What is the time and space complexity of Course Schedule?

Time complexity: O(V + E). Space complexity: O(V + E).

Course Schedule

Med

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Solution Guide: Course Schedule

Approach

Build directed edges pre -> course and indegree counts. Remove zero-indegree nodes repeatedly; if all nodes are processed, there is no cycle.

Complexity Analysis

Time: O(V + E)
Space: O(V + E)

Pattern

Topological Sort (Kahn)

Why It Works

A valid course order exists only if no cycle prevents completing prerequisites. Kahn’s process consumes all reachable zero-indegree courses only when graph is acyclic.

Updated Feb 2026