(n); 
      
    } 
} 
  
// This code is contributed by vt_m 

Python3

# Python 3 program to print all N-bit binary 
  
# function to generate n digit numbers 
def printRec(number, extraOnes, remainingPlaces): 
      
    # if number generated  
    if (0 == remainingPlaces): 
        print(number, end = " ") 
        return
      
    # Append 1 at the current number and  
    # reduce the remaining places by one  
    printRec(number + "1", extraOnes + 1,  
             remainingPlaces - 1) 
  
    # If more ones than zeros, append 0 to  
    # the current number and reduce the  
    # remaining places by one 
    if (0 < extraOnes): 
        printRec(number + "0", extraOnes - 1,  
                         remainingPlaces - 1);  
  
def printNums(n): 
    str = "" 
    printRec(str, 0, n) 
  
# Driver Code 
if __name__ == '__main__': 
    n = 4
    printNums(n) 
  
# This code is contributed by 
# Surendra_Gangwar 

C#

// C# program to print all N-bit binary 
using System; 
  
class GFG { 
      
    // function to generate n digit numbers 
    static void printRec(String number,  
                         int extraOnes,  
                         int remainingPlaces) 
    { 
          
        // if number generated  
        if (0 == remainingPlaces)  
        { 
            Console.Write( number +" "); 
            return; 
        } 
      
        // Append 1 at the current number and  
        // reduce the remaining places by one  
        printRec(number + "1", extraOnes + 1,  
                        remainingPlaces - 1); 
      
        // If more ones than zeros, append  
        // 0 to the current number and  
        // reduce the remaining places  
        // by one 
        if (0 < extraOnes)  
            printRec(number + "0", extraOnes - 1,  
                            remainingPlaces - 1);  
    } 
    static void printNums(int n) 
    { 
        String str = ""; 
        printRec(str, 0, n); 
    } 
      
    // Driver code 
    public static void Main ()  
    { 
        int n = 4; 
        printNums(n); 
      
    } 
} 
  
// This code is contributed by Nitin Mittal. 

PHP

<?php 
// PHP program to print all N-bit binary 
  
// function to generate n digit numbers 
function printRec($number, $extraOnes,  
                  $remainingPlaces) 
{ 
    // if number generated  
    if (0 == $remainingPlaces)  
    { 
        echo( $number . " "); 
        return; 
    } 
  
    // Append 1 at the current number and  
    // reduce the remaining places by one  
    printRec($number . "1", $extraOnes + 1,  
                      $remainingPlaces - 1); 
  
    // If more ones than zeros, append 0 to the  
    // current number and reduce the remaining  
    // places by one 
    if (0 < $extraOnes)  
        printRec($number . "0", $extraOnes - 1,  
                          $remainingPlaces - 1);  
} 
  
function printNums($n) 
{ 
    $str = ""; 
    printRec($str, 0, $n); 
} 
  
// Driver Code 
$n = 4; 
printNums($n); 
  
// This code is contributed by Mukul Singh.  

Output:

 1111 1110 1101 1100 1011 1010

This article is contributed by Pranav. 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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My Personal Notes

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

C++

Java

Python3

C#

PHP

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