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Can Inventory Satisfy a Nested Recipe?

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Problem statement

There are n item types. For item i, ingredients[i][j] is an ingredient item and quantities[i][j] is how many units of it are required to make one unit of item i.

An item with an empty ingredient list is a raw material. inventory[i] gives the available units of each raw material; inventory entries for composite items are zero. Recipe dependencies form a directed acyclic graph.

Return whether the inventory contains enough raw materials to make amount units of target.

Function

canMakeRecipe(ingredients: int[][], quantities: int[][], inventory: int[], target: int, amount: int) → boolean

Examples

Example 1

ingredients = [[],[],[0,1]]quantities = [[],[],[2,3]]inventory = [4,6,0]target = 2amount = 2return = true

Two target items require four units of raw item 0 and six units of raw item 1, exactly matching inventory.

Example 2

ingredients = [[],[0],[1]]quantities = [[],[3],[2]]inventory = [5,0,0]target = 2amount = 1return = false

The nested recipe expands to six units of raw item 0, but only five are available.

Example 3

ingredients = [[],[],[0],[1,2]]quantities = [[],[],[2],[1,3]]inventory = [6,1,0,0]target = 3amount = 1return = true

The target needs one unit of raw item 1 and three copies of item 2, which expand to six units of raw item 0.

Constraints

1 <= n <= 1000.
ingredients.length = quantities.length = inventory.length = n.
ingredients[i].length = quantities[i].length.
Every ingredient index is valid, every quantity and amount is positive, and recipe dependencies are acyclic.
Only raw items have nonzero inventory.
Expanding the requested recipe visits at most 200000 recipe nodes, counting repeated dependency paths.
Every fully expanded raw-material requirement fits in a signed 64-bit integer.