2064-minimized-maximum-of-products-distributed-to-any-store.rb

# frozen_string_literal: true

# 2064. Minimized Maximum of Products Distributed to Any Store
# https://leetcode.com/problems/minimized-maximum-of-products-distributed-to-any-store
# Medium

=begin
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
=end

# @param {Integer} n
# @param {Integer[]} quantities
# @return {Integer}
def minimized_maximum(n, quantities)
  ok = quantities.max
  ng = 0
  while (ok - ng).abs > 1
    mid = (ok + ng) / 2
    if quantities.sum { |q| (q + mid - 1) / mid } <= n
      ok = mid
    else
      ng = mid
    end
  end
  ok
end

# **************** #
#       TEST       #
# **************** #

require "test/unit"
class Test_minimized_maximum < Test::Unit::TestCase
  def test_
    assert_equal 3, minimized_maximum(6, [11, 6])
    assert_equal 5, minimized_maximum(7, [15, 10, 10])
    assert_equal 100000, minimized_maximum(1, [100000])
  end
end