Topological sort of a task-dependency DAG

Problem Given a directed acyclic graph (DAG) of task dependencies, return a valid execution order (topological sort) in which every task appears after all the tasks it depends on.

Input / Output

• Input: n tasks (0..n-1) and a list of directed edges [a, b] meaning task a must run before task b.
• Output: any valid topological ordering of all n tasks, or an indication that none exists (the graph has a cycle).

Constraints

• 1 ≤ n ≤ 1e5, edges up to ~2e5.
• Must run in linear time; the graph may be disconnected.

Example

• n = 4, edges = [[0,1],[0,2],[1,3],[2,3]] → [0, 1, 2, 3] (or [0, 2, 1, 3]).
• edges = [[0,1],[1,0]] → no valid order (cycle).

Expected approach

• Kahn's algorithm: compute in-degrees, repeatedly pop a 0-in-degree node, decrement neighbours; if fewer than n nodes are emitted, a cycle exists.
• DFS alternative: post-order push onto a stack, using a visiting/visited colour scheme for cycle detection.
• Time O(V + E), space O(V + E).