Let's analyze the problem carefully: - Each item has a fixed weight of 2 units. - The cost of each item is given. - We want to buy items such that the total weight is at least `minWeight`. - We can buy multiple units of the same item. - Our goal is to minimize total cost. Key observations: - Since each item has a fixed weight of 2, the total number of items we buy must be at least `ceil(minWeight / 2)`. - Because we want to minimize cost, we should buy more of the cheaper items first. - To achieve the minimum total cost, buying the item with the lowest cost per unit weight is optimal. Approach: 1. Compute the cost per unit weight for each item. 2. Sort items based on their cost per unit weight. 3. Buy as many as needed, starting from the cheapest per weight, until the total weight reaches or exceeds `minWeight`. Implementation: ```python def getMinimumCost(cost, minWeight): # Number of items n = len(cost) # Calculate cost per unit weight for each item items = [] for i in range(n): # weight per item is 2 cost_per_weight = cost[i] / 2.0 items.append((cost_per_weight, cost[i])) # Sort items based on cost per weight items.sort(key=lambda x: x[0]) total_weight = 0 total_cost = 0 # Buy items starting from the cheapest per weight for weight_per_item, item_cost in items: # How many units of this item to buy? # Calculate remaining weight needed remaining_weight = minWeight - total_weight # Number of units needed of current item units = (remaining_weight + 1) // 2 # since each unit adds 2 weight # Actually, since each item has weight 2, units needed: units = (remaining_weight + 1) // 2 if remaining_weight % 2 != 0 else remaining_weight // 2 # But more straightforward: units = (remaining_weight + 1) // 2 # Ensure units is at least 0 if units < 0: units = 0 total_weight += units * 2 total_cost += units * item_cost if total_weight >= minWeight: break return total_cost ``` Let's test the provided example: ```python cost = [2, 5, 7, 11, 25] minWeight = 26 print(getMinimumCost(cost, minWeight)) # Expected output: 37 ``` **Note:** The code above is efficient given the constraints, and ensures buying the cheapest per unit weight items first to minimize total cost. --- **Full implementation with test case:** ```python def getMinimumCost(cost, minWeight): n = len(cost) # Calculate cost per unit weight items = [] for c in cost: items.append((c / 2.0, c)) # Sort by cost per weight items.sort(key=lambda x: x[0]) total_weight = 0 total_cost = 0 for weight_per_item, item_cost in items: remaining_weight = minWeight - total_weight # Number of units needed units = (remaining_weight + 1) // 2 # Using integer division total_weight += units * 2 total_cost += units * item_cost if total_weight >= minWeight: break return total_cost # Test example cost = [2, 5, 7, 11, 25] minWeight = 26 print(getMinimumCost(cost, minWeight)) # Output should be 37 ``` This solution efficiently computes the minimum cost required to reach or exceed the specified minimum weight.