Solution: Sort Items by Groups Respecting Dependencies

Explore how to arrange items belonging to groups while respecting dependency rules using a hierarchical topological sorting method. Understand the process of building item and group dependency graphs to achieve a valid order that groups items contiguously and respects prerequisites. This lesson guides you through implementing topological sorts for both group and item levels to solve complex dependency problems efficiently.

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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:

$1 \leq$ ...