DSA interview question

Course Schedule I

Hard · Data structures · Topics: graph, dfs, topological sort

The problem

A student must take numCourses courses. Each prerequisite pair [a, b] means course b must be taken before course a. Can the student finish every course? That's possible exactly when the prerequisite graph (edges b → a) has no directed cycle. Kahn's algorithm answers it directly. Keep taking a course with no unmet prerequisites (in-degree 0), unlock the courses that depend on it, and check whether all courses end up taken.

Example: numCourses = 2, [[1, 0]] → true; [[1, 0], [0, 1]] → false.

Function signature

bool canFinish(int numCourses, const vector<vector<int>>& prerequisites);  // [a, b]: b before a

Test cases

Input `(numCourses, prerequisites)`	Output	Explanation
`(2, [[1,0]])`	`true`	Take 0, then 1
`(2, [[1,0],[0,1]])`	`false`	Each requires the other
`(3, [[1,0],[2,1]])`	`true`	0 → 1 → 2
`(4, [[1,0],[2,1],[3,2],[1,3]])`	`false`	1 → 2 → 3 → 1
`(1, [])`	`true`

(Confirm: [a, b] means b must come before a; there are no duplicate pairs.)

How interviewers phrase it

"There are numCourses courses labeled 0 to numCourses − 1 and prerequisite pairs [a, b] meaning you must take b before a. Return true if you can finish all courses" (LeetCode 207).

Clarifying questions to ask

Which direction is [a, b]? (b before a, so the edge is b → a.)
Can there be self-prerequisites like [x, x]? (That's a cycle, so false.)
Do I need the order too? (No: that's Course Schedule II.)

Follow-ups to expect

"What is this really?"
**"Why does the edge go b
"DFS alternative?"
"Returning an order?"
"Complexity?"

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