Check if a number can be represented as sum of non zero powers of 2

Given an integer N, the task is to check whether N can be represented as the sum of powers of 2 where all the powers are > 0 i.e. 2⁰ cannot contribute to the sum.

Examples:

Input: N = 10
Output: 1
2³ + 2¹ = 10

Input: N = 9
Output: 0

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

Approach: There are two cases:

When N is even then it can always be represented as the sum of powers of 2 when power > 0.
When N is odd then it can never be represented as the sum of powers of 2 if 2⁰ is not included in the sum.

Below is the implementation of the above approach:

C++

// C++ implementation of the approach 
#include <bits/stdc++.h> 
using namespace std; 
  
// Function that return true if n 
// can be represented as the sum 
// of powers of 2 without using 2^0 
bool isSumOfPowersOfTwo(int n) 
{ 
    if (n % 2 == 1) 
        return false; 
    else
        return true; 
} 
  
// Driver code 
int main() 
{ 
    int n = 10; 
    if (isSumOfPowersOfTwo(n)) 
        cout << "Yes"; 
    else
        cout << "No"; 
  
    return 0; 
} 

Java

// Java implementation of the approach 
class GFG { 
  
    // Function that return true if n 
    // can be represented as the sum 
    // of powers of 2 without using 2^0 
    static boolean isSumOfPowersOfTwo(int n) 
    { 
        if (n % 2 == 1) 
            return false; 
        else
            return true; 
    } 
  
    // Driver code 
    public static void main(String args[]) 
    { 
        int n = 10; 
        if (isSumOfPowersOfTwo(n)) 
            System.out.print("Yes"); 
        else
            System.out.print("No"); 
    } 
} 

Python3

# Python3 implementation of the approach  
  
# Function that return true if n  
# can be represented as the sum  
# of powers of 2 without using 2^0 
def isSumOfPowersOfTwo(n): 
    if n % 2 == 1: 
        return False
    else: 
        return True
  
# Driver code 
n = 10
if isSumOfPowersOfTwo(n): 
    print("Yes") 
else: 
    print("No") 
  
# This code is contributed 
# by Shrikant13 

C#

// C# implementation of the approach 
using System; 
  
class GFG { 
  
    // Function that return true if n 
    // can be represented as the sum 
    // of powers of 2 without using 2^0 
    static bool isSumOfPowersOfTwo(int n) 
    { 
        if (n % 2 == 1) 
            return false; 
        else
            return true; 
    } 
  
    // Driver code 
    public static void Main() 
    { 
        int n = 10; 
        if (isSumOfPowersOfTwo(n)) 
            Console.WriteLine("Yes"); 
        else
            Console.WriteLine("No"); 
    } 
} 

PHP

<?php 
// PHP implementation of the approach 
  
// Function that return true if n 
// can be represented as the sum 
// of powers of 2 without using 2^0 
function isSumOfPowersOfTwo($n) 
{ 
    if ($n % 2 == 1) 
        return false; 
    else
        return true; 
} 
  
// Driver code 
$n = 10; 
if (isSumOfPowersOfTwo($n)) 
    echo("Yes"); 
else
    echo("No"); 
  
// This code is contributed  
// by Code_Mech 
?> 

Output:

Yes

Time Complexity: O(1)

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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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