Course Schedule II

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Problem

Given numCourses courses and a list of prerequisite pairs, return a valid ordering of all courses that satisfies every prerequisite, or an empty array if no valid ordering exists (i.e., the prerequisites contain a cycle).

Examples

Example 1

Input:numCourses = 4, prerequisites = [[1,0],[2,0],[3,1],[3,2]]

Output:[0,1,2,3]

[0,2,1,3] is also valid.

Constraints

1 <= numCourses <= 2000

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How to approach it: the Graphs pattern

A graph models relationships as nodes and edges, which can be directed or undirected, weighted or not. Most graph problems come down to choosing the right traversal — DFS, BFS, or union-find — for what you're trying to find.

Look for this pattern when

The problem involves connections between items (islands, courses with prerequisites, friend networks, grids).
You need the shortest path in an unweighted graph (BFS) or need to explore every reachable node (DFS).
You're asking "are these two things connected?" repeatedly (union-find).

Read the full Graphs guide →

Video walkthroughs

Original problem on LeetCode ↗