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

Suppose we have a range of cost from lowCost to upCost and another range of quantity from lowQuant to upQuant. We need to check whether we can find the given ratio r where r = cost/quantity, with lowCost ? cost ? upCost and lowQuant ? quantity ? upQuant.

So, if the input is like lowCost = 2, upCost = 10, lowQuant = 3, upQuant = 9 and r = 3, then the output will be True as the cost = r * quantity = 3 * 3 = 9 where cost is in range [2, 10] and quantity is in [3, 9].

Algorithm

To solve this problem, we will follow these steps ?

• For each quantity i in range [lowQuant, upQuant], calculate cost = i * ratio
• If the calculated cost falls within [lowCost, upCost], return True
• If no valid combination is found, return False

Example

Let us see the following implementation to get better understanding ?

def can_we_find_r(l_cost, u_cost, l_quant, u_quant, ratio):
    for i in range(l_quant, u_quant + 1):
        res = i * ratio
        if (l_cost <= res and res <= u_cost):
            return True
    return False

l_cost = 2
u_cost = 10
l_quant = 3
u_quant = 9
ratio = 3

print(can_we_find_r(l_cost, u_cost, l_quant, u_quant, ratio))

True

How It Works

The function iterates through each possible quantity value from 3 to 9. For each quantity, it calculates the corresponding cost using cost = quantity * ratio. When quantity = 3, cost = 3 × 3 = 9, which falls within the cost range [2, 10], so the function returns True.

Alternative Approach Using Mathematical Range

We can also solve this more efficiently by calculating the valid cost range directly ?

def can_we_find_r_optimized(l_cost, u_cost, l_quant, u_quant, ratio):
    # Calculate the range of possible costs
    min_cost = l_quant * ratio
    max_cost = u_quant * ratio
    
    # Check if the cost ranges overlap
    return not (max_cost < l_cost or min_cost > u_cost)

l_cost = 2
u_cost = 10
l_quant = 3
u_quant = 9
ratio = 3

print(can_we_find_r_optimized(l_cost, u_cost, l_quant, u_quant, ratio))

True

Comparison

Conclusion

Both approaches determine if a given ratio can be achieved within specified cost and quantity ranges. The iterative method is straightforward but less efficient for large ranges, while the mathematical approach provides constant-time solution by checking range overlap.