ORIGINAL CODING QUESTION
Count valid dependency orders
Count vertex permutations in which every directed edge u→v places u before v. Cyclic inputs have zero orders.
Original exercise · hard. Editorial role relevance does not imply a company has asked this question.
Input and output
n m, then m vertex pairs (u,v). Vertices are zero-based.
Constraints
1 ≤ n ≤ 10; 0 ≤ m ≤ 30; no repeated edges; vertex IDs in [0,n). The count fits signed 32-bit.
Example 1
Input
3 2 0 2 1 2
Output
2
Vertices 0 and 1 can swap order; both precede 2.
Example 2
Input
2 2 0 1 1 0
Output
0
The cycle has no valid order.
Explain your approach
Explain your time and auxiliary space complexity. Which input makes your algorithm work hardest?
Private grading inputs, expected outputs and canonical reference implementations are withheld. Authored expected outputs were cross-checked with independent reference oracles; compiler/runtime behavior still needs a verified execution provider.
Hint 1
A placed-vertex set determines which vertices are available.
Hint 2
Each candidate’s prerequisites must all be placed.
Hint 3
Memoize counts by the placed bitmask.
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