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Find if it is possible to get a ratio from given ranges of costs and quantities in C++
Concept
With respect of the given range of cost from lowCost to upCost and range of quantity from lowQuant to upQuant, determine if it is possible to obtain a given ratio r where r=cost/quantity, and lowCost <= cost <= upCost and lowQuant <= quantity <= upQuant.
Input
lowCost = 2, upCost = 10, lowQuant = 3, upQuant = 9 r = 3
Output
Yes
Explanation
Here, cost = r * quantity = 3 * 3 = 9 where cost is in [1, 10] and quantity is in [2, 8]
Input
lowCost = 15, upCost = 31, lowQuant = 6, upQuant = 13 r = 8
Output
No
Explanation
Here, cost = r * quantity = 8 * 6 = 48 where cost is not in [15, 31] and though quantity is in [6, 13]
Method
With respect of the given formula, following equation can be easily deduced −
cost=quantity * r. Where, r is indicated as ratio between cost and quantity.
With respect of above equation, logic can be easily deduced. Verify the product of every value of quantity with r and it should be noted that if any value of the product lies between lowCost and upCost, then answer is Yes otherwise it is No.
Example
// C++ program to find if it is
// possible to get the ratio r
#include <bits/stdc++.h>
using namespace std;
// Here, returns true if it is
// possible to obtain ratio r
// from given cost and
// quantity ranges.
bool isRatioPossible1(int lowCost1, int upCost1,
int lowQuant1, int upQuant1,
int r1){
for (int i = lowQuant1; i <= upQuant1; i++){
// Used to calculate cost corresponding
// to value of i
int ans1 = i * r1;
if (lowCost1 <= ans1 && ans1 <= upCost1)
return true;
}
return false;
}
// Driver Code
int main(){
int lowCost1 = 2, upCost1 = 10,
lowQuant1 = 3, upQuant1 = 9,
r1 = 3;
if (isRatioPossible1(lowCost1, upCost1,
lowQuant1, upQuant1, r1))
cout << "Yes";
else
cout << "No";
return 0;
}Output
Yes
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