Course Schedule II - Algorithm

$1.$ Build an adjacency list and an in-degree array from the prerequisites. For each pair $[a, b]$, add edge $b \to a$ and increment indegree[a].

$2.$ Push every course with $indegree = 0$ into a queue. These courses have no prerequisites.

$3.$ While the queue is not empty, pop a course $u$, add it to the result. For each neighbor $v$ of $u$, decrement indegree[v]. If indegree[v] becomes $0$, push $v$ into the queue.

$4.$ After the loop, check the result size. If it equals $n$, return the result. Otherwise, a cycle exists, so return an empty array.

This runs in $O(V + E)$ time and uses $O(V + E)$ space.