Minimum Emergency Restock Days Under Inventory Bounds with Checkpoints

You manage an inventory system with capacity max_products. You are given an integer array task of length n, where task[i] is the net inventory change at the end of day i (positive = incoming, negative = outgoing). You may choose to perform an "emergency restock" on some days; a restock happens at the beginning of that day and instantly sets inventory to max_products (that day counts as one restock day). Constraints: Inventory must never exceed max_products at any time. Only on days with task[i] == 0, the end-of-day inventory must be non-negative (inventory_end >= 0). On other days, inventory is allowed to go negative. Given initial inventory init (inventory at the beginning of day 0), compute the minimum number of emergency restock days required. Input Line 1: integer n Line 2: n integers task[i] Line 3: integer init Line 4: integer max_products Output The minimum number of restock days Constraints (assumed) 1 <= n <= 2e5 -1e9 <= task[i] <= 1e9 0 <= init <= max_products <= 1e9 Example Input: 6 -3 -3 0 -2 5 0 2 10 Output: 1 Example Input 6 -3 -3 0 -2 5 0 2 10 Output 1