CodingHardcod-g396

Subject Combinatorial countingLevel Senior–Staff~30 minCommon in Algorithms & data structures interviewsIndustries Software development

Question

Compute C(n, r) = n! / (r! * (n-r)!) modulo a prime p, for potentially large n. Return 0 if r < 0 or r > n. Constraints: 0 <= n <= 100000, p is prime with p > n (so all factorials are invertible mod p). You must never compute the full factorials as big integers proportional to n; work entirely under the modulus.

Implement

ncr_mod_p(n: int, r: int, p: int) → int

Examples

in[5,2,1000000007]out10

What a strong answer looks like

State your approach and its time/space complexity out loud before you optimize. Handle the edge cases (empty input, duplicates, overflow), and say why you chose this over the brute force. Green tests are the floor, not the grade.

Learn the concepts

Vibe coding: describe the solution in plain language (or narrate it) and the coach grades your approach. Generating runnable code from your description is coming next.

Run or narrate your approach, then ask the coach.