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

 `// C++ program to print first n numbers``// with exactly two set bits``#include ``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;``}`

## Java

 `// 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`

## Python3

 `# 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`

## C#

 `// 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.`

## Javascript

 ``

## PHP

 ` 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``?>`

Output :

`3 5 6 9`

Time Complexity : O(n)

Auxiliary Space: O(1)

#### Approach#2: Using while and join

The approach is to start from the integer 3 and check whether the number of set bits in its binary representation is equal to 2 or not. If it has exactly 2 set bits, then add it to the list of numbers with 2 set bits until the list has n elements.

#### Algorithm

1. Initialize an empty list res to store the integers with exactly two set bits.
2. Initialize an integer variable i to 3.
3. While the length of the list res is less than n, do the following:
a. Check whether the number of set bits in the binary representation of i is equal to 2 or not using the count() method of the string.
b. If the number of set bits is equal to 2, then append i to the list res.
c. Increment i by 1.
4. Return the list res.

## C++

 `#include ``#include ``using` `namespace` `std;` `int` `countSetBits(``int` `num) {``    ``int` `count = 0;``    ``while` `(num > 0) {``        ``count += num & 1;``        ``num >>= 1;``    ``}``    ``return` `count;``}` `vector<``int``> numbersWithTwoSetBits(``int` `n) {``    ``vector<``int``> res;``    ``int` `i = 3;``    ``while` `(res.size() < n) {``        ``if` `(countSetBits(i) == 2) {``            ``res.push_back(i);``        ``}``        ``i++;``    ``}``    ``return` `res;``}` `int` `main() {``    ``int` `n = 3;``    ``vector<``int``> result = numbersWithTwoSetBits(n);` `    ``cout << ``"Result: "``;``    ``for` `(``int` `i = 0; i < result.size(); i++) {``        ``cout << result[i] << ``" "``;``    ``}``    ``cout << endl;` `    ``return` `0;``}`

## Java

 `// Java program for the above approach``import` `java.util.ArrayList;``import` `java.util.List;` `public` `class` `GFG {``    ``// Function to count the number of set bits (binary 1s)``    ``// in an integer``    ``static` `int` `countSetBits(``int` `num)``    ``{``        ``int` `count = ``0``;``        ``while` `(num > ``0``) {``            ``count += num & ``1``; ``// Increment count if the last``                              ``// bit is set (1)``            ``num >>= ``1``; ``// Right shift to check the next bit``        ``}``        ``return` `count;``    ``}` `    ``// Function to generate 'n' numbers with exactly two set``    ``// bits in their binary representation``    ``static` `List numbersWithTwoSetBits(``int` `n)``    ``{``        ``List res = ``new` `ArrayList<>();``        ``int` `i = ``3``; ``// Start from 3 as the first number with``                   ``// two set bits``        ``while` `(res.size() < n) {``            ``if` `(countSetBits(i)``                ``== ``2``) { ``// Check if the number has exactly``                        ``// two set bits``                ``res.add(``                    ``i); ``// Add the number to the result list``            ``}``            ``i++; ``// Move to the next number``        ``}``        ``return` `res;``    ``}` `    ``public` `static` `void` `main(String[] args)``    ``{``        ``int` `n = ``3``; ``// Number of numbers with two set bits to``                   ``// generate``        ``List result = numbersWithTwoSetBits(``            ``n); ``// Get the generated numbers` `        ``for` `(``int` `num : result) {``            ``System.out.print(``                ``num + ``" "``); ``// Display the generated numbers``        ``}``        ``System.out.println();``    ``}``}` `// This code is contributed by Susobhan Akhuli`

## Python3

 `def` `numbersWithTwoSetBits(n):``    ``res ``=` `[]``    ``i ``=` `3``    ``while` `len``(res) < n:``        ``if` `bin``(i).count(``'1'``) ``=``=` `2``:``            ``res.append(i)``        ``i ``+``=` `1``    ``return` `res``n ``=` `3``result ``=` `numbersWithTwoSetBits(n)``output_string ``=` `' '``.join(``str``(x) ``for` `x ``in` `result)``print``(output_string)`

## C#

 `using` `System;``using` `System.Collections.Generic;` `class` `Program``{``    ``// Function to count the number of set bits (binary 1s) in an integer``    ``static` `int` `CountSetBits(``int` `num)``    ``{``        ``int` `count = 0;``        ``while` `(num > 0)``        ``{``            ``count += num & 1; ``// Increment count if the last bit is set (1)``            ``num >>= 1; ``// Right shift to check the next bit``        ``}``        ``return` `count;``    ``}` `    ``// Function to generate 'n' numbers with exactly two set bits in their binary representation``    ``static` `List<``int``> NumbersWithTwoSetBits(``int` `n)``    ``{``        ``List<``int``> res = ``new` `List<``int``>();``        ``int` `i = 3; ``// Start from 3 as the first number with two set bits``        ``while` `(res.Count < n)``        ``{``            ``if` `(CountSetBits(i) == 2) ``// Check if the number has exactly two set bits``            ``{``                ``res.Add(i); ``// Add the number to the result list``            ``}``            ``i++; ``// Move to the next number``        ``}``        ``return` `res;``    ``}` `    ``static` `void` `Main(``string``[] args)``    ``{``        ``int` `n = 3; ``// Number of numbers with two set bits to generate``        ``List<``int``> result = NumbersWithTwoSetBits(n); ``// Get the generated numbers` `        ``Console.Write(``"Result: "``);``        ``foreach` `(``int` `num ``in` `result)``        ``{``            ``Console.Write(num + ``" "``); ``// Display the generated numbers``        ``}``        ``Console.WriteLine();``    ``}``}`

## Javascript

 `// Javascript program for the above approach` `// Function to count the number of set bits (binary 1s)``// in an integer``function` `countSetBits(num) {``    ``let count = 0;``    ``while` `(num > 0) {``        ``count += num & 1; ``// Increment count if the last``                          ``// bit is set (1)``        ``num >>= 1; ``// Right shift to check the next bit``    ``}``    ``return` `count;``}` `// Function to generate 'n' numbers with exactly two set``// bits in their binary representation``function` `numbersWithTwoSetBits(n) {``    ``let res = [];``    ``let i = 3; ``// Start from 3 as the first number with``               ``// two set bits``    ``while` `(res.length < n) {``        ``if` `(countSetBits(i) === 2) { ``// Check if the number has exactly``                                     ``// two set bits``            ``res.push(i); ``// Add the number to the result list``        ``}``        ``i++; ``// Move to the next number``    ``}``    ``return` `res;``}` `// Number of numbers with two set bits to generate``let n = 3;``// Get the generated numbers``let result = numbersWithTwoSetBits(n);` `// Display the generated numbers``console.log(result.join(``' '``));` `// This code is contributed by Susobhan Akhuli`

Output
```3 5 6

```

Time Complexity: O(n log n), where n is the number of integers with exactly two set bits. This is because we are checking the number of set bits in the binary representation of each integer, which takes O(log n) time.

Space Complexity: O(n), where n is the number of integers with exactly two set bits. This is because we are storing the list of integers with two set bits in memory.

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