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++
// C++ implementation of the approach#include <iostream>using namespace std;// Function that returns true// if n is a Mersenne numberint 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 arrayint 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 codeint 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
// Java implementation of the approachclass 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
# 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#
//C# implementation of the approachusing 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 |
Javascript
<script>// Javascript implementation of the approach// Function that returns true// if n is a Mersenne numberfunction 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 arrayfunction 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 Codelet arr = [ 17, 6, 7, 63, 3 ];let n = arr.length;document.write(sumOfMersenne(arr, n));// This code is contributed by jana_sayantan</script> |
Output:
73
Time Complexity : O(nlogn)
Auxiliary Space: O(1)
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