Solution: Sort Items by Groups Respecting Dependencies

Explore hierarchical topological sorting to arrange items by groups while respecting dependency constraints. Understand how to build dependency graphs for items and groups, assign unique groups, and apply Kahn’s algorithm to ensure valid linear ordering that meets both item and group-level dependencies.

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Statement
Solution
- Time complexity
- Space complexity

Statement

You are given $n$ items indexed from $0$ to $n − 1$ . Each item belongs to $0$ or one of m groups, described by the array group, where:

group[i] represents the group of the $i^{th}$ item.
If group[i] $==-1$ , the item isn’t assigned to any existing group and should be treated as belonging to its own unique group.

You’re also given a list, beforeItems, where beforeItems[i] contains all items that must precede item $i$ in the final ordering.

Your goal is to arrange all $n$ items in a list that satisfies both of the following rules:

Dependency order: Every item must appear after all the items listed in beforeItems[i].
Group continuity: All items that belong to the same group must appear next to each other in the final order.

If there are multiple valid orderings, return any of them. If there’s no possible ordering, return an empty list.

Constraints:

$1 \leq$ ...