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Program to balance the given Chemical Equation

  • Difficulty Level : Medium
  • Last Updated : 17 Nov, 2021

Given the values x, y, p, q of a simple chemical equation of the type: 
b_{1}\text{ }A_{x} + b_{2}\text{ }B_{y} \rightarrow b_{3}\text{ }A_{p}B_{q}
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:  

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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)))




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