Solve graph and linked list tasks

You are given three independent coding tasks.

1) Determine which items can be produced (dependency graph)

You have:

• recipes : a list of n item names.
• ingredients[i] : a list of names required to produce recipes[i] .
• supplies : a list of names you already have available in unlimited quantity.

Any ingredient name may refer either to a basic supply or to another recipe. You may produce a recipe only if all of its required ingredients are currently available (either from the initial supplies or from recipes you have already produced).

Task: Return all recipes that can eventually be produced.

Notes/constraints:

• Recipe/ingredient names are strings.
• Cycles may exist (e.g., A depends on B and B depends on A).
• n can be large; assume the total number of ingredient references across all recipes can be up to ~2e5.

2) Signal propagation time in a weighted directed graph

You are given a directed graph with positive edge weights:

• n nodes labeled 1..n
• edges : a list of triples (u, v, w) meaning an edge from u to v with travel time w > 0
• a starting node k

A signal starts at node k at time 0 and travels along directed edges, accumulating time.

Task: Compute the time when all nodes have received the signal (i.e., the maximum of the shortest-path times from k to every node). If some node is unreachable, return -1.

Notes/constraints:

• n up to ~1e5, |edges| up to ~2e5.
• Weights are positive integers.

3) Check whether a singly linked list has odd or even length

You are given the head of a singly linked list.

Task: Determine whether the list length is odd or even using O(1) extra space and without explicitly computing the length with a counter.

Output: Return something like "odd" / "even" (or a boolean), as long as the meaning is clear.

Notes/constraints:

• Empty list should be handled (define it as even length 0 ).