Shopping Cart Minimum Billing

Problem Compute the minimum bill for a cart. Each product is [price, tag1, tag2, …] (tags may be "EMPTY"). Each discount is [tag, type, amount]: type 0 → the price becomes amount; type 1 → amount% off retail; type 2 → amount subtracted from retail. For each product apply the single best (cheapest) discount among those matching its tags; truncate each discounted price to an integer; sum them.

Input / Output

• Input: products[][], discounts[][].
• Output: integer total minimum cost.

Constraints

• Products and discounts up to 10^3–10^5 scale.
• A product with only "EMPTY" tags is not eligible for any discount and pays retail.

Example

• Product [100, "sale"], discounts [["sale",1,10],["sale",2,5]] → min(90, 95) = 90.