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 = 10Input: N = 9
Output: 0
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; } |
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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"); } } |
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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 = 10if isSumOfPowersOfTwo(n): print("Yes") else: print("No") # This code is contributed # by Shrikant13 |
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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"); } } |
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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 ?> |
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Output:
Yes
Time Complexity: O(1)
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