Programa para hallar la razón común de tres números

Dados a:b y b:c. La tarea es escribir un programa para encontrar la razón a:b:c
Ejemplos: 
 

Input: a:b = 2:3, b:c = 3:4
Output: 2:3:4

Input:  a:b = 3:4, b:c = 8:9
Output: 6:8:9

Enfoque: El truco consiste en hacer que el término común ‘b’ sea igual en ambas proporciones. Por tanto, multiplica la primera razón por b ₂ (término b de la segunda razón) y la segunda razón por b ₁ .
 

Dado: a:b ₁ y b ₂ :c 
Solución: a:b:c = (a*b ₂ ):(b ₁ *b ₂ ):(c*b ₁ )
Por ejemplo: 
Si a : b = 5 : 9 y b : c = 7 : 4, luego encuentre a : b : c.
Solución: 
Aquí, haz que el término común ‘b’ sea igual en ambas proporciones. 
Por lo tanto, multiplica la primera razón por 7 y la segunda razón por 9. 
Entonces, a : b = 35 : 63 y b : c = 63 : 36 
Por lo tanto, a : b : c = 35 : 63 : 36

A continuación se muestra la implementación del enfoque anterior: 
 

// C++ implementation of above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to print a:b:c
void solveProportion(int a, int b1, int b2, int c)
{
    int A = a * b2;
    int B = b1 * b2;
    int C = b1 * c;
 
    // To print the given proportion
    // in simplest form.
    int gcd = __gcd(__gcd(A, B), C);
 
    cout << A / gcd << ":"
         << B / gcd << ":"
         << C / gcd;
}
 
// Driver code
int main()
{
 
    // Get the ratios
    int a, b1, b2, c;
 
    // Get ratio a:b1
    a = 3;
    b1 = 4;
 
    // Get ratio b2:c
    b2 = 8;
    c = 9;
 
    // Find the ratio a:b:c
    solveProportion(a, b1, b2, c);
 
    return 0;
}

// Java implementation of above approach
 
import java.util.*;
import java.lang.*;
import java.io.*;
class GFG{
 
static int __gcd(int a,int b){
    return b==0 ? a : __gcd(b, a%b);
}   
 
// Function to print a:b:c
static void solveProportion(int a, int b1, int b2, int c)
{
    int A = a * b2;
    int B = b1 * b2;
    int C = b1 * c;
  
    // To print the given proportion
    // in simplest form.
    int gcd = __gcd(__gcd(A, B), C);
  
    System.out.print( A / gcd + ":"
         + B / gcd + ":"
         + C / gcd);
}
  
// Driver code
public static void  main(String args[])
{
  
    // Get the ratios
    int a, b1, b2, c;
  
    // Get ratio a:b1
    a = 3;
    b1 = 4;
  
    // Get ratio b2:c
    b2 = 8;
    c = 9;
  
    // Find the ratio a:b:c
    solveProportion(a, b1, b2, c);
}
}

# Python 3 implementation
# of above approach
import math
 
# Function to print a:b:c
def solveProportion(a, b1, b2, c):
 
    A = a * b2
    B = b1 * b2
    C = b1 * c
 
    # To print the given proportion
    # in simplest form.
    gcd1 = math.gcd(math.gcd(A, B), C)
 
    print( str(A // gcd1) + ":" +
           str(B // gcd1) + ":" +
           str(C // gcd1))
 
# Driver code
if __name__ == "__main__":
 
    # Get ratio a:b1
    a = 3
    b1 = 4
 
    # Get ratio b2:c
    b2 = 8
    c = 9
 
    # Find the ratio a:b:c
    solveProportion(a, b1, b2, c)
 
# This code is contributed
# by ChitraNayal

// C# implementation of above approach
using System;
 
class GFG
{
static int __gcd(int a,int b)
{
    return b == 0 ? a : __gcd(b, a % b);
}
 
// Function to print a:b:c
static void solveProportion(int a, int b1,
                            int b2, int c)
{
    int A = a * b2;
    int B = b1 * b2;
    int C = b1 * c;
 
    // To print the given proportion
    // in simplest form.
    int gcd = __gcd(__gcd(A, B), C);
 
    Console.Write( A / gcd + ":" +
                   B / gcd + ":" +
                   C / gcd);
}
 
// Driver code
public static void Main()
{
 
    // Get the ratios
    int a, b1, b2, c;
 
    // Get ratio a:b1
    a = 3;
    b1 = 4;
 
    // Get ratio b2:c
    b2 = 8;
    c = 9;
 
    // Find the ratio a:b:c
    solveProportion(a, b1, b2, c);
}
}
 
// This code is contributed
// by Akanksha Rai(Abby_akku)

<?php
// PHP implementation of above approach
 
function __gcd($a, $b)
{
    return $b == 0 ? $a : __gcd($b, $a % $b);
}
 
// Function to print a:b:c
function solveProportion($a, $b1, $b2, $c)
{
    $A = $a * $b2;
    $B = $b1 * $b2;
    $C = $b1 * $c;
 
    // To print the given proportion
    // in simplest form.
    $gcd = __gcd(__gcd($A, $B), $C);
 
    echo ($A / $gcd) . ":" .
         ($B / $gcd) . ":" . ($C / $gcd);
}
 
// Driver code
 
// Get the ratios
// Get ratio a:b1
$a = 3;
$b1 = 4;
 
// Get ratio b2:c
$b2 = 8;
$c = 9;
 
// Find the ratio a:b:c
solveProportion($a, $b1, $b2, $c);
 
// This code is contributed by mits
?>

<script>
    // Javascript implementation of above approach
     
    function __gcd(a, b)
    {
        return b == 0 ? a : __gcd(b, a % b);
    }
 
    // Function to print a:b:c
    function solveProportion(a, b1, b2, c)
    {
        let A = a * b2;
        let B = b1 * b2;
        let C = b1 * c;
 
        // To print the given proportion
        // in simplest form.
        let gcd = __gcd(__gcd(A, B), C);
 
        document.write( A / gcd + ":" + B / gcd + ":" + C / gcd);
    }
 
    // Get the ratios
    let a, b1, b2, c;
   
    // Get ratio a:b1
    a = 3;
    b1 = 4;
   
    // Get ratio b2:c
    b2 = 8;
    c = 9;
   
    // Find the ratio a:b:c
    solveProportion(a, b1, b2, c);
     
    // This code is contributed by divyeshrabadiya07.
</script>

6:8:9

Complejidad de tiempo: O(log(A+B)), donde A=a*b2 y B = b1*b2

Complejidad espacial : O(1)