Program to balance the given Chemical Equation

Given the values x, y, p, q of a simple chemical equation of the type: 

The task is to find the values of constants b₁, b₂, b₃ such that the equation is balanced on both sides and it must be the reduced form.

Examples:

Input: x = 2, y = 3, p = 4, q = 5 
Output: b1 = 6, b2 = 5, b3 = 3

Input: x = 1, y = 2, p = 3, q = 1 
Output: b1 = 6, b2 = 1, b3 = 2  

Approach: 

1. Check if p % x = 0 and q % y = 0 or not.

2. If yes, then we can simply say that 

b1 = p / x, 
b2 = q / y, and 
b3 = 1

3. Else we need to use gcd to compute b1, b2, b3. We need the reduced form so gcd can help with it.

Below is the implementation of the above approach. 

C++

// C++ program to balance
// the given Chemical Equation
#include <bits/stdc++.h>
using namespace std;

// Function to calculate GCD
int gcd(int a, int b)
{
    if (b == 0)
        return a;
    return gcd(b, a % b);
}

// Function to calculate b1, b2 and b3
void balance(int x, int y, int p, int q)
{
    // Variable declaration
    int b1, b2, b3;

    if (p % x == 0 && q % y == 0) {
        b1 = p / x;
        b2 = q / y;
        b3 = 1;
    }

    else {
        p = p * y;
        q = q * x;
        b3 = x * y;

        // temp variable to store gcd
        int temp = gcd(p, gcd(q, b3));

        // Computing GCD
        b1 = p / temp;
        b2 = q / temp;
        b3 = b3 / temp;
    }

    cout << b1 << " " << b2
         << " " << b3 << endl;
}

// Driver code
int main()
{
    int x = 2, y = 3, p = 4, q = 5;

    balance(x, y, p, q);
}

Java

// Java program to balance
// the given Chemical Equation

import java.util.*;

class GFG{

// Function to calculate GCD
static int gcd(int a, int b)
{
    if (b == 0)
        return a;
    return gcd(b, a % b);
}

// Function to calculate b1, b2 and b3
static void balance(int x, int y, int p, int q)
{
    // Variable declaration
    int b1, b2, b3;

    if (p % x == 0 && q % y == 0) {
        b1 = p / x;
        b2 = q / y;
        b3 = 1;
    }

    else {
        p = p * y;
        q = q * x;
        b3 = x * y;

        // temp variable to store gcd
        int temp = gcd(p, gcd(q, b3));

        // Computing GCD
        b1 = p / temp;
        b2 = q / temp;
        b3 = b3 / temp;
    }

    System.out.print(b1 + " " +  b2
        + " " +  b3 +"\n");
}

// Driver code
public static void main(String[] args)
{
    int x = 2, y = 3, p = 4, q = 5;

    balance(x, y, p, q);
}
}

// This code contributed by Rajput-Ji

Python3

# Python 3 program to balance
# the given Chemical Equation

# Function to calculate GCD
def gcd(a,b):
    if (b == 0):
        return a
    return gcd(b, a % b)

# Function to calculate b1, b2 and b3
def balance(x, y, p, q):

    # Variable declaration
    if (p % x == 0 and q % y == 0):
        b1 = p // x
        b2 = q // y
        b3 = 1

    else:
        p = p * y
        q = q * x
        b3 = x * y

        # temp variable to store gcd
        temp = gcd(p, gcd(q, b3))

        # Computing GCD
        b1 = p // temp
        b2 = q // temp
        b3 = b3 // temp

    print(b1,b2,b3)

# Driver code
if __name__ == '__main__':
    x = 2
    y = 3
    p = 4
    q = 5

    balance(x, y, p, q)

# This code is contributed by Surendra_Gangwar

C#

// C# program to balance
// the given Chemical Equation

using System;

public class GFG{

// Function to calculate GCD
static int gcd(int a, int b)
{
    if (b == 0)
        return a;
    return gcd(b, a % b);
}

// Function to calculate b1, b2 and b3
static void balance(int x, int y, int p, int q)
{
    // Variable declaration
    int b1, b2, b3;

    if (p % x == 0 && q % y == 0) {
        b1 = p / x;
        b2 = q / y;
        b3 = 1;
    }

    else {
        p = p * y;
        q = q * x;
        b3 = x * y;

        // temp variable to store gcd
        int temp = gcd(p, gcd(q, b3));

        // Computing GCD
        b1 = p / temp;
        b2 = q / temp;
        b3 = b3 / temp;
    }

    Console.Write(b1 + " " + b2
                  + " " + b3 +"\n");
}

// Driver code
public static void Main(String[] args)
{
    int x = 2, y = 3, p = 4, q = 5;

    balance(x, y, p, q);
}
}

// This code is contributed by Rajput-Ji

Javascript

<script>

// Javascript program to balance
// the given Chemical Equation

// Function to calculate GCD
function gcd(a, b)
{
    if (b == 0)
        return a;
    return gcd(b, a % b);
}

// Function to calculate b1, b2 and b3
function balance(x, y, p, q)
{
    // Variable declaration
    let b1, b2, b3;

    if (p % x == 0 && q % y == 0) {
        b1 = p / x;
        b2 = q / y;
        b3 = 1;
    }

    else {
        p = p * y;
        q = q * x;
        b3 = x * y;

        // temp variable to store gcd
        let temp = gcd(p, gcd(q, b3));

        // Computing GCD
        b1 = p / temp;
        b2 = q / temp;
        b3 = b3 / temp;
    }

    document.write(b1 + " " +  b2
        + " " +  b3 +"\n");
}

// Driver Code

    let x = 2, y = 3, p = 4, q = 5;

    balance(x, y, p, q);

</script>

Output:

6 5 3

Time Complexity: O(log(max(a, b)))

Auxiliary Space: O(log(max(a, b)))