Amenable numbers

Given a number N, the task is to check if N is an Amenable Number or not. If N is an Amenable number then print “Yes” else print “No”.

Amenable numbers are numbers if there exists a multiset of integers whose size, sum and product equal to the number. 
For example, 8 is an Amenable Number because there is a multiset of integers {-1, -1, 1, 1, 1, 1, 2, 4} whose size, sum and product is 8. 

Examples:

Input: N = 8 
Output: Yes 
Explanation:
8 is an Amenable Number because there is a multiset of integers {-1, -1, 1, 1, 1, 1, 2, 4} whose size, sum and product is 8.
Input: N = 30 
Output: No 
Explanation:
30 is not an Amenable Number because there doesn’t exists a multiset of integers whose size, sum and product is 30. 

Approach:
The first few Amenable Numbers are 1, 5, 8, 9, 12, 13, 16, 17, 20, 21….. which can be represented as the form 4K or 4K + 1. 
Therefore, any number N of the form 4K or 4K + 1 is an Amenable Numbers.
Below is the implementation of the above approach:

C++

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;

// Function to check if N
// is Amenable number
bool isAmenableNum(int N)
{

    // Return true if N is of the form
    // 4K or 4K + 1
    return (N % 4 == 0
            || (N - 1) % 4 == 0);
}

// Driver Code
int main()
{
    // Given Number
    int n = 8;

    // Function Call
    if (isAmenableNum(n))
        cout << "Yes";
    else
        cout << "No";
    return 0;
}

Java

// Java program for the above approach
class GFG{

// Function to check if N
// is Amenable number
static boolean isAmenableNum(int N)
{

    // Return true if N is of the form
    // 4K or 4K + 1
    return (N % 4 == 0 || (N - 1) % 4 == 0);
}

// Driver code
public static void main(String[] args)
{
    int n = 8;

    if (isAmenableNum(n))
    {
        System.out.println("Yes");
    }
    else
    {
        System.out.println("No");
    }
}
}

// This code is contributed by shubham

Python3

# Python3 program for the above approach
import math

# Function to check if N
# is Amenable number
def isAmenableNum(N):

    # Return true if N is of the
    # form 4K or 4K + 1
    return (N % 4 == 0 or
           (N - 1) % 4 == 0);

# Driver code

# Given number
N = 8;

# Function call
if (isAmenableNum(N)):
    print("Yes");
else:
    print("No");

# This code is contributed by rock_cool

C#

// C# program for the above approach
using System;
class GFG{

// Function to check if N
// is Amenable number
static bool isAmenableNum(int N)
{

    // Return true if N is of the form
    // 4K or 4K + 1
    return (N % 4 == 0 || (N - 1) % 4 == 0);
}

// Driver code
public static void Main(String[] args)
{
    int n = 8;

    if (isAmenableNum(n))
    {
        Console.WriteLine("Yes");
    }
    else
    {
        Console.WriteLine("No");
    }
}
}

// This code is contributed by amal kumar choubey

Javascript

<script>
// Javascript program for the above approach

    // Function to check if N
    // is Amenable number
    function isAmenableNum( N)
    {

        // Return true if N is of the form
        // 4K or 4K + 1
        return (N % 4 == 0 || (N - 1) % 4 == 0);
    }

    // Driver code
    let n = 8;

    if (isAmenableNum(n)) {
        document.write("Yes");
    } else {
        document.write("No");
    }


// This code is contributed by Rajput-Ji.
</script>

Output:

Yes

Time Complexity: O(1)
Auxiliary Space: O(1)