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