Create leetcode_2064_minimized_maximum_of_products_distributed_to_any_store.py

Author: zjkang

python/binary_search/leetcode_2064_minimized_maximum_of_products_distributed_to_any_store.py

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+"""
+author: Zhengjian Kang
+date: 11/15/2021
+
+残酷群每日一题: 11/23/2021
+
+https://leetcode.com/problems/minimized-maximum-of-products-distributed-to-any-store/
+
+2064. Minimized Maximum of Products Distributed to Any Store
+
+note: binary search by value
+
+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 <= 10^5
+1 <= quantities[i] <= 10^5
+"""
+
+class Solution:
+    def minimizedMaximum(self, n: int, quantities: List[int]) -> int:
+        left, right = 1, max(quantities)
+        
+        def is_larger_than_n(val):
+            count = 0
+            for x in quantities:
+                count += (x+val-1) // val
+            return count > n
+        
+        while left < right:
+            mid = left + (right - left) // 2
+            if is_larger_than_n(mid):
+                left = mid + 1
+            else:
+                right = mid
+            
+        return left
+