2064. Minimized Maximum of Products Distributed to Any Store

Minimized Maximum of Products Distributed to Any Store (LeetCode 2064) is a Medium Data Structures and Algorithms interview problem you can solve, run and submit on Thita.ai. It belongs to the Binary Search Patterns pattern, in the On Answer / Condition Function subpattern.

How to solve Minimized Maximum of Products Distributed to Any Store

Minimized Maximum of Products Distributed to Any Store is a Binary Search on Answer Space problem, part of Binary Search Patterns. Learn binary search on answer space for optimization problems like Koko eating bananas and capacity to ship packages.

Work towards the solution in these steps:

1. There exists a monotonic nature such that when x is smaller than some number, there will be no way to distribute, and when x is not smaller than that number, there will always be a way to distribute.
2. If you are given a number k, where the number of products given to any store does not exceed k, could you determine if all products can be distributed?
3. Implement a function canDistribute(k), which returns true if you can distribute all products such that any store will not be given more than k products, and returns false if you cannot. Use this function to binary search for the smallest possible k.

The reference solution runs in O(nlogm) time and O(1) space.

The Minimized Maximum of Products Distributed to Any Store solution and editorial walks through the full approach with reference code.

Problem statement

You are given an integer n indicating there are n specialty retail stores. There are m product types of varying amounts, which are given as a 0-indexed integer array quantities, where quantities[i] represents the number of products of the ith product type.

You need to distribute all products to the retail stores following these rules:

- A store can only be given at most one product type but can be given any amount of it.

- After distribution, each store will have been given some number of products (possibly 0). Let x represent the maximum number of products given to any store. You want x to be as small as possible, i.e., you want to minimize the maximum number of products that are given to any store.

Return the minimum possible x.

Example 1:

Input: n = 6, quantities = [11,6] Output: 3 Explanation: One optimal way is: - The 11 products of type 0 are distributed to the first four stores in these amounts: 2, 3, 3, 3 - The 6 products of type 1 are distributed to the other two stores in these amounts: 3, 3 The maximum number of products given to any store is max(2, 3, 3, 3, 3, 3) = 3.

Example 2:

Input: n = 7, quantities = [15,10,10] Output: 5 Explanation: One optimal way is: - The 15 products of type 0 are distributed to the first three stores in these amounts: 5, 5, 5 - The 10 products of type 1 are distributed to the next two stores in these amounts: 5, 5 - The 10 products of type 2 are distributed to the last two stores in these amounts: 5, 5 The maximum number of products given to any store is max(5, 5, 5, 5, 5, 5, 5) = 5.

Example 3:

Input: n = 1, quantities = [100000] Output: 100000 Explanation: The only optimal way is: - The 100000 products of type 0 are distributed to the only store. The maximum number of products given to any store is max(100000) = 100000.

Constraints:

- m == quantities.length

- 1 <= m <= n <= 105

- 1 <= quantities[i] <= 105

Topics and companies

Topics: Array, Binary Search, Greedy.

How to practise Minimized Maximum of Products Distributed to Any Store on Thita.ai

Starter code is provided in C, C#, C++, Go, Java, JavaScript and Python. Your solution runs against 5 test cases for this problem, with the AI coach available for a hint when you are stuck rather than a finished answer. The reference solution runs in O(nlogm) time and O(1) space.

Open Minimized Maximum of Products Distributed to Any Store in the code editor, or read the Minimized Maximum of Products Distributed to Any Store editorial for a worked solution with its approach and complexity analysis.

Where Minimized Maximum of Products Distributed to Any Store sits in the DSA pattern sheet

• Binary Search Patterns pattern guide
• On Answer / Condition Function subpattern
• The full DSA patterns sheet

Problems related to Minimized Maximum of Products Distributed to Any Store

Other problems that use the same On Answer / Condition Function and Binary Search Patterns techniques:

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• Koko Eating Bananas — Medium, same subpattern
• Maximum Candies Allocated to K Children — Medium, same subpattern
• Minimize Max Distance to Gas Station — Hard, same subpattern
• Minimum Limit of Balls in a Bag — Medium, same subpattern
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Minimized Maximum of Products Distributed to Any Store FAQ