Introduction

In this blog post, we will explore how to solve the LeetCode problem "1648" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

You have an inventory of different colored balls, and there is a customer that wants orders balls of any color. The customer weirdly values the colored balls. Each colored ball's value is the number of balls of that color you currently have in your inventory. For example, if you own 6 yellow balls, the customer would pay 6 for the first yellow ball. After the transaction, there are only 5 yellow balls left, so the next yellow ball is then valued at 5 (i.e., the value of the balls decreases as you sell more to the customer). You are given an integer array, inventory, where inventory[i] represents the number of balls of the ith color that you initially own. You are also given an integer orders, which represents the total number of balls that the customer wants. You can sell the balls in any order. Return the maximum total value that you can attain after selling orders colored balls. As the answer may be too large, return it modulo 109 + 7. Example 1: Input: inventory = [2,5], orders = 4 Output: 14 Explanation: Sell the 1st color 1 time (2) and the 2nd color 3 times (5 + 4 + 3). The maximum total value is 2 + 5 + 4 + 3 = 14. Example 2: Input: inventory = [3,5], orders = 6 Output: 19 Explanation: Sell the 1st color 2 times (3 + 2) and the 2nd color 4 times (5 + 4 + 3 + 2). The maximum total value is 3 + 2 + 5 + 4 + 3 + 2 = 19. Constraints: 1 <= inventory.length <= 105 1 <= inventory[i] <= 109 1 <= orders <= min(sum(inventory[i]), 109)

Explanation

Here's the solution to the problem:

• Binary Search for Optimal Value: We use binary search to find the minimum value 'x' such that selling all balls with value greater than 'x' satisfies the order requirement.

• Calculate Total Value: Once we find 'x', we calculate the total value obtained by selling balls with values greater than 'x'. For each color, we determine how many balls we can sell at values greater than 'x' and calculate their contribution to the total value using the arithmetic series formula.

• Modulo Arithmetic: We perform all calculations modulo 10⁹ + 7 to prevent overflow.

• Runtime Complexity: O(N log M), where N is the length of the inventory and M is the maximum value in the inventory.

• Storage Complexity: O(1)

Code

    def maxProfit(inventory, orders):
    """
    Calculates the maximum total value that can be attained after selling orders colored balls.

    Args:
        inventory (list[int]): An integer array where inventory[i] represents the number of balls of the ith color that you initially own.
        orders (int): The total number of balls that the customer wants.

    Returns:
        int: The maximum total value that you can attain after selling orders colored balls, modulo 10^9 + 7.
    """

    MOD = 10**9 + 7

    def calculate_sold(val):
        """
        Calculates the number of balls sold if we sell all balls with value greater than val.
        """
        sold = 0
        for count in inventory:
            if count > val:
                sold += (count - val)
        return sold

    def calculate_profit(val):
        """
        Calculates the total profit if we sell all balls with value greater than val.
        """
        profit = 0
        for count in inventory:
            if count > val:
                n = count - val
                profit = (profit + (count + val + 1) * n // 2) % MOD
        return profit

    # Binary search for the optimal value
    left, right = 0, max(inventory)
    while left < right:
        mid = (left + right) // 2
        if calculate_sold(mid) >= orders:
            right = mid
        else:
            left = mid + 1

    # Calculate the profit based on the optimal value
    x = left
    profit = calculate_profit(x)
    remaining_orders = orders - calculate_sold(x)

    profit = (profit + remaining_orders * x) % MOD

    return profit