Find if a molecule can be formed from 3 atoms using their valence numbers

Valence number of an atom is defined as the exact number of bonds the atom must form with other atoms. Given valence number of 3 atoms, the task is to determine if they can form a molecule together or not. Atoms can form multiple bonds with each other.

Examples:

Input: 2 4 2
Output: YES
The bonds are between the following atoms:
1 - 2
1 - 2
2 - 3
2 - 3

Input: 1 2 3
Output: NO

Approach: Let the valence numbers be a, b and c. Let c be the largest. We have 2 cases in which the molecule cannot be formed:



  • a+b+c is odd: Since every bond decreases the valence number of 2 atoms by 1, the sum of valence numbers should be an even number.
  • a+b < c: In this case, c will be left unsatisfied even if every bond is formed with it.

Below is the implementation of the above approach:

C++

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// C++ implementation of the above approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to check if it is possible
void printPossible(int a, int b, int c)
{
    if ((a + b + c) % 2 != 0 || a + b < c)
        cout << "NO";
    else
        cout << "YES";
}
  
// Driver code
int main()
{
    int a = 2, b = 4, c = 2;
    printPossible(a, b, c);
  
  return 0;
}

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Java

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// Java implementation of the above approach 
  
import java.io.*;
  
class GFG {
    // Function to check if it is possible 
static void printPossible(int a, int b, int c) 
    if ((a + b + c) % 2 != 0 || a + b < c) 
        System.out.println("NO"); 
    else
        System.out.println("YES"); 
  
// Driver code 
    public static void main (String[] args) {
  
    int a = 2, b = 4, c = 2
    printPossible(a, b, c); 
    
  
// This code is contributed by akt_mit

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Python3

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# Python 3 implementation of the
# above approach 
  
# Function to check if it is possible 
def printPossible( a, b, c):
  
    if ((a + b + c) % 2 != 0 or a + b < c):
        print ("NO")
    else:
        print ("YES")
  
# Driver code 
if __name__ == "__main__":
  
    a = 2
    b = 4
    c = 2
    printPossible(a, b, c)
  
# This code is contributed 
# by ChitraNayal

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C#

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// C# implementation of the above approach
using System;
  
class GFG
{
  
// Function to check if it is possible
static void printPossible(int a, int b, int c)
{
    if ((a + b + c) % 2 != 0 || a + b < c)
        Console.Write("NO");
    else
        Console.Write("YES");
}
  
// Driver code
public static void Main()
{
    int a = 2, b = 4, c = 2;
    printPossible(a, b, c);
}
}
  
// This code is contributed
// by Akanksha Rai

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PHP

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<?php
// PHP implementation of the above approach
  
// Function to check if it is possible
function printPossible($a, $b, $c)
{
    if (($a + $b + $c) % 2 != 0 || 
         $a + $b < $c)
        echo ("NO");
    else
        echo ("YES");
}
  
// Driver code
$a = 2;
$b = 4;
$c = 2;
printPossible($a, $b, $c);
  
// This code is contributed 
// by Shivi_Aggarwal
?>

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Output:

Yes

Time complexity: O(1)



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