Print first n numbers with exactly two set bits

Given a number n, print first n positive integers with exactly two set bits in their binary representation.

Examples :

Input: n = 3
Output: 3 5 6
The first 3 numbers with two set bits are 3 (0011),
5 (0101) and 6 (0110)

Input: n = 5
Output: 3 5 6 9 10 12



A Simple Solution is to consider all positive integers one by one starting from 1. For every number, check if it has exactly two sets bits. If a number has exactly two set bits, print it and increment count of such numbers.

An Efficient Solution is to directly generate such numbers. If we clearly observe the numbers, we can rewrite them as given below pow(2,1)+pow(2,0), pow(2,2)+pow(2,0), pow(2,2)+pow(2,1), pow(2,3)+pow(2,0), pow(2,3)+pow(2,1), pow(2,3)+pow(2,2), ………

All numbers can be generated in increasing order according to higher of two set bits. The idea is to fix higher of two bits one by one. For current higher set bit, consider all lower bits and print the formed numbers.

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// C++ program to print first n numbers
// with exactly two set bits
#include <iostream>
using namespace std;
  
// Prints first n numbers with two set bits
void printTwoSetBitNums(int n)
{
    // Initialize higher of two sets bits
    int x = 1;
  
    // Keep reducing n for every number
    // with two set bits.
    while (n > 0)
    {
        // Consider all lower set bits for
        // current higher set bit
        int y = 0;
        while (y < x)
        {
            // Print current number
            cout << (1 << x) + (1 << y) << " ";
  
            // If we have found n numbers
            n--;
            if (n == 0)
                return;
  
            // Consider next lower bit for current
            // higher bit.
            y++;
        }
  
        // Increment higher set bit
        x++;
    }
}
  
// Driver code
int main()
{
    printTwoSetBitNums(4);
  
    return 0;
}

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// Java program to print first n numbers
// with exactly two set bits
import java.io.*;
  
class GFG 
{
    // Function to print first n numbers with two set bits
    static void printTwoSetBitNums(int n)
    {
        // Initialize higher of two sets bits
        int x = 1;
   
        // Keep reducing n for every number
        // with two set bits
        while (n > 0)
        {
            // Consider all lower set bits for
            // current higher set bit
            int y = 0;
            while (y < x)
            {
                // Print current number
                System.out.print(((1 << x) + (1 << y)) +" ");
   
                // If we have found n numbers
                n--;
                if (n == 0)
                    return;
   
                // Consider next lower bit for current
                // higher bit.
                y++;
            }
   
            // Increment higher set bit
            x++;
        }
    }
      
    // Driver program
    public static void main (String[] args) 
    {
        int n = 4;
        printTwoSetBitNums(n);
    }
}
  
// This code is contributed by Pramod Kumar

chevron_right


Python3

filter_none

edit
close

play_arrow

link
brightness_4
code

# Python3 program to print first n 
# numbers with exactly two set bits 
  
# Prints first n numbers 
# with two set bits 
def printTwoSetBitNums(n) :
  
    # Initialize higher of
    # two sets bits 
    x = 1
  
    # Keep reducing n for every 
    # number with two set bits. 
    while (n > 0) :
      
        # Consider all lower set bits 
        # for current higher set bit 
        y = 0
        while (y < x) :
          
            # Print current number 
            print((1 << x) + (1 << y), 
                          end = " " )
  
            # If we have found n numbers 
            n -= 1
            if (n == 0) :
                return
  
            # Consider next lower bit 
            # for current higher bit. 
            y += 1
          
        # Increment higher set bit 
        x += 1
      
# Driver code 
printTwoSetBitNums(4
  
# This code is contributed 
# by Smitha

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# program to print first n numbers
// with exactly two set bits
using System;
  
class GFG 
    {
          
    // Function to print first n
    // numbers with two set bits
    static void printTwoSetBitNums(int n)
    {
          
        // Initialize higher of 
        // two sets bits
        int x = 1;
    
        // Keep reducing n for every
        // number with two set bits
        while (n > 0)
        {
              
            // Consider all lower set bits 
            // for current higher set bit
            int y = 0;
            while (y < x)
            {
                  
                // Print current number
                Console.Write(((1 << x) +
                                (1 << y)) +" ");
    
                // If we have found n numbers
                n--;
                if (n == 0)
                    return;
    
                // Consider next lower bit 
                // for current higher bit.
                y++;
            }
    
            // Increment higher set bit
            x++;
        }
    }
       
    // Driver program
    public static void Main() 
    {
        int n = 4;
        printTwoSetBitNums(n);
    }
}
   
// This code is contributed by Anant Agarwal.

chevron_right


PHP

filter_none

edit
close

play_arrow

link
brightness_4
code

<?php
// PHP program to print 
// first n numbers with 
// exactly two set bits
  
// Prints first n numbers 
// with two set bits
function printTwoSetBitNums($n)
{
    // Initialize higher of
    // two sets bits
    $x = 1;
  
    // Keep reducing n for 
    // every number with 
    // two set bits.
    while ($n > 0)
    {
        // Consider all lower set 
        // bits for current higher 
        // set bit
        $y = 0;
        while ($y < $x)
        {
            // Print current number
            echo (1 << $x) + (1 << $y), " ";
  
            // If we have found n numbers
            $n--;
            if ($n == 0)
                return;
  
            // Consider next lower 
            // bit for current 
            // higher bit.
            $y++;
        }
  
        // Increment higher set bit
        $x++;
    }
}
  
// Driver code
printTwoSetBitNums(4);
  
// This code is contributed by Ajit
?>

chevron_right



Output :

3 5 6 9

Time Complexity : O(n)

This article is contributed by Bharath Reddy Appareddy. 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.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.



My Personal Notes arrow_drop_up



Article Tags :
Practice Tags :


1


Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.