Minimum Shipping Capacity

DESCRIPTION (inspired by Leetcode.com)

You're a logistics manager preparing to ship products from a warehouse. Each product type has both a quantity and a weight per item. Shipping boxes have TWO constraints:

1. Capacity limit: Maximum number of items per box
2. Weight limit: Maximum weight (kg) per box

Rules:

• Each product type must be packed separately
• All boxes have the same capacity and weight limits
• A box can hold at most capacity items OR maxWeightPerBox kg, whichever comes first
• Items must be whole numbers (can't pack fractional items)

Given arrays of quantities and weights per item, plus box and weight constraints, find the minimum box capacity needed to ship all products.

Example 1:

Input:

quantities = [8, 12, 5]
weights = [2, 3, 1]  # kg per item
maxBoxes = 6
maxWeightPerBox = 20  # kg

Output: 5

Explanation: With capacity 5:

• Product 0 (8 items @ 2kg): min(5, 10, 8) = 5 items/box → needs 2 boxes (5 + 3 items)
• Product 1 (12 items @ 3kg): min(5, 6, 12) = 5 items/box → needs 3 boxes (5 + 5 + 2 items)
• Product 2 (5 items @ 1kg): min(5, 20, 5) = 5 items/box → needs 1 box Total: 6 boxes ≤ 6 ✓

Example 2:

Input:

quantities = [10, 15, 8]
weights = [5, 2, 3]
maxBoxes = 10
maxWeightPerBox = 15

Output: 4

Explanation: With capacity 4:

• Product 0 (10 items @ 5kg): min(4, ⌊15/5⌋, remaining) = 3 items/box → needs 4 boxes
• Product 1 (15 items @ 2kg): min(4, ⌊15/2⌋, remaining) = 4 items/box → needs 4 boxes
• Product 2 (8 items @ 3kg): min(4, ⌊15/3⌋, remaining) = 4 items/box → needs 2 boxes Total: 10 boxes ≤ 10 ✓