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Find if it is possible to get a ratio from given ranges of costs and quantities

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  • Last Updated : 13 Feb, 2022
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Given the range of cost from lowCost to upCost and range of quantity from lowQuant to upQuant, find if it is possible to get a given ration ratio r where r = \frac{cost}{quantity}   , and lowCost <= cost <= upCost and lowQuant <= quantity <= upQuant.
Examples : 
 

Input : lowCost = 1, upCost = 10, 
        lowQuant = 2, upQuant = 8
        r = 3
Output : Yes
Explanation:
cost / quantity = 6 / 2 = 3
where cost is in [1, 10] and quantity
is in [2, 8]

Input : lowCost = 14, upCost = 30, 
        lowQuant = 5, upQuant = 12
        r = 9
Output : No

 

Approach: From the given formula, following equation can be easily deduced: cost = quantity*r   .
From this equation, logic can be easily deduced. Check the product of every value of quantity with r and if any value of the product lies between lowCost and upCost, then answer is Yes otherwise it is No.
Below is the implementation of above approach: 
 

C++




// C++ program to find if it is
// possible to get the ratio r
#include <bits/stdc++.h>
using namespace std;
 
// Returns true if it is
// possible to get ratio r
// from given cost and
// quantity ranges.
bool isRatioPossible(int lowCost, int upCost,
                     int lowQuant, int upQuant,
                     int r)
{
    for (int i = lowQuant; i <= upQuant; i++)
    {
 
        // Calculating cost corresponding
        // to value of i
        int ans = i * r;
        if (lowCost <= ans && ans <= upCost)
            return true;
    }
 
    return false;
}
 
// Driver Code
int main()
{
    int lowCost = 14, upCost = 30,
        lowQuant = 5, upQuant = 12,
        r = 9;
 
    if (isRatioPossible(lowCost, upCost,
                        lowQuant, upQuant, r))
        cout << "Yes";
    else
        cout << "No";
    return 0;
}

Java




// Java program to find if it is
// possible to get the ratio r
import java.io.*;
 
class Ratio
{
 
    // Returns true if it is
    // possible to get ratio r
    // from given cost and
    // quantity ranges.
    static boolean isRatioPossible(int lowCost, int upCost,
                                   int lowQuant, int upQuant,
                                   int r)
    {
        for (int i = lowQuant; i <= upQuant; i++)
        {
 
            // Calculating cost corresponding
            // to value of i
            int ans = i * r;
            if (lowCost <= ans && ans <= upCost)
                return true;
        }
 
        return false;
    }
 
    // Driver Code
    public static void main(String args[])
    {
        int lowCost = 14, upCost = 30,
            lowQuant = 5, upQuant = 12, r = 9;
 
        if (isRatioPossible(lowCost, upCost,
                            lowQuant, upQuant, r))
            System.out.println("Yes");
        else
            System.out.println("No");
    }
}

Python3




# Python 3 program to find if it
# is possible to get the ratio r
 
# Returns true if it is
# possible to get ratio r
# from given cost and
# quantity ranges.
def isRatioPossible(lowCost, upCost,
                    lowQuant, upQuant, r) :
     
    for i in range(lowQuant, upQuant + 1) :
         
        # Calculating cost corresponding
        # to value of i
        ans = i * r
         
        if (lowCost <= ans and ans <= upCost) :
            return True
             
    return False
 
     
# Driver Code
lowCost = 14; upCost = 30
lowQuant = 5; upQuant = 12; r = 9
 
if (isRatioPossible(lowCost, upCost,
                    lowQuant,upQuant, r)) :
    print( "Yes" )
else :
    print( "No" )
     
# This code is contributed
# by Nikita Tiwari.

C#




// C# program to find if it is
// possible to get the ratio r
using System;
 
class Ratio
{
 
    // Returns true if it is
    // possible to get ratio r
    // from given cost and
    // quantity ranges.
    static bool isRatioPossible(int lowCost, int upCost,
                                int lowQuant, int upQuant,
                                int r)
    {
        for (int i = lowQuant; i <= upQuant; i++)
        {
 
            // Calculating cost corresponding
            // to value of i
            int ans = i * r;
            if (lowCost <= ans && ans <= upCost)
                return true;
        }
 
        return false;
    }
 
    // Driver Code
    public static void Main()
    {
        int lowCost = 14, upCost = 30,
            lowQuant = 5, upQuant = 12, r = 9;
 
        if (isRatioPossible(lowCost, upCost,
                            lowQuant, upQuant, r))
            Console.WriteLine("Yes");
        else
            Console.WriteLine("No");
    }
}
 
// This code is contributed by vt_m.

PHP




<?php
//PHP program to find if it is
// possible to get the ratio r
 
// Returns true if it is
// possible to get ratio r
// from given cost and
// quantity ranges.
function isRatioPossible($lowCost, $upCost,
                         $lowQuant, $upQuant,$r)
{
    for ($i = $lowQuant; $i <= $upQuant; $i++)
    {
 
        // Calculating cost corresponding
        // to value of i
        $ans = $i * $r;
        if ($lowCost <= $ans && $ans <= $upCost)
            return true;
    }
 
    return false;
}
 
// Driver Code
$lowCost = 14; $upCost = 30;
$lowQuant = 5; $upQuant = 12; $r = 9;
 
if (isRatioPossible($lowCost, $upCost,
                    $lowQuant, $upQuant, $r))
    echo "Yes";
else
    echo "No";
 
# This code is contributed by ajit
?>

Javascript




<script>
 
// JavaScript program to find if it is
// possible to get the ratio r
 
    // Returns true if it is
    // possible to get ratio r
    // from given cost and
    // quantity ranges.
    function isRatioPossible(lowCost, upCost,
                                   lowQuant, upQuant,
                                   r)
    {
        for (let i = lowQuant; i <= upQuant; i++)
        {
   
            // Calculating cost corresponding
            // to value of i
            let ans = i * r;
            if (lowCost <= ans && ans <= upCost)
                return true;
        }
   
        return false;
    }
 
// Driver code
 
        let lowCost = 14, upCost = 30,
            lowQuant = 5, upQuant = 12, r = 9;
   
        if (isRatioPossible(lowCost, upCost,
                            lowQuant, upQuant, r))
            document.write("Yes");
        else
            document.write("No");
            
</script>

Output : 

No

 Time Complexity: O(|uq-lq|), where uq is upQuant and lq is lowQuant.

Auxiliary Space: O(1)


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