Given an array of integers arr[], the task is to find the sum of all the Mersenne numbers from the array. A number is a Mersenne number if it is greater than 0 and is one less than some power of 2. First few Mersenne numbers are 1, 3, 7, 15, 31, 63, 127, …
Examples:
Input: arr[] = {17, 6, 7, 63, 3}
Output: 73
Only 7, 63 and 3 are Mersenne numbers i.e. 7 + 63 + 3 = 73Input: arr[] = {1, 3, 11, 45}
Output: 4
Approach: Initialise sum = 0 and start traversing all the elements of the array, if current element is one less than some power of 2 and is greater than 0 then update sum = sum + arr[i]. Print the sum in the end.
Below is the implementation of the above approach:
// C++ implementation of the approach #include <iostream> using namespace std;
// Function that returns true // if n is a Mersenne number int isMersenne( int n)
{ while (n != 0)
{
int r = n % 2;
if (r == 0)
return false ;
n /= 2;
}
return true ;
} // Function to return the sum of all the // Mersenne numbers from the given array int sumOfMersenne( int arr[], int n)
{ // To store the required sum
int sum = 0;
for ( int i = 0; i < n; i++)
{
// If current element is a Mersenne number
if (arr[i] > 0 && isMersenne(arr[i]))
{
sum += arr[i];
}
}
return sum;
} // Driver code int main()
{ int arr[] = { 17, 6, 7, 63, 3 };
int n = sizeof (arr) / sizeof ( int );
cout << (sumOfMersenne(arr, n));
return 0;
} // This code is contributed by jit_t |
// Java implementation of the approach class GFG {
// Function that returns true
// if n is a Mersenne number
static boolean isMersenne( int n)
{
while (n != 0 ) {
int r = n % 2 ;
if (r == 0 )
return false ;
n /= 2 ;
}
return true ;
}
// Function to return the sum of all the
// Mersenne numbers from the given array
static int sumOfMersenne( int [] arr, int n)
{
// To store the required sum
int sum = 0 ;
for ( int i = 0 ; i < n; i++) {
// If current element is a Mersenne number
if (arr[i] > 0 && isMersenne(arr[i])) {
sum += arr[i];
}
}
return sum;
}
// Driver code
public static void main(String[] args)
{
int [] arr = { 17 , 6 , 7 , 63 , 3 };
int n = arr.length;
System.out.print(sumOfMersenne(arr, n));
}
} |
# Python3 implementation of the approach # Function that returns true # if n is a Mersenne number def isMersenne(n) :
while (n ! = 0 ) :
r = n % 2 ;
if (r = = 0 ) :
return False ;
n / / = 2 ;
return True ;
# Function to return the sum of all the # Mersenne numbers from the given array def sumOfMersenne(arr, n) :
# To store the required sum
sum = 0 ;
for i in range (n) :
# If current element is a Mersenne number
if (arr[i] > 0 and isMersenne(arr[i])) :
sum + = arr[i];
return sum ;
# Driver code if __name__ = = "__main__" :
arr = [ 17 , 6 , 7 , 63 , 3 ];
n = len (arr);
print (sumOfMersenne(arr, n));
# This code is contributed by AnkitRai01 |
//C# implementation of the approach using System;
class GFG
{ // Function that returns true
// if n is a Mersenne number
static bool isMersenne( int n)
{
while (n != 0)
{
int r = n % 2;
if (r == 0)
return false ;
n /= 2;
}
return true ;
}
// Function to return the sum of all the
// Mersenne numbers from the given array
static int sumOfMersenne( int [] arr, int n)
{
// To store the required sum
int sum = 0;
for ( int i = 0; i < n; i++)
{
// If current element is a Mersenne number
if (arr[i] > 0 && isMersenne(arr[i]))
{
sum += arr[i];
}
}
return sum;
}
// Driver code
static public void Main ()
{
int [] arr = { 17, 6, 7, 63, 3 };
int n = arr.Length;
Console.WriteLine(sumOfMersenne(arr, n));
}
} // This code is contributed by jit_t |
<script> // Javascript implementation of the approach // Function that returns true // if n is a Mersenne number function isMersenne( n)
{ while (n != 0)
{
let r = n % 2;
if (r == 0)
return false ;
n = Math.floor(n / 2);
}
return true ;
} // Function to return the sum of all the // Mersenne numbers from the given array function sumOfMersenne(arr, n)
{ // To store the required sum
let sum = 0;
for (let i = 0; i < n; i++)
{
// If current element is a Mersenne number
if (arr[i] > 0 && isMersenne(arr[i]))
{
sum += arr[i];
}
}
return sum;
} // Driver Code let arr = [ 17, 6, 7, 63, 3 ]; let n = arr.length; document.write(sumOfMersenne(arr, n)); // This code is contributed by jana_sayantan </script> |
73
Time Complexity : O(nlogn)
Auxiliary Space: O(1)