Finding Maximum Profit in Item Sales Based on Categories and Prices

Discover how to solve the 'Maximum Profit' problem by determining the optimal sales order based on item categories and prices. This article delves into how to achieve the highest possible profit by calculating the profit for each item according to the number of distinct categories sold before it, using a robust algorithm. This guide is ideal for preparing for programming interviews and understanding sales profit optimization strategies.

Original auricle published on interviewspreparation.com please check it for more in depth guide.

I recently came across a Reddit discussion where an interviewee was asked to develop a strategy for calculating maximum profit. You can find the discussion by searching for ‘Reddit maximum profit HackerRank’. In this article, I’ll walk you through the algorithm for solving the maximum profit problem with category-based items, providing solutions in both Python and C#. Stay with us to be well-prepared for this technical interview question.

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Additionally, the original problem is available on the HackerRank platform, where you can explore more interview questions.

HackerRank Problem Statement

Given n items, each with a category and a price, the challenge is to figure out the sales sequence that results in the highest total profit. The profit for selling an item is calculated as the product of its price and the count of distinct categories sold before that item, including its own category.

Feeling unsure? It’s normal to feel a bit nervous with new interview questions. Don’t worry; I’ll break it down with an example for better understanding.

You have n items, each associated with a specific category and price. Your objective is to determine the best order to sell these items to maximize profit. The profit from selling an item is computed by multiplying its price by the number of unique categories that have been sold so far, including the item’s category.

Example Breakdown

To better understand the category-based item profit problem, let’s go through an example.

Example:

Number of Items (n): 4
Categories (category): [3, 1, 2, 3]
Prices (price): [2, 1, 4, 4]
One possible optimal order for selling these items is:

Sell the 2nd item (category[2] = 1, price[2] = 1):
Profit = 1 * 1 = 1
(Only 1 unique category has been sold.)

Sell the 1st item (category[1] = 3, price[1] = 2):
Profit = 2 * 2 = 4
(Now, 2 unique categories have been sold.)

Sell the 3rd item (category[3] = 2, price[3] = 4):
Profit = 4 * 3 = 12
(Three unique categories have been sold.)

Sell the 4th item (category[4] = 3, price[4] = 4):
Profit = 4 * 3 = 12
(The number of unique categories remains 3.)

Total Profit = 1 + 4 + 12 + 12 = 29

def findMaximumProfit(category, price):
    # Combine categories with prices
    items = list(zip(category, price))

    # Sort items by price in descending order
    items.sort(key=lambda x: -x[1])

    # Track the number of unique categories sold
    unique_categories = set()
    total_profit = 0

    for cat, prc in items:
        # Add the category to the set of sold categories
        unique_categories.add(cat)

        # Calculate the profit
        profit = prc * len(unique_categories)
        total_profit += profit

    return total_profit

Summary

To achieve maximum profit when selling items based on categories and prices, pair each item's category with its price. Sort these items by price in descending order. Track unique categories using a set, and compute each item's profit by multiplying its price by the number of unique categories sold up to that point. Summing these profits provides the total maximum profit. Implement this approach in C# or any programming language of your choice for optimal results.

Good luck with your interview preparation, and stay tuned to interviewspreparation.com for more valuable insights.