Warehouse Packer's Dilemma
Alloha veggies is a new grocery store. As part of stock clearance guidlines of the store, given many piles of fresh product, follow the rules given below to stack the products in orderly manner.
There are total of n piles of products. The number of product in each pile is represented by the array numProducts. Select any subarray from the array numProducts and pickup product from the subarray such that number of product you pick from the ith pile is strictly less than the number of products you pick from the (i+1)th pile for all the indices i of the subarray. Find Maximum number of products that can be picked.
Example  numProducts = [7,4,5,2,6,5] Ans : 12 Subarray choosen (0,2). i.e [7,4,5] From the 0th index pile, we choose only 3 products. So, 3 from 0th pile, 4 from 1st pile, and 5 from 2nd pile. Total 12 products.
Names
Here are some potential names for this problem:
Max Incremental Product Picking
Greedy Product Stacking
Incremental Subarray Product Selection
Ordered Subarray Sum Maximization
Monotonically Increasing Subarray Aggregation
The key ideas the name aims to convey are:
Picking/selecting products in a greedy incremental way
Considering all subarrays to maximize the total
Following a monotonic ordering rule within subarrays
Aggregating products from the subarrays into a total sum
Greedily optimizing the total count selected
Some other ideas that capture aspects of the problem:
Warehouse Packer’s Dilemma
Storekeeper’s Stacking Challenge
Stockroom Optimization Puzzle
Overall, a descriptive name like “Greedy Incremental Subarray Product Picking” or “Monotonically Increasing Subarray Aggregation” would accurately characterize the essence of this problem.
Solution
Here is Python code to find the maximum number of products that can be picked following the given rules:


The key steps are:
 Consider all possible subarrays within num_products
 For each subarray, greedily choose products from each pile, picking at most 1 more than the previous pile
 Update the max_count based on the maximum products picked from each subarray
This greedy approach ensures we follow the rules by incrementally increasing the picked products per pile within a subarray.