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17. Course Schedule II

mediumAsked at GitLab

Return any valid course ordering that satisfies the prerequisite dependencies, or an empty list if the graph has a cycle.

By Alex Chen, Founder, InterviewChamp.AI · Last verified

Problem

Given numCourses and prerequisite pairs [a, b] meaning b precedes a, return an order in which you can take all courses. If no order exists (cycle), return [].

Constraints

  • 1 <= numCourses <= 2000
  • 0 <= prerequisites.length <= numCourses*(numCourses-1)

Examples

Example 1

Input
numCourses=2, prerequisites=[[1,0]]
Output
[0,1]

Example 2

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

Approaches

1. DFS post-order

DFS each node; on finish push to a list, then reverse. Detect cycles with gray markers.

Time
O(V+E)
Space
O(V+E)
const out=[]; const col=new Array(n).fill(0);
const dfs=u=>{ if (col[u]===1) return false; if (col[u]===2) return true;
  col[u]=1; for (const v of g[u]) if (!dfs(v)) return false;
  col[u]=2; out.push(u); return true; };
for (let i=0;i<n;i++) if (!dfs(i)) return [];
return out.reverse();

Tradeoff:

2. Kahn's topological sort

Process zero-in-degree nodes via a queue, appending each to the result. If the result has all n nodes, return it; otherwise return [].

Time
O(V+E)
Space
O(V+E)
function findOrder(n, pre){
  const g = Array.from({length:n}, () => []);
  const inDeg = new Array(n).fill(0);
  for (const [a, b] of pre){ g[b].push(a); inDeg[a]++; }
  const q = [], order = [];
  for (let i = 0; i < n; i++) if (inDeg[i] === 0) q.push(i);
  while (q.length){
    const u = q.shift();
    order.push(u);
    for (const v of g[u]) if (--inDeg[v] === 0) q.push(v);
  }
  return order.length === n ? order : [];
}

Tradeoff:

GitLab-specific tips

GitLab will press you to articulate why Kahn's BFS naturally falls out of how their CI scheduler streams ready jobs onto a runner pool the instant their prerequisites land.

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Output

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