Possible two sets from first N natural numbers difference of sums as D

Given N and D, find if it is possible to make two sets from first N natural numbers such that the difference between the sum of 2 sets(individually) is D. 

Examples :

Input  : 5 7
Output : yes
Explanation: Keeping 1 and 3 in one set,
and 2, 4 and 5 are in other set.
Sum of set 1 = 4
Sum of set 2 = 11 
So, the difference D = 7 
Which is the required difference

Input  : 4 5
Output : no

Approach :

Let s1 and s2 be the two sets. 
Here we know that 
sum(s1) + sum(s2) = N*(N+1)/2 and 
sum(s1) - sum(s2) = D
Adding above 2 equations, we get 
2*sum(s1) = N*(N+1)/2 + D
If sum(S1) and sum(S2) are integers, then only we can split the first N natural numbers into two sets. For that N*(N+1)/2 + D must be an even number. 

Implementation:

C++

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

// Function returns true if it is 
// possible to split into two
// sets otherwise returns false
bool check(int N, int D)
{    
    int temp = (N * (N + 1)) / 2 + D;
    return (temp % 2 == 0);
}

// Driver code
int main()
{
    int N = 5;
    int M = 7;
    if (check(N, M))
        cout << "yes";
    else
        cout << "no";

    return 0;
}

C

// C program for implementing 
// above approach
#include <stdio.h>
#include <stdbool.h>

// Function returns true if it is 
// possible to split into two
// sets otherwise returns false
bool check(int N, int D)
{    
    int temp = (N * (N + 1)) / 2 + D;
    return (temp % 2 == 0);
}

// Driver code
int main()
{
    int N = 5;
    int M = 7;
    if (check(N, M))
        printf("yes");
    else
        printf("no");

    return 0;
}

// This code is contributed by kothavvsaakash.

Java

// Java program for implementing 
// above approach

class GFG
{
    
    // Function returns true if it is 
    // possible to split into two
    // sets otherwise returns false
    static boolean check(int N, int D)
    { 
        int temp = (N * (N + 1)) / 2 + D;
        return (temp % 2 == 0);
    }
    
    // Driver code
    static public void main (String args[])
    {
        int N = 5;
        int M = 7;
        if (check(N, M))
            System.out.println("yes");
        else
            System.out.println("no");
    }
}

// This code is contributed by Smitha.

Python3

# Python program for implementing
# above approach

# Function returns true if it is
# possible to split into two
# sets otherwise returns false
def check(N, D):
    temp = N * (N + 1) // 2 + D
    return (bool(temp % 2 == 0))

# Driver code
N = 5
M = 7
if check(N, M):
    print("yes")
else:
    print("no")

# This code is contributed by Shrikant13.

C#

// C# program for implementing 
// above approach
using System;

class GFG
{
    
    // Function returns true if it is 
    // possible to split into two
    // sets otherwise returns false
    static bool check(int N, int D)
    { 
        int temp = (N * (N + 1)) / 2 + D;
        return (temp % 2 == 0);
    }
    
    // Driver code
    static public void Main ()
    {
        int N = 5;
        int M = 7;
        if (check(N, M))
            Console.Write("yes");
        else
            Console.Write("no");
    }
}

// This code is contributed by Ajit.

PHP

<?php
// PHP program for implementing 
// above approach

// Function returns true if it is 
// possible to split into two
// sets otherwise returns false
function check($N, $D)
{ 
    $temp = ($N * ($N + 1)) / 2 + $D;
    return ($temp % 2 == 0);
}

// Driver code
$N = 5;
$M = 7;
if (check($N, $M))
    echo("yes");
else
    echo("no");

// This code is contributed by Ajit.

JavaScript

<script>

// javascript program for implementing 
// above approach

// Function returns true if it is 
// possible to split into two
// sets otherwise returns false
function check( N,  D)
{    
    let temp = (N * (N + 1)) / 2 + D;
    return (temp % 2 == 0);
}

// Driver code

    let N = 5;
    let M = 7;
    if (check(N, M))
       document.write( "yes");
    else
       document.write("no");

// This code contributed by aashish1995

</script>

Output

yes

Time Complexity: O(1), the code will run in a constant time.
Auxiliary Space: O(1), no extra space is required, so it is a constant.

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