Course Schedule — Interview Guide

• Model courses as a directed graph; the question is whether the graph has a cycle.
• Kahn's algorithm (BFS on in-degree) detects cycles and produces a topological order.
• DFS with white/gray/black coloring detects back-edges (cycles) too.

from collections import deque, defaultdict
def can_finish(n, pre):
    g = defaultdict(list); indeg = [0] * n
    for a, b in pre:
        g[b].append(a); indeg[a] += 1
    q = deque([i for i in range(n) if indeg[i] == 0])
    taken = 0
    while q:
        c = q.popleft(); taken += 1
        for nb in g[c]:
            indeg[nb] -= 1
            if indeg[nb] == 0: q.append(nb)
    return taken == n

• Course Schedule II: return a valid order, or [] if impossible.
• Course Schedule III: each course has a last-day deadline; maximize the number taken.
• Parallelize: find the minimum number of semesters with a limit on courses per semester.